Adaptive Procedures for Discriminating Between Arbitrary Tensor-Product Quantum States

Brandsen, Sarah; Lian, Mengke; Stubbs, Kevin D.; Rengaswamy, Narayanan; Pfister, Henry D.

doi:10.1109/isit44484.2020.9174234

Cited by 4 publications

(9 citation statements)

References 10 publications

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“…j | for all k ∈ {1, ..., n} and j ∈ {1, 2}, it has been shown that the optimal collective success probability, P SDP can be achieved through locally-adaptive strategies [10,33]. The collective success probability, P SDP , is found using semidefinite programming techniques introduced by [32].…”

Section: Numerical Results For Rlnn Performancementioning

confidence: 99%

“…In the special case of binary state discrimination (m = 2), it has been shown [10,33] that locally-greedy algorithms are optimal for distinguishing between pure tensor product states. Thus, for pure binary state discrimination, the success probability of the optimal collective measurement can be achieved through a simple locally-greedy algorithm.…”

Section: Pure State Discriminationmentioning

confidence: 99%

“…We know that dynamic programming can be used to find an optimal local approach [9]. However, even in the simplest case where m = 2, the complexity grows like O(2 n nQ), where n is the number of qubit subsystems and Q is the number of different local measurements considered [10].…”

Section: Introductionmentioning

confidence: 99%

“…These specific results help complete the picture regarding the optimality of locally adaptive protocols in four key regimes: pure binary state discrimination, mixed binary state discrimination, pure non-binary state discrimination, and mixed non-binary state discrimination. Prior to this work it was known that locally adaptive, projective measurement strategies are optimal for pure binary state discrimination [10,33] and are in general are not optimal for both pure and mixed nonbinary state discrimination [34,35]. In contrast to the pure state case, few analytical results are known for mixed binary state discrimination.…”

Section: Introductionmentioning

confidence: 99%

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Reinforcement Learning with Neural Networks for Quantum Multiple Hypothesis Testing

Brandsen

Stubbs

Pfister

2022

Quantum

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Reinforcement learning with neural networks (RLNN) has recently demonstrated great promise for many problems, including some problems in quantum information theory. In this work, we apply RLNN to quantum hypothesis testing and determine the optimal measurement strategy for distinguishing between multiple quantum states {ρj} while minimizing the error probability. In the case where the candidate states correspond to a quantum system with many qubit subsystems, implementing the optimal measurement on the entire system is experimentally infeasible. We use RLNN to find locally-adaptive measurement strategies that are experimentally feasible, where only one quantum subsystem is measured in each round. We provide numerical results which demonstrate that RLNN successfully finds the optimal local approach, even for candidate states up to 20 subsystems. We additionally demonstrate that the RLNN strategy meets or exceeds the success probability for a modified locally greedy approach in each random trial.While the use of RLNN is highly successful for designing adaptive local measurement strategies, in general a significant gap can exist between the success probability of the optimal locally-adaptive measurement strategy and the optimal collective measurement. We build on previous work to provide a set of necessary and sufficient conditions for collective protocols to strictly outperform locally adaptive protocols. We also provide a new example which, to our knowledge, is the simplest known state set exhibiting a significant gap between local and collective protocols. This result raises interesting new questions about the gap between theoretically optimal measurement strategies and practically implementable measurement strategies.

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Section: Numerical Results For Rlnn Performancementioning

confidence: 99%

Section: Pure State Discriminationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Reinforcement Learning with Neural Networks for Quantum Multiple Hypothesis Testing

Brandsen

Stubbs

Pfister

2022

Quantum

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show abstract

Section: Introductionmentioning

confidence: 99%

Reinforcement Learning with Neural Networks for Quantum Multiple Hypothesis Testing

Brandsen,

Stubbs,

Pfister

2020

Preprint

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Reinforcement learning with neural networks (RLNN) has recently demonstrated great promise for many problems, including some problems in quantum information theory. In this work, we apply RLNN to quantum hypothesis testing and determine the optimal measurement strategy for distinguishing between multiple quantum states {ρ j } while minimizing the error probability. In the case where the candidate states correspond to a quantum system with many qubit subsystems, implementing the optimal measurement on the entire system is experimentally infeasible.In this work, we focus on using RLNN to find locally-adaptive measurement strategies that are experimentally feasible, where only one quantum subsystem is measured in each round. We provide numerical results which demonstrate that RLNN successfully finds the optimal local approach, even for candidate states up to 20 subsystems. We additionally introduce a min-entropy based locally adaptive protocol, and demonstrate that the RLNN strategy meets or exceeds the min-entropy success probability in each random trial.While the use of RLNN is highly successful for designing adaptive local measurement strategies, we find that there can be a significant gap between success probability of any locally-adaptive measurement strategy and the optimal collective measurement. As evidence of this, we exhibit a collection of pure tensor product quantum states which cannot be optimally distinguished by any locally-adaptive strategy. This counterexample raises interesting new questions about the gap between theoretically optimal measurement strategies and practically implementable measurement strategies.

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Discriminating qubit amplitude damping channels

Rexiti¹,

Mancini²

2021

J. Phys. A: Math. Theor.

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We address the issue of the discrimination between two-qubit amplitude damping channels by exploring several strategies. For the single-shot, we show that the excited state does not always give the optimal input, and that side entanglement assistance has limited benefit. On the contrary, feedback assistance from the environment is more beneficial. For the two-shot, we prove the in-utility of entangled inputs. Then focusing on individual (local) measurements, we find the optimal adaptive strategy.

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Adaptive Procedures for Discriminating Between Arbitrary Tensor-Product Quantum States

Cited by 4 publications

References 10 publications

Reinforcement Learning with Neural Networks for Quantum Multiple Hypothesis Testing

Reinforcement Learning with Neural Networks for Quantum Multiple Hypothesis Testing

Reinforcement Learning with Neural Networks for Quantum Multiple Hypothesis Testing

Discriminating qubit amplitude damping channels

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