Jiangwei Shang

Jiangwei Shang

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Journal Articles

Prescriptive preparation and verification of nonstabilizer states

Published in Physical Review Applied, 2026

High-fidelity quantum-state preparation is a central task in quantum information science. In practice, it is commonly guided either by full quantum state tomography, which becomes prohibitively resource-intensive as system size grows, or by empirically chosen measurement settings that lack principled optimality. Here, we show that quantum state verification (QSV) can be elevated from a purely diagnostic tool to a prescriptive framework for quantum-state preparation, directly specifying experimentally optimal measurements and quantitative fidelity indicators without full state reconstruction. We experimentally realize this prescriptive paradigm using a three-qubit nonstabilizer W state and a modified homogeneous QSV protocol. The verification measurements not only certify the prepared state with high confidence but also serve as a tomography-free indicator that systematically informs the preparation procedure. Using only nine measurement settings and 104 samples, we achieve high-fidelity state preparation consistent with full tomography that requires orders of magnitude more resources. Beyond the present implementation, the prescriptive structure of QSV is naturally compatible with closed-loop feedback control, outlining a pathway toward genuine real-time quantum-state preparation in future low-latency platforms.

Recommended citation: Jian Li, Ye-Chao Liu, Xiao-Xiao Chen, Zhe Meng, Xing-Yan Fan, Wen-Hao Wang, Jie Ma, An-Ning Zhang, Jiangwei Shang (2026). "Prescriptive preparation and verification of nonstabilizer states." Physical Review Applied. 26(1): 014074.
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Sampling quantum states with inequality constraints

Published in Entropy, 2026

Random samples of quantum states with specific properties are useful for various applications, such as Monte Carlo integration over the state space. In the high-dimensional situations that one already encounters when working with a few qubits, the quantum state space has a very complicated boundary, and it is challenging to incorporate the specific properties into the sampling algorithm. In this paper, we present the Sequentially Constrained Monte Carlo (SCMC) algorithm as a practical and versatile method for sampling quantum states in accordance with properties that can be stated as inequalities. We apply the SCMC algorithm to the generation of samples of bound entangled states; for example, we obtain nearly ten thousand bound, entangled, two-qutrit states in a few minutes, compared with less than ten such states per day from independence sampling in our implementation. In the second application, we draw samples of high-dimensional quantum states from a narrowly peaked target distribution and observe, for the system sizes investigated, that SCMC sampling remains computationally manageable as the dimensions grow. In yet another application, the SCMC algorithm produces uniformly distributed quantum states in regions bounded by values of the problem-specific target distribution; such samples are needed when estimating parameters from the probabilistic data acquired in quantum experiments.

Recommended citation: Weijun Li, Rui Han, Jiangwei Shang, Hui Khoon Ng, Berthold-Georg Englert (2026). "Sampling quantum states with inequality constraints." Entropy. 28(6): 614.
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Error-mitigated quantum state tomography using neural networks

Published in arXiv:2602.09733, 2026

The reliable characterization of quantum states is a fundamental task in quantum information science. For this purpose, quantum state tomography provides a standard framework for reconstructing quantum states from measurement data, yet it is often degraded by experimental noise. Mitigating such noise is therefore essential for the accurate estimation of the states in realistic settings. In this work, we propose a scalable tomography method based on multilayer perceptron networks that mitigate unknown noise through supervised learning. This approach is data-driven and thus does not rely on explicit assumptions about the noise model or measurement, making it readily extendable to general quantum systems. Numerical simulations, ranging from special pure states to random mixed states, demonstrate that the proposed method effectively mitigates noise across a broad range of scenarios, compared with the case without mitigation.

Recommended citation: Yixuan Hu, Mengru Ma, Jiangwei Shang (2026). "Error-mitigated quantum state tomography using neural networks." arXiv:2602.09733.
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Simultaneous reconstruction of quantum process and noise via corrupted sensing

Published in arXiv preprint arXiv:2602.05604, 2026

Quantum processes, including quantum gates and channels, are integral to various quantum information tasks, making the efficient characterization of these processes and their underlying noise critically important. Here, we propose a framework for quantum process tomography in the presence of corrupted noise that is able to simultaneously reconstruct the process and corrupted noise. Firstly, within the Choi-state representation, we derive the corresponding generalized restricted isometry property and demonstrate the simultaneous reconstruction of various quantum gates under sparse noise. Moreover, in comparison with the Choi-state scheme, the process-matrix representation is employed to simultaneously reconstruct sparse noise and a broader range of target quantum gates. Our results demonstrate that significant reduction in experimental configurations is achievable even under corrupted noise.

Recommended citation: Mengru Ma, Jiangwei Shang (2026). "Simultaneous reconstruction of quantum process and noise via corrupted sensing." arXiv preprint arXiv:2602.05604.
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Beating the optimal verification of entangled states via collective strategies

Published in Physical Review A, 2025

In the realm of quantum information processing, the efficient characterization of entangled states poses an overwhelming challenge, rendering the traditional methods including quantum tomography unfeasible and impractical. To tackle this problem, we propose a new verification scheme using collective strategies, showcasing arbitrarily high efficiency that beats the optimal verification with global measurements. Our collective scheme can be implemented in various experimental platforms and scalable for large systems with a linear scaling on hardware requirement, and distributed operations are allowed. Notably, larger ensembles can always improve the efficiency further, but without increasing the quantum memory. More importantly, the approach consumes only a few copies of the entangled states, while ensuring the preservation of unmeasured ones, and even boosting their fidelity for any subsequent tasks. Furthermore, our protocol provides additional insight into the specific types of noise affecting the system, thereby facilitating potential targeted improvements. These advancements hold promise for a wide range of applications, offering a pathway towards more robust and efficient quantum information processing.

Recommended citation: Ye-Chao Liu, Jiangwei Shang (2025). "Beating the optimal verification of entangled states via collective strategies." Physical Review A. 112(6): L060401.
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Multipartite entanglement measures: A review

Published in Fundamental Research, 2025

Quantum entanglement, a fundamental aspect of quantum mechanics, has captured significant attention in the era of quantum information science. In multipartite quantum systems, entanglement plays a crucial role in facilitating various quantum information processing tasks, such as quantum teleportation and dense coding. In this article, we review the theory of multipartite entanglement measures, with a particular focus on the genuine as well as the operational meaning of multipartite entanglement measures. By providing a thorough and valuable insight on this field, we hope that this review would inspire and guide researchers in their endeavors to further develop novel approaches for characterizing multipartite entanglement.

Recommended citation: Mengru Ma, Yinfei Li, Jiangwei Shang (2025). "Multipartite entanglement measures: A review." Fundamental Research. 5(6): 2489.
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Real-time preparation and verification of nonstabilizer states

Published in arXiv preprint arXiv:2507.11180, 2025

Entanglement lies at the heart of quantum information science, serving as a key resource for quantum communication, computation, and metrology. Consequently, high-precision entangled state preparation and efficient verification are essential for practical quantum technologies. Quantum state verification (QSV) has recently gained much attention as an efficient and experiment-friendly approach for verifying entangled states. In this work, we experimentally demonstrate a QSV protocol for verifying three-qubit nonstabilizer W state via a modified homogeneous strategy. Notably, our implementation extends QSV beyond its standard role by integrating the state preparation process, thus guiding and validating the real-time generation of high-fidelity target states. Specifically, we realize the efficient verification with a favorable scaling of the required number of copies versus infidelity as −1.39, outperforming the standard quantum limit of −2. Meanwhile, a fidelity of 97.07(±0.26)% via direct estimation is achieved using only 9 measurement settings and 10^4 samples, which is independently confirmed by quantum state tomography to be 98.58(±0.12)% with approximately 10^6 measurements. This work presents the first experimental demonstration of QSV actively assisted with state preparation, establishing it as a powerful and resource-efficient alternative to full tomography for real-time quantum state engineering.

Recommended citation: Jian Li, Ye-Chao Liu, Xiao-Xiao Chen, Zhe Meng, Xing-Yan Fan, Wen-Hao Wang, Jie Ma, An-Ning Zhang, Jiangwei Shang (2025). "Real-time preparation and verification of nonstabilizer states." arXiv preprint arXiv:2507.11180.
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Corrupted sensing quantum state tomography

Published in New Journal of Physics, 2025

The reliable characterization of quantum states as well as any potential noise in various quantum systems is crucial for advancing quantum technologies. In this work we propose the concept of corrupted sensing quantum state tomography which enables the simultaneous reconstruction of quantum states and structured noise with the aid of simple Pauli measurements only. Without additional prior information, we investigate the reliability and robustness of the framework. The power of our protocol is demonstrated by assuming sparse Gaussian and Poisson noise for low-rank state tomography. In particular, our approach is able to achieve a high quality of the recovery with incomplete sets of measurements and is also suitable for performance improvement of large quantum systems. It is envisaged that the techniques can become a practical tool to greatly reduce the cost and computational effort for quantum tomography in noisy quantum systems.

Recommended citation: Mengru Ma, Jiangwei Shang (2025). "Corrupted sensing quantum state tomography." New Journal of Physics. 27(5): 054501.
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Verification of Entangled States Under Noisy Measurements

Published in Advanced Quantum Technologies, 2025

Entanglement plays an indispensable role in numerous quantum information and quantum computation tasks, underscoring the need for efficiently verifying entangled states. In recent years, quantum state verification has received increasing attention, yet the challenge of addressing noise effects in implementing this approach remains unsolved. In this work, a systematic assessment of the performance of quantum state verification protocols is provided in the presence of measurement noise. Based on the analysis, a necessary and sufficient condition is provided to uniquely identify the target state under noisy measurements. Moreover, this work proposes a symmetric hypothesis testing verification algorithm with noisy measurements. Then, relying on W states, an SDP program is demonstrated to calculate the infidelity threshold for arbitrary measurement noise. Subsequently, using a noisy nonadaptive verification strategy of GHZ and stabilizer states, the noise effects on the verification efficiency are analytically illustrated. From both analytical and numerical perspectives, this work demonstrates that the noisy verification protocol exhibits a negative quadratic relationship between the sample complexity and the infidelity. Our method can be easily applied to real experimental settings, thereby demonstrating its promising prospects.

Recommended citation: Lan Zhang, Yinfei Li, Ye-Chao Liu, Jiangwei Shang (2025). "Verification of Entangled States Under Noisy Measurements." Advanced Quantum Technologies. 8(9): 2400575.
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Estimating many properties of a quantum state via quantum reservoir processing

Published in Physical Review Research, 2024

Estimating properties of a quantum state is an indispensable task in various applications of quantum information processing. To predict properties in the postprocessing stage, it is inherent to first perceive the quantum state with a measurement protocol and store the information acquired. In this paper, we propose a general framework for constructing classical approximations of arbitrary quantum states with quantum reservoirs. A key advantage of our method is that only a single local measurement setting is required for estimating arbitrary properties, while most of the previous methods need an exponentially increasing number of measurement settings. To estimate M properties simultaneously, the size of the classical approximation scales as \ln M . Moreover, this estimation scheme is extendable to higher-dimensional systems and hybrid systems with nonidentical local dimensions, which makes it exceptionally generic. We support our theoretical findings with extensive numerical simulations.

Recommended citation: Yinfei Li, Sanjib Ghosh, Jiangwei Shang, Qihua Xiong, Xiangdong Zhang (2024). "Estimating many properties of a quantum state via quantum reservoir processing." Physical Review Research. 6(1): 013211.
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Efficient Verification of Arbitrary Entangled States with Homogeneous Local Measurements

Published in Advanced Quantum Technologies, 2023

Quantum state verification (QSV) is the task of relying on local measurements only to verify that a given quantum device does produce the desired target state. Up to now, certain types of entangled states can be verified efficiently or even optimally by QSV. However, given an arbitrary entangled state, how to design its verification protocol remains an open problem. In this work, we present a systematic strategy to tackle this problem by considering the locality of what we initiate as the choice-independent measurement protocols, whose operators can be directly achieved when they are homogeneous. Taking several typical entangled states as examples, we show the explicit procedures of the protocol design using standard Pauli projections, demonstrating the superiority of our method for attaining better QSV strategies. Moreover, our framework can be naturally extended to other tasks such as the construction of entanglement witness, and even parameter estimation.

Recommended citation: Ye‐Chao Liu, Yinfei Li, Jiangwei Shang, Xiangdong Zhang (2023). "Efficient Verification of Arbitrary Entangled States with Homogeneous Local Measurements." Advanced Quantum Technologies. 6(8): 2300083.
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Unified direct parameter estimation via quantum reservoirs

Published in arXiv preprint arXiv:2305.06878, 2023

Estimating properties of a quantum state is an indispensable task in various applications of quantum information processing. To predict properties in the post-processing stage, it is inherent to first perceive the quantum state with a measurement protocol and store the information acquired. In this work, we propose a general framework for constructing classical approximations of arbitrary quantum states with quantum reservoirs. A key advantage of our method is that only a single local measurement setting is required for estimating arbitrary properties, while most of the previous methods need exponentially increasing number of measurement settings. To estimate M properties simultaneously, the size of the classical approximation scales as \ln M . Moreover, this estimation scheme is extendable to higher-dimensional systems and hybrid systems with non-identical local dimensions, which makes it exceptionally generic. We support our theoretical findings with extensive numerical simulations.

Recommended citation: Yinfei Li, Sanjib Ghosh, Jiangwei Shang, Qihua Xiong, Xiangdong Zhang (2023). "Unified direct parameter estimation via quantum reservoirs." arXiv preprint arXiv:2305.06878.
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Universal classical optical computing inspired by quantum information process

Published in Annalen der Physik, 2022

Quantum computing has attracted much attention in recent decades, since it is believed to solve certain problems substantially faster than traditional computing methods. Theoretically, such an advance can be obtained by networks of the quantum operators in universal gate sets, one famous example of which is formed by CNOT gate and single qubit gates. However, realizing a device that performs practical quantum computing is tricky. This is because it requires a scalable qubit system with long coherence time and good controls, which is harsh for most current platforms. Here, we demonstrate that the information process based on a relatively stable system—classical optical system, can be considered as an analogy of universal quantum computing. By encoding the information via the polarization state of classical beams, the optical computing elements that corresponds to the universal gate set are presented and their combination for a general information process are theoretically illustrated. Taking the analogy of two-qubit processor as an example, we experimentally verify that our proposal works well. Considering the potential of optical system for reliable and low-energy-consuming computation, our results open a new way towards advanced information processing with high quality and efficiency.

Recommended citation: Yifan Sun, Qian Li, Ling‐Jun Kong, Jiangwei Shang, Xiangdong Zhang (2022). "Universal classical optical computing inspired by quantum information process." Annalen der Physik. 534(12): 2200360.
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Geometric mean of bipartite concurrences as a genuine multipartite entanglement measure

Published in Physical Review Research, 2022

In this paper, we propose the geometric mean of bipartite concurrences as a genuine multipartite entanglement measure. This measure achieves the maximum value for absolutely maximally entangled states and has desirable properties for quantifying potential quantum resources. The simplicity and symmetry in the definition facilitates its computation for various multipartite entangled states including the GHZ states and the W states. With explicit examples, we show that our measure results in distinct entanglement orderings from other measures and can detect differences in certain types of genuine multipartite entanglement while other measures cannot. These results justify the potential application of our measure for tasks involving genuine multipartite entanglement.

Recommended citation: Yinfei Li, Jiangwei Shang (2022). "Geometric mean of bipartite concurrences as a genuine multipartite entanglement measure." Physical Review Research. 4(2): 023059.
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Statistical Methods for Quantum State Verification and Fidelity Estimation

Published in Advanced Quantum Technologies, 2022

The efficient and reliable certification of quantum states is essential for various quantum information processing tasks as well as for the general progress on the implementation of quantum technologies. In the last few years several methods have been introduced which use advanced statistical methods to certify quantum states in a resource-efficient manner. In this article we present a review of the recent progress in this field. We first explain how the verification and fidelity estimation of a quantum state can be discussed in the language of hypothesis testing. Then, we explain in detail various strategies for the verification of entangled states with local measurements or measurements assisted by local operations and classical communication. Finally, we discuss several extensions of the problem, such as the certification of quantum channels and the verification of entanglement.

Recommended citation: Xiao-Dong Yu, Jiangwei Shang, Otfried Gühne (2022). "Statistical Methods for Quantum State Verification and Fidelity Estimation." Advanced Quantum Technologies. 5: 2100126.
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Operational detection of entanglement via quantum designs

Published in Annalen der Physik, 2022

From an operational point of view, several new entanglement detection criteria are proposed using quantum designs. These criteria are constructed by considering the correlations defined with quantum designs. Counter‐intuitively, the criteria with more settings are exactly equivalent to the corresponding ones with the minimal number of settings, namely the symmetric informationally complete positive operator‐valued measures (SIC POVMs). Fundamentally, this observation highlights the potentially unique role played by SIC POVMs in quantum information processing. Experimentally, this provides the minimal number of settings that one should choose for detecting entanglement. Furthermore, it is found that nonlinear criteria are not always better than linear ones for the task of entanglement detection.

Recommended citation: Xin Yan, Ye‐Chao Liu, Jiangwei Shang (2022). "Operational detection of entanglement via quantum designs." Annalen der Physik. 534(5): 2100594.
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Reliable experimental certification of one-way Einstein-Podolsky-Rosen steering

Published in Physical Review Research, 2022

Quantum steering is a recently defined form of quantum correlation which lies at the heart of quantum mechanics. In contrast to other types of quantum correlations, quantum steering is inherently asymmetric, which implies that it could manifest in one direction but not in the opposite direction. This rather peculiar phenomenon, known as one-way steering, has been demonstrated in several experiments, but subtlety remains. In fact, all experiments were shown to be ambiguous until a very recent conclusive one, which, however, made crucial use of a high-dimensional embedding to get around assumptions. This leaves the question open of whether the one-way steering phenomenon can be reliably demonstrated in the genuine two-qubit system. Here, we report such an experimental demonstration of one-way steering for a family of two-qubit states. Our experimental setup and results thus resolve the subtlety caused …

Recommended citation: Qiang Zeng, Jiangwei Shang, H Chau Nguyen, Xiangdong Zhang (2022). "Reliable experimental certification of one-way Einstein-Podolsky-Rosen steering." Physical Review Research. 4(1): 013151.
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Efficient verification of entangled continuous-variable quantum states with local measurements

Published in Physical Review Research, 2021

Continuous-variable quantum states are of particular importance in various quantum information processing tasks including quantum communication and quantum sensing. However, a bottleneck has emerged with the fast increasing in size of the quantum systems which severely hinders their efficient characterization. In this work, we establish a systematic framework for verifying entangled continuous-variable quantum states by employing local measurements only. Our protocol is able to achieve the unconditionally high verification efficiency which is quadratically better than quantum tomography as well as other nontomographic methods. Specifically, we demonstrate the power of our protocol by showing the efficient verification of entangled two-mode and multimode coherent states with local measurements.

Recommended citation: Ye-Chao Liu, Jiangwei Shang, Xiangdong Zhang (2021). "Efficient verification of entangled continuous-variable quantum states with local measurements." Physical Review Research. 3(4): L042004.
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Sequentially constrained Monte Carlo sampler for quantum states

Published in arXiv preprint arXiv:2109.14215, 2021

Random samples of quantum states with specific properties are useful for various applications, such as Monte Carlo integration over the state space. In the high-dimensional situations that one encounters already for a few qubits, the quantum state space has a very complicated boundary, and it is challenging to incorporate the specific properties into the sampling algorithm. In this paper, we present the Sequentially Constrained Monte Carlo (SCMC) algorithm as a powerful and versatile method for sampling quantum states in accordance with any desired properties that can be stated as inequalities. We apply the SCMC algorithm to the generation of samples of bound entangled states; for example, we obtain nearly ten thousand bound entangled two-qutrit states in a few minutes – a colossal speed-up over independence sampling, which yields less than ten such states per day. In the second application, we draw samples of high-dimensional quantum states from a narrowly peaked target distribution and observe that SCMC sampling remains efficient as the dimension grows. In yet another application, the SCMC algorithm produces uniformly distributed quantum states in regions bounded by values of the problem-specific target distribution; such samples are needed when estimating parameters from the probabilistic data acquired in quantum experiments.

Recommended citation: Weijun Li, Rui Han, Jiangwei Shang, Hui Khoon Ng, Berthold-Georg Englert (2021). "Sequentially constrained Monte Carlo sampler for quantum states." arXiv preprint arXiv:2109.14215.
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Universally optimal verification of entangled states with nondemolition measurements

Published in Physical Review Letters, 2021

The efficient and reliable characterization of quantum states plays a vital role in most, if not all, quantum information processing tasks. In this work, we present a universally optimal protocol for verifying entangled states by employing the so-called quantum nondemolition measurements, such that the verification efficiency is equivalent to that of the optimal global strategy. Instead of being probabilistic as the standard verification strategies, our protocol is constructed sequentially, which is thus more favorable for experimental realizations. In addition, the target states are preserved in the protocol after each measurement, so can be reused in any subsequent tasks. We demonstrate the power of our protocol for the optimal verification of Bell states, arbitrary two-qubit pure states, and stabilizer states. We also prove that our protocol is able to perform tasks including fidelity estimation and state preparation.

Recommended citation: Ye-Chao Liu, Jiangwei Shang, Rui Han, Xiangdong Zhang (2021). "Universally optimal verification of entangled states with nondemolition measurements." Physical Review Letters. 126(9): 090504.
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Efficient verification of quantum processes

Published in Physical Review A, 2020

Quantum processes, such as quantum circuits, quantum memories, and quantum channels, are essential ingredients in almost all quantum information processing tasks. However, the characterization of these processes remains a daunting task due to the exponentially increasing amount of resources required by traditional methods. Here, by first proposing the concept of quantum process verification, we establish two efficient and practical protocols for verifying quantum processes which can provide an exponential improvement over the standard quantum process tomography and a quadratic improvement over the method of direct fidelity estimation. The efficacy of our protocols is illustrated with the verification of various quantum gates as well as the processes of well-known quantum circuits. Moreover, our protocols are readily applicable with current experimental techniques since only local measurements are …

Recommended citation: Ye-Chao Liu, Jiangwei Shang, Xiao-Dong Yu, Xiangdong Zhang (2020). "Efficient verification of quantum processes." Physical Review A. 101(4): 042315.
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Demonstration of a flexible scheme for two-qubit quantum computation with single photon

Published in AIP Advances, 2020

To build a quantum computing device, which is capable of generating arbitrary input states and performing universal unitary gate operations (UUGOs), is an important goal in the field of quantum information science. However, only a few special quantum computations have been reported by now based on specific input states and well-designed information processors. Here, we demonstrate a flexible scheme for two-qubit quantum computations by employing the polarization and the spatial mode of a single photon. Two-qubit UUGOs both in free-space optics and for arbitrary pure input states consisting of separable states and entangled states are presented. Quantum state tomography and process tomography are used to characterize the fidelity of the output states and the gate operations we considered. Beyond a demonstration, we believe that our work also enriches the techniques of bulk-optics for quantum …

Recommended citation: Zhenwei Yang, Jiangwei Shang, Xiangdong Zhang (2020). "Demonstration of a flexible scheme for two-qubit quantum computation with single photon." AIP Advances. 10(3): 035019.
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Experimental optimal orienteering via parallel and antiparallel spins

Published in Physical Review Letters, 2020

Antiparallel spins are superior in orienteering to parallel spins. This intriguing phenomenon is tied to entanglement associated with quantum measurements rather than quantum states. Using photonic systems, we experimentally realize the optimal orienteering protocols based on parallel spins and antiparallel spins, respectively. The optimal entangling measurements for decoding the direction information from parallel spins and antiparallel spins are realized using photonic quantum walks, which is a useful idea that is of wide interest in quantum information processing and foundational studies. Our experiments clearly demonstrate the advantage of antiparallel spins over parallel spins in orienteering. In addition, entangling measurements can extract more information than local measurements even if no entanglement is present in the quantum states.

Recommended citation: Jun-Feng Tang, Zhibo Hou, Jiangwei Shang, Huangjun Zhu, Guo-Yong Xiang, Chuan-Feng Li, Guang-Can Guo (2020). "Experimental optimal orienteering via parallel and antiparallel spins." Physical Review Letters. 124(6): 060502.
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Efficient verification of Dicke states

Published in Physical Review Applied, 2019

Among various multipartite entangled states, Dicke states stand out because their entanglement is maximally persistent and robust under particle losses. Although much attention has been attracted for their potential applications in quantum information processing and foundational studies, the characterization of Dicke states remains as a challenging task in experiments. Here, we propose efficient and practical protocols for verifying arbitrary n-qubit Dicke states in both adaptive and nonadaptive ways. Our protocols require only two distinct settings based on Pauli measurements besides permutations of the qubits. To achieve infidelity and confidence level 1-delta, the total number of tests required is only O(n epsilon^-1 ln delta^-1). This performance is exponentially more efficient than all previous protocols based on local measurements, including quantum state tomography and direct fidelity estimation, and is comparable to the best global strategy. Our protocols are readily applicable with current experimental techniques and are able to verify Dicke states of hundreds of qubits.

Recommended citation: Ye-Chao Liu, Xiao-Dong Yu, Jiangwei Shang, Huangjun Zhu, Xiangdong Zhang (2019). "Efficient verification of Dicke states." Physical Review Applied. 12(4): 044020.
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Proper error bars for self-calibrating quantum tomography

Published in Physical Review A, 2019

Self-calibrating quantum state tomography aims at reconstructing the unknown quantum state and certain properties of the measurement devices from the same data. Since the estimates of the state and device parameters come from the same data, one should employ a joint estimation scheme, including the construction and reporting of joint state-device error regions, to quantify uncertainty. We explain how to do this naturally within the framework of optimal error regions. As an illustrative example, we apply our procedure to the double-crosshair measurement of the BB84 scenario in quantum cryptography and so reconstruct the state and estimate the detection efficiencies simultaneously and reliably. We also discuss the practical situation of a satellite-based quantum key distribution scheme, for which self-calibration and proper treatment of the data are necessities.

Recommended citation: Jun Yan Sim, Jiangwei Shang, Hui Khoon Ng, Berthold-Georg Englert (2019). "Proper error bars for self-calibrating quantum tomography." Physical Review A. 100(2): 022333.
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Optimal verification of general bipartite pure states

Published in npj Quantum Information, 2019

The efficient and reliable verification of quantum states plays a crucial role in various quantum information processing tasks. We consider the task of verifying entangled states using one-way and two-way classical communication and completely characterize the optimal strategies via convex optimization. We solve these optimization problems using both analytical and numerical methods, and the optimal strategies can be constructed for any bipartite pure state. Compared with the nonadaptive approach, our adaptive strategies significantly improve the efficiency of quantum state verification. Moreover, these strategies are experimentally feasible, as only few local projective measurements are required.

Recommended citation: Xiao-Dong Yu, Jiangwei Shang, Otfried Gühne (2019). "Optimal verification of general bipartite pure states." npj Quantum Information. 5: 112.
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Bound entangled states fit for robust experimental verification

Published in Quantum, 2018

Preparing and certifying bound entangled states in the laboratory is an intrinsically hard task, due to both the fact that they typically form narrow regions in state space, and that a certificate requires a tomographic reconstruction of the density matrix. Indeed, the previous experiments that have reported the preparation of a bound entangled state relied on such tomographic reconstruction techniques. However, the reliability of these results crucially depends on the extra assumption of an unbiased reconstruction. We propose an alternative method for certifying the bound entangled character of a quantum state that leads to a rigorous claim within a desired statistical significance, while bypassing a full reconstruction of the state. The method is comprised by a search for bound entangled states that are robust for experimental verification, and a hypothesis test tailored for the detection of bound entanglement that is naturally equipped with a measure of statistical significance. We apply our method to families of 3×3 states and 4×4 systems, and find that the experimental certification of bound entangled states is well within reach.

Recommended citation: Gael Sentís, Johannes N Greiner, Jiangwei Shang, Jens Siewert, Matthias Kleinmann (2018). "Bound entangled states fit for robust experimental verification." Quantum. 2: 113.
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Deterministic realization of collective measurements via photonic quantum walks

Published in Nature Communications, 2018

Collective measurements on identically prepared quantum systems can extract more information than local measurements, thereby enhancing information-processing efficiency. Although this nonclassical phenomenon has been known for two decades, it has remained a challenging task to demonstrate the advantage of collective measurements in experiments. Here we introduce a general recipe for performing deterministic collective measurements on two identically prepared qubits based on quantum walks. Using photonic quantum walks, we realize experimentally an optimized collective measurement with fidelity 0.9946 without post selection. As an application, we achieve the highest tomographic efficiency in qubit state tomography to date. Our work offers an effective recipe for beating the precision limit of local measurements in quantum state tomography and metrology. In addition, our study opens an avenue for harvesting the power of collective measurements in quantum information processing and for exploring the intriguing physics behind this power.

Recommended citation: Zhibo Hou, Jun-Feng Tang, Jiangwei Shang, Huangjun Zhu, Jian Li, Yuan Yuan, Kang-Da Wu, Guo-Yong Xiang, Chuan-Feng Li, Guang-Can Guo (2018). "Deterministic realization of collective measurements via photonic quantum walks." Nature Communications. 9(1): 1414.
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Superfast maximum likelihood reconstruction for quantum tomography

Published in Phys. Rev. A, 2017

Conventional methods for computing maximum-likelihood estimators (MLE) often converge slowly in practical situations, leading to a search for simplifying methods that rely on additional assumptions for their validity. In this work, we provide a fast and reliable algorithm for maximum likelihood reconstruction that avoids this slow convergence. Our method utilizes the state-of-the-art convex optimization scheme—an accelerated projected-gradient method—that allows one to accommodate the quantum nature of the problem in a different way than in the standard methods. We demonstrate the power of our approach by comparing its performance with other algorithms for n-qubit state tomography. In particular, an 8-qubit situation that purportedly took weeks of computation time in 2005 can now be completed in under a minute for a single set of data, with far higher accuracy than previously possible. This refutes the common claim that MLE reconstruction is slow, and reduces the need for alternative methods that often come with difficult-to-verify assumptions. In fact, recent methods assuming Gaussian statistics or relying on compressed sensing ideas are demonstrably inapplicable for the situation under consideration here. Our algorithm can be applied to general optimization problems over the quantum state space; the philosophy of projected gradients can further be utilized for optimization contexts with general constraints.

Recommended citation: Jiangwei Shang, Zhengyun Zhang, Hui Khoon Ng (2017). "Superfast maximum likelihood reconstruction for quantum tomography." Phys. Rev. A. 95: 062336.
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Optimal error intervals for properties of the quantum state

Published in Phys. Rev. A, 2016

Quantum state estimation aims at determining the quantum state from observed data. Estimating the full state can require considerable efforts, but one is often only interested in a few properties of the state, such as the fidelity with a target state, or the degree of correlation for a specified bipartite structure. Rather than first estimating the state, one can, and should, estimate those quantities of interest directly from the data. We propose the use of optimal error intervals as a meaningful way of stating the accuracy of the estimated property values. Optimal error intervals are analogs of the optimal error regions for state estimation [New J. Phys. 15, 123026 (2013)]. They are optimal in two ways: They have the largest likelihood for the observed data and the pre-chosen size, and are the smallest for the pre-chosen probability of containing the true value. As in the state situation, such optimal error intervals admit a simple description in terms of the marginal likelihood for the data for the properties of interest. Here, we present the concept and construction of optimal error intervals, report on an iterative algorithm for reliable computation of the marginal likelihood (a quantity difficult to calculate reliably), explain how plausible intervals — a notion of evidence provided by the data — are related to our optimal error intervals, and illustrate our methods with single-qubit and two-qubit examples.

Recommended citation: Xikun Li, Jiangwei Shang, Hui Khoon Ng, Berthold-Georg Englert (2016). "Optimal error intervals for properties of the quantum state." Phys. Rev. A. 94(6): 062112.
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Monte Carlo sampling from the quantum state space. II

Published in New Journal of Physics, 2015

High-quality random samples of quantum states are needed for a variety of tasks in quantum information and quantum computation. Searching the high-dimensional quantum state space for a global maximum of an objective function with many local maxima or evaluating an integral over a region in the quantum state space are but two exemplary applications of many. These tasks can only be performed reliably and efficiently with Monte Carlo methods, which involve good samplings of the parameter space in accordance with the relevant target distribution. We show how the Markov-chain Monte Carlo method known as Hamiltonian Monte Carlo, or hybrid Monte Carlo, can be adapted to this context. It is applicable when an efficient parameterization of the state space is available. The resulting random walk is entirely inside the physical parameter space, and the Hamiltonian dynamics enable us to take big steps, thereby avoiding strong correlations between successive sample points while enjoying a high acceptance rate. We use examples of single and double qubit measurements for illustration.

Recommended citation: Yi-Lin Seah, Jiangwei Shang, Hui Khoon Ng, David John Nott and Berthold-Georg Englert (2015). "Monte Carlo sampling from the quantum state space. II." New Journal of Physics. 17(4): 043018.
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Monte Carlo sampling from the quantum state space. I

Published in New Journal of Physics, 2015

High-quality random samples of quantum states are needed for a variety of tasks in quantum information and quantum computation. Searching the high-dimensional quantum state space for a global maximum of an objective function with many local maxima or evaluating an integral over a region in the quantum state space are but two exemplary applications of many. These tasks can only be performed reliably and efficiently with Monte Carlo methods, which involve good samplings of the parameter space in accordance with the relevant target distribution. We show how the standard strategies of rejection sampling, importance sampling, and Markov-chain sampling can be adapted to this context, where the samples must obey the constraints imposed by the positivity of the statistical operator. For illustration, we generate sample points in the probability space of qubits, qutrits, and qubit pairs, both for tomographically complete and incomplete measurements. We use these samples for various purposes: establish the marginal distribution of the purity; compute the fractional volume of separable two-qubit states; and calculate the size of regions with bounded likelihood.

Recommended citation: Jiangwei Shang, Yi-Lin Seah, Hui Khoon Ng, David John Nott and Berthold-Georg Englert (2015). "Monte Carlo sampling from the quantum state space. I." New Journal of Physics. 17(4): 043017.
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Quantum state tomography: Mean squared error matters, bias does not

Published in arXiv preprint arXiv:1405.5350, 2014

Because of the constraint that the estimators be bona fide physical states, any quantum state tomography scheme - including the widely used maximum likelihood estimation - yields estimators that may have a bias, although they are consistent estimators. Schwemmer et al. (arXiv:1310.8465 [quant-ph]) illustrate this by observing a systematic underestimation of the fidelity and an overestimation of entanglement in estimators obtained from simulated data. Further, these authors argue that the simple method of linear inversion overcomes this (perceived) problem of bias, and there is the suggestion to abandon time-tested estimation procedures in favor of linear inversion. Here, we discuss the pros and cons of using biased and unbiased estimators for quantum state tomography. We conclude that the little occasional benefit from the unbiased linear-inversion estimation does not justify the high price of using unphysical estimators, which are typically the case in that scheme.

Recommended citation: Jiangwei Shang, Hui Khoon Ng, Berthold-Georg Englert (2014). "Quantum state tomography: Mean squared error matters, bias does not." arXiv preprint arXiv:1405.5350.
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Conference Papers

Paper Title Number 4

Published in GitHub Journal of Bugs, 2024

This paper is about fixing template issue #693.

Recommended citation: Your Name, You. (2024). "Paper Title Number 3." GitHub Journal of Bugs. 1(3).
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