Spin chains and channels with memory

Abstract

In most studies of the channel 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. This work has led to speculation that interesting non-analytic behaviour may occur in the capacity. Motivated by these observations, we connect the study of channel capacities under correlated error to the study of critical behaviour in many-body physics. This connection enables us the techniques of many-body physics to either completely solve or understand qualitatively a number of interesting models of correlated error. The models can display analogous behaviour to associated many-body systems, including `phase transitions'.

V2: changes in presentation, some additional comments on generalisation. V3: In accordance with published version, most (but not all) details of proofs now included. A separate paper will shortly be submitted separately with all details and more results

References in corpus (15)

• Mixed State Entanglement and Quantum Error Correction
• "Deconfined" quantum critical points
• Entanglement enhanced information transmission over a quantum channel with correlated noise
• Quantum Channels with Memory
• Quantum phase transitions in matrix product systems
• Experimental demonstration of entanglement-enhanced classical communication over a quantum channel with correlated noise
• Quantum Lost and Found
• Entangled states maximize the two qubit channel capacity for some Pauli channels with memory
• Quantum channels with a finite memory
• Inverting quantum decoherence by classical feedback from the environment
• A dynamical model for 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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• Teleportation-Induced Correlated Quantum Channels
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• Non-Markovian dynamics in two-qubit dephasing channels with an application to superdense coding
• Transmission of classical and quantum information through a quantum memory channel with damping
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• Spin chain model for correlated quantum channels
• Simple upper and lower bounds on the ultimate success probability for discriminating arbitrary finite-dimensional quantum processes
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• Repeatable quantum memory channels
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• New Phase Transitions in Optimal States for Memory Channels
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