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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Evaluating the quantum capacity of bosonic dephasing channel

Li-zhen Jiang, Xiaoyu Chen

Published Oct 6, 2010• 4 citations
Publisher

Abstract

Phase damping is the main decoherence in the evolution of quantum states. In most of the known quantum computing and quantum information processing, devices have amplitude damping times that are around 1-2 orders of magnitude larger than the corresponding dephasing times. For lossy optical fibre as a quantum channel, the quantum capacity is well known. The channel is degradable. We know that dephasing channel is also degradable, thus it can be anticipate that the channel capacity is available. We calculate the capacity with various methods in this paper.

DOI
10.1117/12.870179

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Phase damping is the main decoherence in the evolution of quantum states. In most of the known quantum computing and quantum information processing, devices have amplitude damping times that are around 1-2 orders of magnitude larger than the corresponding dephasing times. For lossy optical fibre as a quantum channel, the quantum capacity is well known. The channel is degradable. We know that dephasing channel is also degradable, thus it can be anticipate that the channel capacity is available. We calculate the capacity with various methods in this paper.
Abstract Evaluating capacities of quantum channels is the first purpose of quantum Shannon theory, but in most cases the task proves to be very hard. Here, we introduce the set of Multi-level Amplitude Damping quantum channels as a generalization of the standard qubit Amplitude Damping Channel to quantum systems of finite dimension d . In the special case of d = 3, by exploiting degradability, data-processing inequalities, and channel isomorphism, we compute the associated quantum and private classical capacities for a rather wide class of maps, extending the set of models whose capacity can be computed known so far. We proceed then to the evaluation of the entanglement assisted quantum and classical capacities.
Traditionally, Quantum Information, and Quantum Communication specifically, have been focused on qubit-based architectures. Recent results, however, highlighted that higher dimensional architectures (qudit-based) may present advantages both in terms of communication and computation; a family of channels called Multi-level Amplitude Damping (MAD) channels, which are a possible qudit generalization of the well known Amplitude Damping Channels, is able to model energy decay processes that may happen during signal transmission. In this work, the Quantum Capacity of 4-dimensional MAD's is studied, relying on a technique for computing it even outside of degradable and antidegradable conditions. We also characterized the complete region of antidegradability and degradability in the parameter space for a generic d-dimensional MAD using both analytical and semi-numerical methods.
The set of Multi-level Amplitude Damping (MAD) quantum channels is introduced as a generalization of the standard qubit Amplitude Damping Channel to quantum systems of finite dimension ddd. In the special case of d=3d=3d=3, by exploiting degradability, data-processing inequalities, and channel isomorphism, we compute the associated quantum and private classical capacities for a rather wide class of maps, extending the set of solvable models known so far. We proceed then to the evaluation of the entanglement assisted, quantum and classical, capacities.
Bosonic qubits encoded in continuous-variable systems provide a promising alternative to two-level qubits for quantum computation and communication. So far, photon loss has been the dominant source of errors in bosonic qubits, but the significant reduction of photon loss in recent bosonic qubit experiments suggests that dephasing errors should also be considered. However, a detailed understanding of the combined photon loss and dephasing channel is lacking. Here, we show that, unlike its constituent parts, the combined loss-dephasing channel is non-degradable, pointing towards a richer structure of this channel. We provide bounds for the capacity of the loss-dephasing channel and use numerical optimization to find optimal single-mode codes for a wide range of error rates.
The primary objective of quantum Shannon theory is to evaluate the capacity of quantum channels. In spite of the existence of rigorous coding theorems that quantify the transmission of information through quantum channels, superadditivity effects limit our understanding of the channel capacities. In this paper, we mainly focus on a family of channels known as multilevel amplitude damping channels. We investigate some of the information capacities of the simplest member of the multilevel amplitude damping channel, a qutrit channel, in the presence of correlations between successive applications of the channel. We find the upper bounds of the single-shot classical capacities and calculate the quantum capacities associated with a specific class of maps after investigating the degradability property of the channels. Additionally, the quantum and classical capacities of the channels have been computed in entanglement-assisted scenarios.