Error exponent of activated non-signaling assisted classical-quantum channel coding

• URL: http://arxiv.org/abs/2410.01084v2
• Date: Mon, 7 Oct 2024 07:52:35 GMT
• Title: Error exponent of activated non-signaling assisted classical-quantum channel coding
• Authors: Aadil Oufkir, Marco Tomamichel, Mario Berta,
• Abstract summary: We find that the optimal exponent--also called reliability function--is equal to the well-known sphere packing bound. Remarkably, there is no critical rate and our characterization remains tight for arbitrarily low rates below the capacity.
• Score: 12.221087476416056
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We provide a tight asymptotic characterization of the error exponent for classical-quantum channel coding assisted by activated non-signaling correlations. Namely, we find that the optimal exponent--also called reliability function--is equal to the well-known sphere packing bound, which can be written as a single-letter formula optimized over Petz-R\'enyi divergences. Remarkably, there is no critical rate and as such our characterization remains tight for arbitrarily low rates below the capacity. On the achievability side, we further extend our results to fully quantum channels. Our proofs rely on semi-definite program duality and a dual representation of the Petz-R\'enyi divergences via Young inequalities.

Related papers

• Rate-reliability functions for deterministic identification [49.126395046088014]
  We find that for positive exponents linear scaling is restored, now with a rate that is a function of the reliability exponents. We extend our results to classical-quantum channels and quantum channels with product input restriction.
  arXiv  Detail & Related papers  (2025-02-04T15:09:14Z)
• Quantum channel coding: Approximation algorithms and strong converse exponents [4.757470449749876]
  We study relaxations of entanglement-assisted quantum channel coding. Non-signaling assistance and the meta-converse are equivalent in terms of success probabilities.
  arXiv  Detail & Related papers  (2024-10-28T15:28:14Z)
• Exponents for classical-quantum channel simulation in purified distance [5.598487000369366]
  We determine the exact error and strong converse exponent for entanglement-assisted classical-quantum channel simulation. We critically use various properties of the quantum fidelity, additional auxiliary channel techniques, approximations via Chebyshev inequalities, and entropic continuity bounds.
  arXiv  Detail & Related papers  (2024-10-14T17:45:41Z)
• Reliability Function of Classical-Quantum Channels [6.959602244161659]
  We study the reliability function of general classical-quantum channels. We prove a lower bound, in terms of the quantum Renyi information in Petz's form, for the reliability function.
  arXiv  Detail & Related papers  (2024-07-17T08:30:27Z)
• Josephson bifurcation readout: beyond the monochromatic approximation [49.1574468325115]
  We analyze properties of bifurcation quantum detectors based on weakly nonlinear superconducting resonance circuits. This circuit can serve as an efficient detector of the quantum state of superconducting qubits.
  arXiv  Detail & Related papers  (2024-05-25T22:22:37Z)
• Enhancing Dispersive Readout of Superconducting Qubits Through Dynamic Control of the Dispersive Shift: Experiment and Theory [47.00474212574662]
  A superconducting qubit is coupled to a large-bandwidth readout resonator. We show a beyond-state-of-the-art two-state-readout error of only 0.25,%$ in 100 ns integration time. The presented results are expected to further boost the performance of new and existing algorithms and protocols.
  arXiv  Detail & Related papers  (2023-07-15T10:30:10Z)
• Non-Parametric Learning of Stochastic Differential Equations with Non-asymptotic Fast Rates of Convergence [65.63201894457404]
  We propose a novel non-parametric learning paradigm for the identification of drift and diffusion coefficients of non-linear differential equations. The key idea essentially consists of fitting a RKHS-based approximation of the corresponding Fokker-Planck equation to such observations.
  arXiv  Detail & Related papers  (2023-05-24T20:43:47Z)
• 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)
• Improved Quantum Algorithms for Fidelity Estimation [77.34726150561087]
  We develop new and efficient quantum algorithms for fidelity estimation with provable performance guarantees. Our algorithms use advanced quantum linear algebra techniques, such as the quantum singular value transformation. We prove that fidelity estimation to any non-trivial constant additive accuracy is hard in general.
  arXiv  Detail & Related papers  (2022-03-30T02:02:16Z)
• 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)
• Tight Exponential Analysis for Smoothing the Max-Relative Entropy and for Quantum Privacy Amplification [56.61325554836984]
  The max-relative entropy together with its smoothed version is a basic tool in quantum information theory. We derive the exact exponent for the decay of the small modification of the quantum state in smoothing the max-relative entropy based on purified distance.
  arXiv  Detail & Related papers  (2021-11-01T16:35:41Z)

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.