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arXiv:quant-ph/0307098 · Physical Review A

Broadband channel capacities

Vittorio Giovannetti, Seth Lloyd, Lorenzo Maccone, Peter W. Shor

Published Dec 31, 2003• 61 citations
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Abstract

We study the communication capacities of bosonic broadband channels in the presence of different sources of noise. In particular we analyze lossy channels in the presence of white noise and thermal bath. In this context, we provide a solution for the entanglement-assisted capacity and upper and lower bounds for the classical and quantum capacities.

DOI
10.1103/physreva.68.062323

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We study the communication capacities of bosonic broadband channels in the presence of different sources of noise. In particular we analyze lossy channels in the presence of white noise and thermal bath. In this context, we provide a solution for the entanglement-assisted capacity and upper and lower bounds for the classical and quantum capacities.
Characterizing information-carrying capacities of bosonic communication channels is of significant practical interest. For thermal noise channels, using coherent (product) states yields an achievable rate for classical communication which is conjectured to be optimal. However, it is not known whether coding strategies using entanglement may perform better. Here we discuss upper bounds on classical capacities of thermal noise channels. These imply that coherent-state coding is close to optimal. Our main tool is a quantum analog of the entropy power inequality introduced Shannon. It gives a lower bound on the output von Neumann entropy when two independent signals combine at a beamsplitter.
Abstract: We determine the exact quantum communication and entanglement-distribution capacities of three fundamental noisy bosonic channels, namely thermal loss, thermal amplification and additive Gaussian noise, assisted by operations that completely preserve positive partial transpose (PPT). These operations are more powerful than local operations and classical communication (LOCC), but cannot generate distillable entanglement on their own. For thermal loss, the unconstrained capacity coincides with the Pirandola–Laurenza–Ottaviani–Banchi (PLOB) bound throughout the non-entanglement-breaking regime. The corresponding upper bounds are also attained for thermal amplification and additive noise. We extend these results to energy-constrained communication, establishing exact capacities for all three channels at every prescribed mean input energy. Our results therefore solve a class of noisy bosonic capacity problems under PPT assistance and establish exact benchmarks for determining whether the same communication rates can be achieved using LOCC alone.
The bosonic thermal-loss channel is a fundamental model for quantum communication. This Gaussian channel models the transmission of bosonic systems subject to both loss and thermal noise. It describes many practical systems, including optical fibers, waveguides and free-space links, where background thermal noise is significant. Determining the channel's two-way-assisted quantum capacity, the maximum rate at which quantum information can be transmitted reliably through the channel with two-way classical assistance, remains an open problem. Here, we improve upon the best known lower bound for this capacity for a wide range of channel parameters. We achieve this by combining an improved qubit-bosonic distribution technique with a recently introduced technique for discovering entanglement distillation protocols.
We determine the exact quantum communication and entanglement-distribution capacities of three fundamental bosonic channels, namely thermal loss, thermal amplification and additive Gaussian noise, assisted by operations that completely preserve positive partial transpose (PPT). These operations are more powerful than local operations and classical communication (LOCC), but cannot generate distillable entanglement on their own. For thermal loss, the unconstrained capacity coincides with the Pirandola-Laurenza-Ottaviani-Banchi (PLOB) bound throughout the non-entanglement-breaking regime. The corresponding upper bounds are also attained for thermal amplification and additive noise. We extend these results to energy-constrained communication, establishing exact capacities for all three channels at every prescribed mean input energy. Our results solve a class of bosonic capacity problems under PPT assistance and establish exact benchmarks for determining whether the same communication rates can be achieved via LOCC alone.
Thermal attenuator channels model the decoherence of quantum systems interacting with a thermal bath, e.g., a two-level system subject to thermal noise and an electromagnetic signal traveling through a fiber or in free-space. Hence determining the quantum capacity of these channels is an outstanding open problem for quantum computation and communication. Here we derive several upper bounds on the quantum capacity of qubit and bosonic thermal attenuators. We introduce an extended version of such channels which is degradable and hence has a single-letter quantum capacity, bounding that of the original thermal attenuators. Another bound for bosonic attenuators is given by the bottleneck inequality applied to a particular channel decomposition. With respect to previously known bounds we report better results in a broad range of attenuation and noise: we can now approximate the quantum capacity up to a negligible uncertainty for most practical applications, e.g., for low thermal noise.
We show how to compute or at least to estimate various capacity-related quantities for bosonic Gaussian channels. Among these are the coherent information, the entanglement-assisted classical capacity, the one-shot classical capacity, and a quantity involving the transpose operation, shown to be a general upper bound on the quantum capacity, even allowing for finite errors. All bounds are explicitly evaluated for the case of a one-mode channel with attenuation or amplification and classical noise.