Many body physics and the capacity of quantum channels with memory

Abstract

In most studies of the capacity of quantum channels, it is assumed that the errors in each use of the channel are independent. However, recent work has begun to investigate the effects of memory or correlations in the error, and has led to suggestions that there can be interesting non-analytic behaviour in the capacity of such channels. In a previous paper we pursued this issue by connecting the study of channel capacities under correlated error to the study of critical behaviour in many-body physics. This connection enables the use of techniques from many-body physics to either completely solve or understand qualitatively a number of interesting models of correlated error with analogous behaviour to associated many-body systems. However, in order for this approach to work rigorously, there are a number of technical properties that need to be established for the lattice systems being considered. In this article we discuss these properties in detail, and establish them for some classes of many-body system.

V1: 17 sides, 5 figures. See posting by M. Hastings 0710.3324 for related results on fermionic systems. V2: 19 sides, 5 figures, extensive changes to improve readability and to correct an imprecise argument. To appear in New J. Phys. Title change due to referee request

References in corpus (19)

• Mixed State Entanglement and Quantum Error Correction
• Entanglement Properties of the Harmonic Chain
• Information transmission through a noisy quantum channel
• Entropy, entanglement, and area: analytical results for harmonic lattice systems
• Entanglement enhanced information transmission over a quantum channel with correlated noise
• Quantum Channels with Memory
• An entanglement-area law for general bosonic harmonic lattice systems
• Experimental demonstration of entanglement-enhanced classical communication over a quantum channel with correlated noise
• Entangled states maximize the two qubit channel capacity for some Pauli channels with memory
• Quantum channels with a finite memory
• Spin chains and channels with memory
• Inverting quantum decoherence by classical feedback from the environment
• Coding Theorem for a Class of Quantum Channels with Long-Term Memory
• A dynamical model for quantum memory channels
• Bounds on classical information capacities for a class of quantum memory channels
• Entanglement enhanced classical capacity of quantum communication channels with correlated noise in arbitrary dimensions
• Entanglement-enhanced classical capacity of two-qubit quantum channels with memory: the exact solution
• A Lower Bound on the Quantum Capacity of Channels with Correlated Errors
• Transition behavior in the capacity of correlated-noisy channels in arbitrary dimensions

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• Master equations for correlated quantum channels
• Non-Markovianity of colored noisy channels
• Enhancement of transmission rates in quantum memory channels with damping
• Classical and quantum capacities of a fully correlated amplitude damping channel
• Memory effects in attenuation and amplification quantum processes
• Teleportation-Induced Correlated Quantum Channels
• Information transmission over an amplitude damping channel with an arbitrary degree of memory
• Quantum Critical Probing and Simulation of Colored Quantum Noise
• Multipartite correlations in quantum collision models
• Transmission of classical and quantum information through a quantum memory channel with damping
• The role of chaos in quantum communication through a dynamical dephasing channel
• Spin chain model for correlated quantum channels
• Quantum Finite-Depth Memory Channels: Case Study