Generalized Quantum Stein's Lemma and Reversibility of Quantum Resource Theories for Classical-Quantum Channels

• URL: http://arxiv.org/abs/2509.13280v1
• Date: Tue, 16 Sep 2025 17:34:37 GMT
• Title: Generalized Quantum Stein's Lemma and Reversibility of Quantum Resource Theories for Classical-Quantum Channels
• Authors: Bjarne Bergh, Nilanjana Datta, Anirudh Khaitan,
• Abstract summary: We extend the recent proof of the Generalized Quantum Stein's Lemma by Hayashi and Yamasaki to classical-quantum (c-q) channels.<n>We analyze the composite hypothesis testing problem of testing a c-q channel $mathcalEotimes n$ against a sequence of sets of c-q channels.
• Score: 8.921166277011347
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We extend the recent proof of the Generalized Quantum Stein's Lemma by Hayashi and Yamasaki [arXiv:2408.02722] to classical-quantum (c-q) channels. We analyze the composite hypothesis testing problem of testing a c-q channel $\mathcal{E}^{\otimes n}$ against a sequence of sets of c-q channels $(\mathcal{S}_n)_n$ (satisfying certain natural assumptions), under parallel strategies. We prove that the optimal asymptotic asymmetric error exponent is given by the regularization of Umegaki channel divergence, minimized over $\mathcal{S}_n$. This allows us to prove the reversibility of resource theories of classical-quantum channels in a natural framework, where the distance between channels (and hence also the notion of approximate interconvertibility of channels) is measured in diamond norm, and the set of free operations is the set of all asymptotically resource non-generating superchannels. The results we obtain are similar to the ones in the concurrent and independent work by Hayashi and Yamasaki [arXiv:2509.07271]. However the proof of the direct part of the GQSL uses different arguments and techniques to deal with the challenges that arise from dealing with c-q channels.

Related papers

• Adversarial Hypothesis Testing for Quantum Channels [57.214837874007856]
  We study adversarial hypothesis testing for quantum-quantum (QQ) and classical-quantum (CQ) channels.<n>For QQ channels with i.i.d. inputs, Bob's knowledge of the input significantly enhances distinguishability.<n>For CQ channels, Bob being informed provides a consistent advantage over the corresponding entanglement-breaking channels for both i.i.d. and general inputs.
  arXiv  Detail & Related papers  (2026-01-15T10:04:10Z)
• Classification and implementation of unitary-equivariant and permutation-invariant quantum channels [0.0]
  Many quantum information tasks use inputs of the form $rhootimes m$, which naturally induce permutation and unitary symmetries.<n>We classify all quantum channels that respect both symmetries.
  arXiv  Detail & Related papers  (2025-10-09T12:35:39Z)
• Exact Quantum Capacity of Decohering Channels in Arbitrary Dimensions [0.0]
  We derive exact analytical expressions for the quantum capacity of a broad class of decohering quantum channels of the form $Lambda(rho)= (1-x)rho + x D(rho)$, where $D(rho)$ represents a structured decoherence process.<n>These channels are shown to be degradable for all noise parameters and in arbitrary dimensions, yielding closed-form, single-letter capacity formulas.
  arXiv  Detail & Related papers  (2025-06-16T12:06:26Z)
• Resolvability of classical-quantum channels [54.825573549226924]
  We study the resolvability of classical-quantum channels in two settings, for the channel output generated from the worst input, and form the fixed independent and identically distributed (i.i.d.) input. For the fixed-input setting, while the direct part follows from the known quantum soft covering result, we exploit the recent alternative quantum Sanov theorem to solve the strong converse.
  arXiv  Detail & Related papers  (2024-10-22T05:18:43Z)
• Deterministic identification over channels with finite output: a dimensional perspective on superlinear rates [49.126395046088014]
  We consider the problem in its generality for memoryless channels with finite output, but arbitrary input alphabets.<n>Our main findings are that the maximum length of messages thus identifiable scales superlinearly as $R,nlog n$ with the block length $n$.<n>We show that it is sufficient to ensure pairwise reliable distinguishability of the output distributions to construct a DI code.
  arXiv  Detail & Related papers  (2024-02-14T11:59:30Z)
• 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)
• Simple and Tighter Derivation of Achievability for Classical Communication over Quantum Channels [7.88657961743755]
  In this work, we show that the pretty-good measurement naturally plays a role as the union bound as well. A judicious application of it considerably simplifies the derivation of one-shot achievability for classical-quantum (c-q) channel coding via an elegant three-line proof. The proposed method applies to deriving one-shot achievability for classical data compression with quantum side information, entanglement-assisted classical communication over quantum channels, and various quantum network information-processing protocols.
  arXiv  Detail & Related papers  (2022-08-03T15:12:01Z)
• Dephasing superchannels [0.09545101073027092]
  We characterise a class of environmental noises that decrease coherent properties of quantum channels by introducing and analysing the properties of dephasing superchannels. These are defined as superchannels that affect only non-classical properties of a quantum channel $mathcalE$. We prove that such superchannels $Xi_C$ form a particular subclass of Schur-product supermaps that act on the Jamiolkowski state $J(mathcalE)$ of a channel $mathcalE$ via a Schur product, $J'=J
  arXiv  Detail & Related papers  (2021-07-14T10:10:46Z)
• Sampling Overhead Analysis of Quantum Error Mitigation: Uncoded vs. Coded Systems [69.33243249411113]
  We show that Pauli errors incur the lowest sampling overhead among a large class of realistic quantum channels. We conceive a scheme amalgamating QEM with quantum channel coding, and analyse its sampling overhead reduction compared to pure QEM.
  arXiv  Detail & Related papers  (2020-12-15T15:51:27Z)
• 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)
• The resource theory of coherence for quantum channels [0.0]
  We show that basis-dependent quantum asymmetric discord can never be more than the $mathcalQI$ REC for any quantum channels. For qubit channels, the relative entropy of coherence (REC) can be equivalent to the REC of their corresponding Choi states.
  arXiv  Detail & Related papers  (2020-06-27T20:58:27Z)
• Quantum Communication Complexity of Distribution Testing [114.31181206328276]
  Two players each receive $t$ samples from one distribution over $[n]$. The goal is to decide whether their two distributions are equal, or are $epsilon$-far apart. We show that the quantum communication complexity of this problem is $tildeO$(tepsilon2))$ qubits when distributions have low $l$-norm.
  arXiv  Detail & Related papers  (2020-06-26T09:05:58Z)
• Using Quantum Metrological Bounds in Quantum Error Correction: A Simple Proof of the Approximate Eastin-Knill Theorem [77.34726150561087]
  We present a proof of the approximate Eastin-Knill theorem, which connects the quality of a quantum error-correcting code with its ability to achieve a universal set of logical gates. Our derivation employs powerful bounds on the quantum Fisher information in generic quantum metrological protocols.
  arXiv  Detail & Related papers  (2020-04-24T17:58:10Z)
• A general theory of comparison of quantum channels (and beyond) [0.0]
  We show that approximate simulability can be characterized by comparing outcome probabilities in certain tests. Results are applied to several specific cases of simulability of quantum channels.
  arXiv  Detail & Related papers  (2020-02-11T07:48:32Z)

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.