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Journal of Applied Physics

Capacity of multiple-input multiple-output quantum depolarizing channels

Hailin Xiao, Shan Ouyang

Published Aug 1, 2012• 4 citations
Publisher

Abstract

Decoherence-free subspaces (DFS) are to utilize the symmetric properties of the interaction between the system and environment so that they can be tolerant against the effect of decoherence. In this paper, we propose multiple-input multiple-output (MIMO) scheme to drive a finite-dimensional quantum system into DFS. For quantum system, the scheme is not only immune to dephasing but also feasible with currently available technology. Motivated by Shannon mutual information, we derive the capacity of MIMO quantum depolarizing channels.

DOI
10.1063/1.4739764

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Decoherence-free subspaces (DFS) are to utilize the symmetric properties of the interaction between the system and environment so that they can be tolerant against the effect of decoherence. In this paper, we propose multiple-input multiple-output (MIMO) scheme to drive a finite-dimensional quantum system into DFS. For quantum system, the scheme is not only immune to dephasing but also feasible with currently available technology. Motivated by Shannon mutual information, we derive the capacity of MIMO quantum depolarizing channels.
Quantum safety communications is a process of quantum key distribution （QKD）. Current QKD technology restricts transmission to a low bit rate. To improve the QKD bit rate and develope high rate and large capacity, we propose a multiple-input-multiple-output（MIMO） quantum key distribution system. The Wigner operator of multi-photon entangled states in MIMO quantum key distribution channel is presented. As a result, the Wigner function of multi-photon double-model squeezed entangled sates and MIMO quantum key distribution channel capacity are also obtained, which will provide theoretical support and technical basis for developing robust space-time processing algorithm of MIMO quantum safety communications and designing optimum high performance system of MIMO quantum key distribution.
Multiple-input multiple-output (MIMO) communication has significantly enhanced classical telecommunication systems by utilizing multiple transmission paths to improve data rate and reliability. Recent studies suggest that MIMO architectures could similarly benefit quantum communications in lossy environments. In this work, we examine MIMO quantum communication in correlated pure-loss channels, where we model losses as probabilistic erasures. Using symmetric quantum cloning in a 2 × 2 MIMO setup, we derive average fidelity expressions to evaluate the performance under varying correlation strength of losses. Our results indicate that MIMO setups provide fidelity benefits in low-correlation scenarios, but these advantages diminish as correlation increases.
Quantum communication is a process of quantum key distribution （QKD）. Current QKD technology restricts communication to a low bit rate. To improve the QKD bit rate and develop high rate and capacity, we propose a multiple-input-multiple-output quantum key distribution system. However, quantum field itself inevitably involves quantum noise （which is determined by the quantum mechanics ）, which restrains the increase of capacity, and limits space resource utilization, that is, the problem of spatial degrees of freedom arises. The quantumization of the photon field and the electromagnetic wave equation satisfying the Schrdinger equation condition are adopted to investigate the upper bound of the spatial degrees of freedom for MIMO quantum channels, which will provide theoretical support and technical basis for developing robust space time processing algorithm for MIMO quantum communication and designing high performance systems.
We present a scheme to drive a finite-dimensional quantum system into the decoherence-free subspaces (DFS) by Lyapunov control. Control fields are established by Lyapunov function. This proposal works well for both closed and open quantum systems, with replacing the DFS by desired subspaces for closed systems. An example which consists of a four-level system with three degenerate states driven by three lasers is presented to gain further insight on the scheme. Numerical simulations for the dynamics of the system are performed and the results are good.
Abstract Determining whether a noisy quantum channel can be used to reliably transmit quantum information is a challenging problem in quantum information theory. This is because it requires computation of the channel’s coherent information for an unbounded number of copies of the channel. In this paper, we devise an elementary perturbative technique to solve this problem in a wide variety of circumstances. Our analysis reveals that a channel’s ability to transmit information is intimately connected to the relative sizes of its input, output, and environment spaces. We exploit this link to develop easy tests which can be used to detect positivity of quantum channel capacities simply by comparing the channels’ input, output, and environment dimensions. Several noteworthy examples, such as the depolarizing and transpose-depolarizing channels (including the Werner-Holevo channel), dephasing channels, generalized Pauli channels, multi-level amplitude damping channels, and (conjugate) diagonal unitary covariant channels, serve to aptly exhibit the utility of our method. Notably, in all these examples, the coherent information of a single copy of the channel turns out to be positive.