Towards the ultimate limits of quantum channel discrimination

• URL: http://arxiv.org/abs/2110.14842v2
• Date: Tue, 1 Mar 2022 08:34:30 GMT
• Title: Towards the ultimate limits of quantum channel discrimination
• Authors: Kun Fang, Gilad Gour, and Xin Wang
• Abstract summary: We make a conjecture on the exponentially strong converse of quantum channel hypothesis testing under coherent strategies. We develop a framework to show the interplay between the strategies of channel discrimination, the operational regimes, and variants of channel divergences.
• Score: 18.836836815159764
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: This note studies the difficulty of discriminating quantum channels under operational regimes. First, we make a conjecture on the exponentially strong converse of quantum channel hypothesis testing under coherent strategies, meaning that any strategy to make the Type II error decays with an exponent larger than the regularized channel relative entropy will unavoidably result in the Type I error converging to one exponentially fast in the asymptotic limit. This conjecture will imply the desirable quantum channel Stein's Lemma and the continuity of the regularized (amortized) Sandwiched R\'{e}nyi channel divergence at $\alpha=1$. We also remark that there was a gap in the proof of the above conjecture in our previous arXiv version. Such gap exists since a lemma basically comes from [Brandao and Plenio, 2010] was found to be false. Second, we develop a framework to show the interplay between the strategies of channel discrimination, the operational regimes, and variants of channel divergences. This framework systematically underlies the operational meaning of quantum channel divergences in quantum channel discrimination. Our work makes an attempt towards understanding the ultimate limit of quantum channel discrimination, as well as its connection to quantum channel divergences in the asymptotic regime.

Related papers

• The multimode conditional quantum Entropy Power Inequality and the squashed entanglement of the extreme multimode bosonic Gaussian channels [53.253900735220796]
  Inequality determines the minimum conditional von Neumann entropy of the output of the most general linear mixing of bosonic quantum modes. Bosonic quantum systems constitute the mathematical model for the electromagnetic radiation in the quantum regime.
  arXiv  Detail & Related papers  (2024-10-18T13:59:50Z)
• A Lie Algebraic Theory of Barren Plateaus for Deep Parameterized Quantum Circuits [37.84307089310829]
  Variational quantum computing schemes train a loss function by sending an initial state through a parametrized quantum circuit. Despite their promise, the trainability of these algorithms is hindered by barren plateaus. We present a general Lie algebra that provides an exact expression for the variance of the loss function of sufficiently deep parametrized quantum circuits.
  arXiv  Detail & Related papers  (2023-09-17T18:14:10Z)
• Normal quantum channels and Markovian correlated two-qubit quantum errors [77.34726150561087]
  We study general normally'' distributed random unitary transformations. On the one hand, a normal distribution induces a unital quantum channel. On the other hand, the diffusive random walk defines a unital quantum process.
  arXiv  Detail & Related papers  (2023-07-25T15:33:28Z)
• Quantum soft-covering lemma with applications to rate-distortion coding, resolvability and identification via quantum channels [7.874708385247353]
  We prove a one-shot quantum covering lemma in terms of smooth min-entropies. We provide new upper bounds on the unrestricted and simultaneous identification capacities of quantum channels.
  arXiv  Detail & Related papers  (2023-06-21T17:53:22Z)
• 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)
• Quantum machine learning channel discrimination [0.0]
  In the problem of quantum channel discrimination, one distinguishes between a given number of quantum channels. This work studies applications of variational quantum circuits and machine learning techniques for discriminating such channels.
  arXiv  Detail & Related papers  (2022-06-20T18:00:05Z)
• Reliable Simulation of Quantum Channels: the Error Exponent [5.8303977553652]
  We study the error exponent of quantum channel simulation, which characterizes the optimal speed of exponential convergence. We obtain an achievability bound for quantum channel simulation in the finite-blocklength setting.
  arXiv  Detail & Related papers  (2021-12-08T18:55:54Z)
• Experimental violations of Leggett-Garg's inequalities on a quantum computer [77.34726150561087]
  We experimentally observe the violations of Leggett-Garg-Bell's inequalities on single and multi-qubit systems. Our analysis highlights the limits of nowadays quantum platforms, showing that the above-mentioned correlation functions deviate from theoretical prediction as the number of qubits and the depth of the circuit grow.
  arXiv  Detail & Related papers  (2021-09-06T14:35:15Z)
• Usefulness of adaptive strategies in asymptotic quantum channel discrimination [43.7637825272776]
  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.
  arXiv  Detail & Related papers  (2020-11-12T18:40:47Z)
• Ultimate limits for multiple quantum channel discrimination [0.966840768820136]
  This paper studies the problem of hypothesis testing with quantum channels. We establish a lower limit for the ultimate error probability affecting the discrimination of an arbitrary number of quantum channels. We also show that this lower bound is achievable when the channels have certain symmetries.
  arXiv  Detail & Related papers  (2020-07-29T03:08:48Z)
• Quantum Statistical Complexity Measure as a Signalling of Correlation Transitions [55.41644538483948]
  We introduce a quantum version for the statistical complexity measure, in the context of quantum information theory, and use it as a signalling function of quantum order-disorder transitions. We apply our measure to two exactly solvable Hamiltonian models, namely: the $1D$-Quantum Ising Model and the Heisenberg XXZ spin-$1/2$ chain. We also compute this measure for one-qubit and two-qubit reduced states for the considered models, and analyse its behaviour across its quantum phase transitions for finite system sizes as well as in the thermodynamic limit by using Bethe ansatz.
  arXiv  Detail & Related papers  (2020-02-05T00:45:21Z)

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.