Generic nonadditivity of quantum capacity in simple channels

• URL: http://arxiv.org/abs/2202.08377v2
• Date: Tue, 13 Jun 2023 17:26:03 GMT
• Title: Generic nonadditivity of quantum capacity in simple channels
• Authors: Felix Leditzky and Debbie Leung and Vikesh Siddhu and Graeme Smith and John A. Smolin
• Abstract summary: Super-additivity of quantum capacity occurs between two weakly additive channels each with large capacity on their own. Our results show that super-additivity is much more prevalent than previously thought.
• Score: 12.4245398967236
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Determining capacities of quantum channels is a fundamental question in quantum information theory. Despite having rigorous coding theorems quantifying the flow of information across quantum channels, their capacities are poorly understood due to super-additivity effects. Studying these phenomena is important for deepening our understanding of quantum information, yet simple and clean examples of super-additive channels are scarce. Here we study a family of channels called platypus channels. Its simplest member, a qutrit channel, is shown to display super-additivity of coherent information when used jointly with a variety of qubit channels. Higher-dimensional family members display super-additivity of quantum capacity together with an erasure channel. Subject to the "spin-alignment conjecture" introduced in the companion paper [IEEE Trans. Inf. Theory 69(6), pp. 3825-3849, 2023; arXiv:2202.08380], our results on super-additivity of quantum capacity extend to lower-dimensional channels as well as larger parameter ranges. In particular, super-additivity occurs between two weakly additive channels each with large capacity on their own, in stark contrast to previous results. Remarkably, a single, novel transmission strategy achieves super-additivity in all examples. Our results show that super-additivity is much more prevalent than previously thought. It can occur across a wide variety of channels, even when both participating channels have large quantum capacity.

Related papers

• The multimode conditional quantum Entropy Power Inequality and the squashed entanglement of the extreme multimode bosonic Gaussian channels [53.253900735220796]
  Inequality determines the minimum conditional von Neumann entropy of the output of the most general linear mixing of bosonic quantum modes. Bosonic quantum systems constitute the mathematical model for the electromagnetic radiation in the quantum regime.
  arXiv  Detail & Related papers  (2024-10-18T13:59:50Z)
• Additivity of quantum capacities in simple non-degradable quantum channels [3.9901365062418312]
  Examples of additivity, while rare, provide key insight into the origins of nonadditivity. Degradable channels, which have additive coherent information, are some of the only channels for which we can calculate the quantum capacity. We construct non-degradable quantum channels that nevertheless have additive coherent information and therefore easily calculated quantum capacity.
  arXiv  Detail & Related papers  (2024-09-05T22:17:29Z)
• 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)
• Noise is resource-contextual in quantum communication [1.8749305679160366]
  Estimating the information transmission capability of a quantum channel remains one of the fundamental problems in quantum information processing. One of the most significant manifestations of this is the superadditivity of the channel capacity. Our constructions demonstrate that noise is context dependent in quantum communication.
  arXiv  Detail & Related papers  (2023-05-01T06:24:03Z)
• The platypus of the quantum channel zoo [12.4245398967236]
  We study a simple, low-dimensional family of quantum channels with exotic quantum information-theoretic features. We generalize the qutrit channel in two ways, and the resulting channels and their capacities display similarly rich behavior.
  arXiv  Detail & Related papers  (2022-02-16T23:54:07Z)
• Entanglement catalysis for quantum states and noisy channels [41.94295877935867]
  We investigate properties of entanglement and its role for quantum communication. For transformations between bipartite pure states, we prove the existence of a universal catalyst. We further develop methods to estimate the number of singlets which can be established via a noisy quantum channel.
  arXiv  Detail & Related papers  (2022-02-10T18:36:25Z)
• Multipartite entanglement to boost superadditivity of coherent information in quantum communication lines with polarization dependent losses [0.0]
  We show that in the limit of the infinite number of channel uses the superadditivity phenomenon takes place whenever the channel is neither degradable nor antidegradable. We also provide a method how to modify the proposed states and get a higher quantum communication rate by doubling the number of channel uses.
  arXiv  Detail & Related papers  (2021-09-08T12:24:44Z)
• Depth-efficient proofs of quantumness [77.34726150561087]
  A proof of quantumness is a type of challenge-response protocol in which a classical verifier can efficiently certify quantum advantage of an untrusted prover. In this paper, we give two proof of quantumness constructions in which the prover need only perform constant-depth quantum circuits.
  arXiv  Detail & Related papers  (2021-07-05T17:45:41Z)
• 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)
• Fault-tolerant Coding for Quantum Communication [71.206200318454]
  encode and decode circuits to reliably send messages over many uses of a noisy channel. For every quantum channel $T$ and every $eps>0$ there exists a threshold $p(epsilon,T)$ for the gate error probability below which rates larger than $C-epsilon$ are fault-tolerantly achievable. Our results are relevant in communication over large distances, and also on-chip, where distant parts of a quantum computer might need to communicate under higher levels of noise.
  arXiv  Detail & Related papers  (2020-09-15T15:10:50Z)
• Entropic singularities give rise to quantum transmission [3.8073142980733]
  Non-additivity allows quantum devices (aka quantum channels) to send more information than expected. We prove a general theorem concerning positivity of a channel's coherent information. A wide class of zero quantum capacity qubit channels can assist an incomplete erasure channel in sending quantum information.
  arXiv  Detail & Related papers  (2020-03-23T16:32:50Z)

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.