Optimal verification and fidelity estimation of maximally entangled states

Hayashi

2019

Phys. Rev. A

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Bipartite and multipartite entangled states are of central interest in quantum information processing and foundational studies. Efficient verification of these states, especially in the adversarial scenario, is a key to various applications, including quantum computation, quantum simulation, and quantum networks. However, little is know about this topic in the adversarial scenario. Here we initiate a systematic study of pure-state verification in the adversarial scenario. In particular, we introduce a general method for determining the minimal number of tests required by a given strategy to achieve a given precision. In the case of homogeneous strategies, we can even derive an analytical formula. Furthermore, we propose a general recipe to verifying pure quantum states in the adversarial scenario by virtue of protocols for the nonadversarial scenario. Thanks to this recipe, the resource cost for verifying an arbitrary pure state in the adversarial scenario is comparable to the counterpart for the nonadversarial scenario, and the overhead is at most three times for high-precision verification. Our recipe can readily be applied to efficiently verify bipartite pure states, stabilizer states, hypergraph states, weighted graph states, and Dicke states in the adversarial scenario. This paper is an extended version of the companion paper [1].

Section: Homogeneous Strategiesmentioning

confidence: 99%

Section: Number Of Required Testsmentioning

confidence: 99%

General framework for verifying pure quantum states in the adversarial scenario

Hayashi

2019

Phys. Rev. A

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“…Recently, a powerful approach known as quantum state verification [5][6][7] has attracted increasing attention. This approach has led to efficient protocols for verifying bipartite pure states [5,6,[8][9][10][11], stabilizer states (including graph states) [7,[12][13][14][15], hypergraph states [16], weighted graph states [17], and Dicke states [18].…”

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confidence: 99%

Efficient Verification of Pure Quantum States in the Adversarial Scenario

Hayashi

2019

Phys. Rev. Lett.

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Efficient verification of pure quantum states in the adversarial scenario is crucial to many applications in quantum information processing, such as blind measurement-based quantum computation and quantum networks. However, little is known about this subject so far. Here we establish a general framework for verifying pure quantum states in the adversarial scenario and clarify the resource cost. Moreover, we propose a simple and general recipe to constructing efficient verification protocols for the adversarial scenario from protocols for the nonadversarial scenario. With this recipe, arbitrary pure states can be verified in the adversarial scenario with almost the same efficiency as in the nonadversarial scenario. Many important quantum states in quantum information processing can be verified in the adversarial scenario with unprecedented high efficiencies.

“…In this case, we have Θ P ≤ Θ ≤ 1, and the maximally entangled state |Φ is an eigenstate of Θ P and Θ with the largest eigenvalue 1. Formally Θ P , Θ are verification operators of |Φ [22], so many results presented in Ref. [22] can be applied to the current study.…”

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confidence: 99%

“…Formally Θ P , Θ are verification operators of |Φ [22], so many results presented in Ref. [22] can be applied to the current study. A simple way for constructing balanced ensembles is to use orthonormal bases: If {|ψ j } j forms an orthonormal basis in H, then the ensemble {|ψ j ψ j |, p j = 1/d} j is balanced.…”

mentioning

confidence: 99%

Efficient verification of quantum gates with local operations

Zhang

2020

Phys. Rev. A

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Efficient verification of the functioning of quantum devices is a key to the development of quantum technologies, but is a daunting task as the system size increases. Here we propose a simple and general framework for verifying unitary transformations that can be applied to both individual quantum gates and gate sets, including quantum circuits. This framework enables efficient verification of many important unitary transformations, including but not limited to all bipartite unitaries, Clifford unitaries, generalized controlled-Z gates, generalized CNOT gates, and CSWAP gate. The sampling complexity increases at most linearly with the system size and is often independent of the system size. Moreover, little overhead is incurred even if one can only prepare Pauli eigenstates and perform local measurements. Our approach is applicable in many scenarios in which randomized benchmarking (RB) does not apply and is thus instrumental to quantum computation and many other applications in quantum information processing.