Usefulness of adaptive strategies in asymptotic quantum channel discrimination

• URL: http://arxiv.org/abs/2011.06569v3
• Date: Sun, 17 Mar 2024 22:20:10 GMT
• Title: Usefulness of adaptive strategies in asymptotic quantum channel discrimination
• Authors: Farzin Salek, Masahito Hayashi, Andreas Winter,
• Abstract summary: We investigate the usefulness of adaptive methods in the framework of binary hypothesis testing. There is a fundamental distinction between adaptive and non-adaptive strategies with respect to the channel uses. We show that adaptive strategies with classical feedback do not increase the discrimination power of the channel beyond non-adaptive product input strategies.
• Score: 43.7637825272776
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Adaptiveness is a key principle in information processing including statistics and machine learning. We investigate the usefulness of adaptive methods in the framework of asymptotic binary hypothesis testing, when each hypothesis represents asymptotically many independent instances of a quantum channel, and the tests are based on using the unknown channel and observing outputs. Unlike the familiar setting of quantum states as hypotheses, there is a fundamental distinction between adaptive and non-adaptive strategies with respect to the channel uses, and we introduce a number of further variants of the discrimination tasks by imposing different restrictions on the test strategies. The following results are obtained: (1) We prove that for classical-quantum channels, adaptive and non-adaptive strategies lead to the same error exponents both in the symmetric (Chernoff) and asymmetric (Hoeffding, Stein) settings. (2) The first separation between adaptive and non-adaptive symmetric hypothesis testing exponents for quantum channels, which we derive from a general lower bound on the error probability for non-adaptive strategies; the concrete example we analyze is a pair of entanglement-breaking channels. (3)We prove, in some sense generalizing the previous statement, that for general channels adaptive strategies restricted to classical feed-forward and product state channel inputs are not superior in the asymptotic limit to non-adaptive product state strategies. (4) As an application of our findings, we address the discrimination power of an arbitrary quantum channel and show that adaptive strategies with classical feedback and no quantum memory at the input do not increase the discrimination power of the channel beyond non-adaptive tensor product input strategies.

Related papers

• Selective Nonparametric Regression via Testing [54.20569354303575]
  We develop an abstention procedure via testing the hypothesis on the value of the conditional variance at a given point. Unlike existing methods, the proposed one allows to account not only for the value of the variance itself but also for the uncertainty of the corresponding variance predictor.
  arXiv  Detail & Related papers  (2023-09-28T13:04:11Z)
• Composite Classical and Quantum Channel Discrimination [6.553031877558699]
  We study the problem of binary composite channel discrimination in the asymmetric setting, where the hypotheses are given by fairly arbitrary sets of channels. We show that there can be an advantage to channel discrimination strategies with composite hypotheses for classical channels, unlike in general general simple hypotheses.
  arXiv  Detail & Related papers  (2023-03-03T15:31:38Z)
• Sequential Quantum Channel Discrimination [19.785872350085878]
  We consider the sequential quantum channel discrimination problem using adaptive and non-adaptive strategies. We show that both types of error probabilities decrease to zero exponentially fast. We conjecture that the achievable rate region is not larger than that achievable with POVMs.
  arXiv  Detail & Related papers  (2022-10-20T08:13:39Z)
• Parallelization of Adaptive Quantum Channel Discrimination in the Non-Asymptotic Regime [11.538345159297839]
  We investigate the performance of parallel and adaptive quantum channel discrimination strategies for a finite number of channel uses. We extend this result to the non-asymptotic regime with finitely many channel uses by explicitly constructing a parallel strategy for any given adaptive strategy.
  arXiv  Detail & Related papers  (2022-06-16T17:52:49Z)
• Optimal Adaptive Strategies for Sequential Quantum Hypothesis Testing [87.17253904965372]
  We consider sequential hypothesis testing between two quantum states using adaptive and non-adaptive strategies. We show that these errors decrease exponentially with decay rates given by the measured relative entropies between the two states.
  arXiv  Detail & Related papers  (2021-04-30T00:52:48Z)
• Learning explanations that are hard to vary [75.30552491694066]
  We show that averaging across examples can favor memorization and patchwork' solutions that sew together different strategies. We then propose and experimentally validate a simple alternative algorithm based on a logical AND.
  arXiv  Detail & Related papers  (2020-09-01T10:17:48Z)
• Understanding Implicit Regularization in Over-Parameterized Single Index Model [55.41685740015095]
  We design regularization-free algorithms for the high-dimensional single index model. We provide theoretical guarantees for the induced implicit regularization phenomenon.
  arXiv  Detail & Related papers  (2020-07-16T13:27:47Z)
• A One-step Approach to Covariate Shift Adaptation [82.01909503235385]
  A default assumption in many machine learning scenarios is that the training and test samples are drawn from the same probability distribution. We propose a novel one-step approach that jointly learns the predictive model and the associated weights in one optimization.
  arXiv  Detail & Related papers  (2020-07-08T11:35:47Z)
• Evaluating the Advantage of Adaptive Strategies for Quantum Channel Distinguishability [6.345523830122166]
  We study the advantage conferred by adaptive strategies in discrimination and distinguishability distillation of generalized amplitude damping channels. There are significant gaps between what can be accomplished with an adaptive strategy versus a non-adaptive strategy.
  arXiv  Detail & Related papers  (2020-01-15T15:31:39Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.