Holevo Capacity of Discrete Weyl Channels

• URL: http://arxiv.org/abs/2003.01942v1
• Date: Wed, 4 Mar 2020 08:19:31 GMT
• Title: Holevo Capacity of Discrete Weyl Channels
• Abstract summary: Holevo capacity is the maximum rate at which a quantum channel can reliably transmit classical information without entanglement. We consider discrete Weyl channels (DWCs) and exploit their symmetry properties to model DWC as a classical symmetric channel. We characterize lower and upper bounds on the Holevo capacity of DWCs using simple computational formulae.
• Score: 10.60025721557741
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Holevo capacity is the maximum rate at which a quantum channel can reliably transmit classical information without entanglement. However, calculating the Holevo capacity of arbitrary quantum channels is a nontrivial and computationally expensive task since it requires the numerical optimization over all possible input quantum states. In this paper, we consider discrete Weyl channels (DWCs) and exploit their symmetry properties to model DWC as a classical symmetric channel. We characterize lower and upper bounds on the Holevo capacity of DWCs using simple computational formulae. Then, we provide a sufficient and necessary condition where the upper and lower bounds coincide. The framework in this paper enables us to characterize the exact Holevo capacity for most of the known special cases of DWCs.

Related papers

• Quantum-Channel Matrix Optimization for Holevo Bound Enhancement [87.57725685513088]
  We propose a unified projected gradient ascent algorithm to optimize the quantum channel given a fixed input ensemble.<n> Simulation results demonstrate that the proposed quantum channel optimization yields higher Holevo bounds than input ensemble optimization.
  arXiv  Detail & Related papers  (2026-02-19T04:15:03Z)
• On the undecidability of quantum channel capacities [2.1088544691147435]
  We show that, for a general quantum channel, it is QMA-hard to compute its quantum capacity, and that the maximal-entanglement-assisted zero-error one-shot classical capacity is uncomputable.
  arXiv  Detail & Related papers  (2026-01-30T02:35:01Z)
• Extreme Capacities in Generalized Direct Sum Channels [9.35201227314384]
  We construct the generalized direct sum (GDS) channel, extending conventional direct sum channels through a direct sum structure in their Kraus operators.<n>This construction forms the basis of the GDS framework, encompassing classes of channels with single-letter formula for quantum capacities and others exhibiting striking capacity features.
  arXiv  Detail & Related papers  (2025-10-12T17:25:18Z)
• On small perturbations of coherent information [7.078713722203906]
  Quantum capacity quantifies the amount of quantum information that can be transmitted by a quantum channel with an arbitrary small probability of error.<n>We develop perturbative methods for analyzing the behavior of coherent information of a quantum channel with respect to small perturbations of the input state.<n>We show how our criteria yield sufficient conditions for superadditivity of one-shot quantum capacity, and also for detecting a positive gap between one-shot private capacity and one-shot quantum capacity.
  arXiv  Detail & Related papers  (2025-07-22T18:02:27Z)
• Quantum Hypothesis Testing Lemma for Deterministic Identification over Quantum Channels [49.126395046088014]
  We show that the existence of a DI code in the quantum setting follows from a suitable packing in a modified space of output quantum states. This result enables us to tighten the capacity lower bound for DI over quantum channels beyond the simultaneous decoding approach.
  arXiv  Detail & Related papers  (2025-04-29T17:57:36Z)
• Riemannian Optimization for Holevo Capacity [5.746235925946808]
  We formulate the computation of the Holevo capacity as an optimization problem on a product manifold constructed from probability distributions. A gradient gradient descent algorithm is proposed to solve the problem, providing lower bounds on the classical capacity of general quantum channels.
  arXiv  Detail & Related papers  (2025-01-20T16:26:21Z)
• On Simultaneous Information and Energy Transmission through Quantum Channels [15.387256204743407]
  We introduce the quantum-classical analogue of the capacity-power function. We generalize results in classical information theory for transmitting classical information through noisy channels.
  arXiv  Detail & Related papers  (2023-09-24T16:46:47Z)
• Adversarial guesswork with quantum side information [2.4554686192257424]
  We show that the guesswork of a classical-quantum channel quantifies the cost incurred in guessing the state transmitted by the channel. We compute the optimal guesswork for the class of so-called highly symmetric informationally complete classical-quantum channels.
  arXiv  Detail & Related papers  (2023-06-22T02:03:45Z)
• The superadditivity effects of quantum capacity decrease with the dimension for qudit depolarizing channels [0.0]
  We study how the gain in quantum capacity of qudit depolarizing channels relates to the dimension of the systems considered. We conclude that when high dimensional qudits experiencing depolarizing noise are considered, the coherent information of the channel is not only an achievable rate but essentially the maximum possible rate for any quantum block code.
  arXiv  Detail & Related papers  (2023-01-24T16:54:09Z)
• A hierarchy of efficient bounds on quantum capacities exploiting symmetry [8.717253904965371]
  We exploit the recently introduced $D#$ in order to obtain a hierarchy of semidefinite programming bounds on various regularized quantities. As applications, we give a general procedure to give efficient bounds on the regularized Umegaki channel divergence. We prove that for fixed input and output dimensions, the regularized sandwiched R'enyi divergence between any two quantum channels can be approximated up to an $epsilon$ accuracy in time.
  arXiv  Detail & Related papers  (2022-03-04T04:34:15Z)
• Commitment capacity of classical-quantum channels [70.51146080031752]
  We define various notions of commitment capacity for classical-quantum channels. We prove matching upper and lower bound on it in terms of the conditional entropy.
  arXiv  Detail & Related papers  (2022-01-17T10:41:50Z)
• Energy-constrained LOCC-assisted quantum capacity of bosonic dephasing channel [0.0]
  We study the LOCC-assisted quantum capacity of bosonic dephasing channel with energy constraint on input states. We derive explicit upper and lower bounds for the energy-constrained LOCC-assisted quantum capacity of the bosonic dephasing channel.
  arXiv  Detail & Related papers  (2021-11-07T20:21:33Z)
• Efficient criteria of quantumness for a large system of qubits [58.720142291102135]
  We discuss the dimensionless combinations of basic parameters of large, partially quantum coherent systems. Based on analytical and numerical calculations, we suggest one such number for a system of qubits undergoing adiabatic evolution.
  arXiv  Detail & Related papers  (2021-08-30T23:50:05Z)
• Quantum Channel State Masking [78.7611537027573]
  Communication over a quantum channel that depends on a quantum state is considered when the encoder has channel side information (CSI) and is required to mask information on the quantum channel state from the decoder. A full characterization is established for the entanglement-assisted masking equivocation region, and a regularized formula is given for the quantum capacity-leakage function without assistance.
  arXiv  Detail & Related papers  (2020-06-10T16:18:03Z)
• Efficient simulatability of continuous-variable circuits with large Wigner negativity [62.997667081978825]
  Wigner negativity is known to be a necessary resource for computational advantage in several quantum-computing architectures. We identify vast families of circuits that display large, possibly unbounded, Wigner negativity, and yet are classically efficiently simulatable. We derive our results by establishing a link between the simulatability of high-dimensional discrete-variable quantum circuits and bosonic codes.
  arXiv  Detail & Related papers  (2020-05-25T11:03:42Z)
• 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)
• Permutation Enhances Classical Communication Assisted by Entangled States [67.12391801199688]
  We show that the capacity satisfies the strong converse property and thus the formula serves as a sharp dividing line between achievable and unachievable rates of communication. As examples, we derive analytically the classical capacity of various quantum channels of interests.
  arXiv  Detail & Related papers  (2020-01-07T01:49:31Z)

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.