Capacities of the covariant Pauli channel

• URL: http://arxiv.org/abs/2206.06106v5
• Date: Mon, 5 Dec 2022 17:00:18 GMT
• Title: Capacities of the covariant Pauli channel
• Authors: Abbas Poshtvan, Vahid Karimipour
• Abstract summary: We study the four well-known capacities of a two- parameter family of qubit Pauli channels. We find exact expressions for the classical capacity and entanglement assisted capacities. We analytically determine the regions where the quantum capacity of the channel vanishes.
• Score: 0.0
• License: http://creativecommons.org/publicdomain/zero/1.0/
• Abstract: We study the four well-known capacities of a two-parameter family of qubit Pauli channels. These are the channels which are covariant under the SO(2) group and contain the depolarizing channel as a special case. We find exact expressions for the classical capacity and entanglement assisted capacities, and analytically determine the regions where the quantum capacity of the channel vanishes. We then use a flag extension to find upper bound for the quantum capacity and private capacity of these channels in the entire region of parameter space and also obtain the lower bound for the quantum capacity by calculating the single shot quantum capacity numerically. In conjunction with previous results on depolarizing channels, our result is one step forward for determining the capacities of the full Pauli channel.

Related papers

• Quantum channels, complex Stiefel manifolds, and optimization [45.9982965995401]
  We establish a continuity relation between the topological space of quantum channels and the quotient of the complex Stiefel manifold. The established relation can be applied to various quantum optimization problems.
  arXiv  Detail & Related papers  (2024-08-19T09:15:54Z)
• A vertical gate-defined double quantum dot in a strained germanium double quantum well [48.7576911714538]
  Gate-defined quantum dots in silicon-germanium heterostructures have become a compelling platform for quantum computation and simulation. We demonstrate the operation of a gate-defined vertical double quantum dot in a strained germanium double quantum well. We discuss challenges and opportunities and outline potential applications in quantum computing and quantum simulation.
  arXiv  Detail & Related papers  (2023-05-23T13:42:36Z)
• Information capacity analysis of fully correlated multi-level amplitude damping channels [0.9790236766474201]
  We investigate some of the information capacities of the simplest member of multi-level Amplitude Damping Channel, a qutrit channel. We find the upper bounds of the single-shot classical capacities and calculate the quantum capacities associated with a specific class of maps.
  arXiv  Detail & Related papers  (2023-05-08T06:10:56Z)
• Pauli component erasing quantum channels [58.720142291102135]
  We propose a family of quantum maps that preserve or completely erase the components of a multi-qubit system. For the corresponding channels, it is shown that the preserved components can be interpreted as a finite vector subspace. We show that the obtained family of channels forms a semigroup and derive its generators.
  arXiv  Detail & Related papers  (2022-05-12T00:11:43Z)
• Exact solution for the quantum and private capacities of bosonic dephasing channels [10.787390511207686]
  We provide the first exact calculation of the quantum, private, two-way assisted quantum, and secret-key capacities of bosonic dephasing channels.
  arXiv  Detail & Related papers  (2022-05-11T19:12:12Z)
• Creating and destroying coherence with quantum channels [62.997667081978825]
  We study optimal ways to create a large amount of quantum coherence via quantum channels. correlations in multipartite systems do not enhance the ability of a quantum channel to create coherence. We show that a channel can destroy more coherence when acting on a subsystem of a bipartite state.
  arXiv  Detail & Related papers  (2021-05-25T16:44:13Z)
• Coherent control and distinguishability of quantum channels via PBS-diagrams [59.94347858883343]
  We introduce a graphical language for coherent control of general quantum channels inspired by practical quantum optical setups involving polarising beam splitters (PBS) We characterise the observational equivalence of purified channels in various coherent-control contexts, paving the way towards a faithful representation of quantum channels under coherent control.
  arXiv  Detail & Related papers  (2021-03-02T22:56:25Z)
• Bounding the quantum capacity with flagged extensions [3.007949058551534]
  We consider flagged extensions of convex combination of quantum channels, and find general sufficient conditions for the degradability of the flagged extension. An immediate application is a bound on the quantum $Q$ and private $P$ capacities of any channel being a mixture of a unitary map and another channel. We then specialize our sufficient conditions to flagged Pauli channels, obtaining a family of upper bounds on quantum and private capacities of Pauli channels.
  arXiv  Detail & Related papers  (2020-08-06T05:28:16Z)
• Partially Coherent Direct Sum Channels [4.2231191686871234]
  We introduce Partially Coherent Direct Sum (PCDS) quantum channels, as a generalization of the already known Direct Sum quantum channels. We derive necessary and sufficient conditions to identify a subset of those maps which are degradable, and provide a simplified expression for their quantum capacities.
  arXiv  Detail & Related papers  (2020-08-02T14:36:11Z)
• 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)
• Quantum and private capacities of low-noise channels [10.098114696565863]
  We determine both the quantum and the private capacities of low-noise quantum channels to leading orders. Super-additivity and degenerate codes have negligible benefit for the quantum capacity. shielding does not improve the private capacity beyond the quantum capacity.
  arXiv  Detail & Related papers  (2017-05-11T18:01:08Z)

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.