Average Contraction Coefficients of Quantum Channels

• URL: http://arxiv.org/abs/2508.08214v1
• Date: Mon, 11 Aug 2025 17:35:15 GMT
• Title: Average Contraction Coefficients of Quantum Channels
• Authors: Ruben Ibarrondo, Daniel Stilck França,
• Abstract summary: We study how noise contracts distinguishability of typical' states, beyond the worst-case.<n>We find a family of moments of contraction for quantum divergences, which interpolate between the worst-case contraction coefficient of a channel and its average behavior.<n>We extend these phase-transition phenomena to random quantum circuits with unital noise.
• Score: 0.7366405857677227
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The data-processing inequality ensures quantum channels reduce state distinguishability, with contraction coefficients quantifying optimal bounds. However, these can be overly optimistic and not representative of the usual behavior. We study how noise contracts distinguishability of `typical' states, beyond the worst-case. To that end, we introduce and study a family of moments of contraction for quantum divergences, which interpolate between the worst-case contraction coefficient of a channel and its average behavior under a chosen ensemble of input states. We establish general properties of these moments, relate moments for different divergences, and derive bounds in terms of channel parameters like the entropy or purity of its Choi state. Focusing on the trace distance, we obtain upper and lower bounds on its average contraction under tensor-product noise channels, and prove that, depending on the local noise strength, there is a phase transition in the limit of many channel uses: below a critical error rate the average contraction remains near unity, whereas above it decays exponentially with system size. We extend these phase-transition phenomena to random quantum circuits with unital noise, showing that constant-depth noisy circuits do not shrink the trace distance on average, even when given highly entangled states as input. In contrast, even at $\log\log n$ depth, the average trace distance can become superpolynomially small. Finally, we explore moments of contraction for f-divergences and discuss applications to local differential privacy, demonstrating that noise regimes ensuring privacy can render outputs essentially indistinguishable on average. Thus, our results provide a fine-grained framework to quantify typical channel noise in quantum information and computation and unveil new phenomena in contraction coefficients, such as phase transitions for average contraction.

Related papers

• Optimizing entanglement distribution via noisy quantum channels [44.99833362998488]
  Entanglement distribution is a crucial problem in quantum information science.<n>We investigate strategies for distributing quantum entanglement between two distant parties through noisy quantum channels.
  arXiv  Detail & Related papers  (2025-06-06T13:48:20Z)
• Bayesian Quantum Amplitude Estimation [49.1574468325115]
  We present BAE, a problem-tailored and noise-aware Bayesian algorithm for quantum amplitude estimation.<n>In a fault tolerant scenario, BAE is capable of saturating the Heisenberg limit; if device noise is present, BAE can dynamically characterize it and self-adapt.<n>We propose a benchmark for amplitude estimation algorithms and use it to test BAE against other approaches.
  arXiv  Detail & Related papers  (2024-12-05T18:09:41Z)
• Reverse-type Data Processing Inequality [11.013342155938801]
  A quantum data processing inequality asserts that two quantum states become harder to distinguish when a noisy channel is applied.<n>A reverse quantum data processing inequality characterizes whether distinguishability is preserved after the application of a noisy channel.<n>In this work, we explore these concepts through contraction and expansion coefficients of the relative entropy of quantum channels.
  arXiv  Detail & Related papers  (2024-11-29T17:56:36Z)
• Universal bounds for quantum metrology in the presence of correlated noise [0.0]
  We derive fundamental bounds for general quantum metrological models involving both temporal or spatial correlations.<n>Although the bounds are not guaranteed to be tight in general, their tightness may be systematically increased by increasing numerical complexity.
  arXiv  Detail & Related papers  (2024-10-02T18:00:00Z)
• Entanglement and operator correlation signatures of many-body quantum Zeno phases in inefficiently monitored noisy systems [49.1574468325115]
  The interplay between information-scrambling Hamiltonians and local continuous measurements hosts platforms for exotic measurement-induced phase transition. We identify a non-monotonic dependence on the local noise strength in both the averaged entanglement and operator correlations. The analysis of scaling with the system size in a finite length chain indicates that, at finite efficiency, this effect leads to distinct MiPTs for operator correlations and entanglement.
  arXiv  Detail & Related papers  (2024-07-16T13:42:38Z)
• Quantum Soft Covering and Decoupling with Relative Entropy Criterion [11.987004396261241]
  We prove covering lemmas by deriving one-shot bounds on the rates in terms of smooth min-entropies and smooth max-divergences. We present a one-shot quantum decoupling theorem with relative entropy criterion.
  arXiv  Detail & Related papers  (2024-02-16T22:31:38Z)
• Accurate and Honest Approximation of Correlated Qubit Noise [39.58317527488534]
  We propose an efficient systematic construction of approximate noise channels, where their accuracy can be enhanced by incorporating noise components with higher qubit-qubit correlation degree.<n>We find that, for realistic noise strength typical for fixed-frequency superconducting qubits, correlated noise beyond two-qubit correlation can significantly affect the code simulation accuracy.
  arXiv  Detail & Related papers  (2023-11-15T19:00:34Z)
• Emergence of noise-induced barren plateaus in arbitrary layered noise models [44.99833362998488]
  In variational quantum algorithms the parameters of a parameterized quantum circuit are optimized in order to minimize a cost function that encodes the solution of the problem. We discuss how, and in which sense, the phenomenon of noise-induced barren plateaus emerges in parameterized quantum circuits with a layered noise model.
  arXiv  Detail & Related papers  (2023-10-12T15:18:27Z)
• Suppressing Amplitude Damping in Trapped Ions: Discrete Weak Measurements for a Non-unitary Probabilistic Noise Filter [62.997667081978825]
  We introduce a low-overhead protocol to reverse this degradation. We present two trapped-ion schemes for the implementation of a non-unitary probabilistic filter against amplitude damping noise. This filter can be understood as a protocol for single-copy quasi-distillation.
  arXiv  Detail & Related papers  (2022-09-06T18:18:41Z)
• Noise correlations behind superdiffusive quantum walks [0.0]
  We study how discrete-time quantum walks behave under short-range correlated noise. For spatial inhomogeneities, we show noise correlations driving quantum walks from the well-known exponentially localized condition to superdiffusive spreading.
  arXiv  Detail & Related papers  (2022-07-26T18:54:28Z)
• High-Order Qubit Dephasing at Sweet Spots by Non-Gaussian Fluctuators: Symmetry Breaking and Floquet Protection [55.41644538483948]
  We study the qubit dephasing caused by the non-Gaussian fluctuators. We predict a symmetry-breaking effect that is unique to the non-Gaussian noise.
  arXiv  Detail & Related papers  (2022-06-06T18:02:38Z)
• Strong Converse for Privacy Amplification against Quantum Side Information [19.624719072006936]
  We establish a one-shot strong converse bound for privacy amplification against quantum side information using trace distance as a security criterion. The result has an application to bounding the information leakage of classical-quantum wiretap channel coding and private communication over quantum channels.
  arXiv  Detail & Related papers  (2022-02-21T14:28:01Z)
• Quantum-enabled communication without a phase reference [1.14219428942199]
  A phase reference has been a standard requirement in continuous-variable quantum sensing and communication protocols. We show that quantum communication and entanglement-assisted communication without a phase reference are possible, when a short-time memory effect is present.
  arXiv  Detail & Related papers  (2020-10-22T18:19:00Z)

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.