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Two-way quantum communication channels

Andrew M. Childs, Debbie Leung, Hoi‐Kwong Lo

Published Jan 1, 2005• 16 citations
OpenAlex

Abstract

We consider communication between two parties using a bipartite quantum operation, which constitutes the most general quantum mechanical model of two-party communication. We primarily focus on the simultaneous forward and backward communication of classical messages. For the case in which the two parties share unlimited prior entanglement, we give inner and outer bounds on the achievable rate region that generalize classical results due to Shannon. In particular, using a protocol of Bennett, Harrow, Leung, and Smolin, we give a one-shot expression in terms of the Holevo information for the entanglement-assisted one-way capacity of a two-way quantum channel. As applications, we rederive two known additivity results for one-way channel capacities: the entanglement-assisted capacity of a general one-way channel, and the unassisted capacity of an entanglement-breaking one-way channel. 1.

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We consider communication between two parties using a bipartite quantum operation, which constitutes the most general quantum mechanical model of two-party communication. We primarily focus on the simultaneous forward and backward communication of classical messages. For the case in which the two parties share unlimited prior entanglement, we give inner and outer bounds on the achievable rate region that generalize classical results due to Shannon. In particular, using a protocol of Bennett, Harrow, Leung, and Smolin, we give a one-shot expression in terms of the Holevo information for the entanglement-assisted one-way capacity of a two-way quantum channel. As applications, we rederive two known additivity results for one-way channel capacities: the entanglement-assisted capacity of a general one-way channel, and the unassisted capacity of an entanglement-breaking one-way channel. 1.
We consider communication between two parties using a bipartite quantum operation, which constitutes the most general quantum mechanical model of two-party communication. We primarily focus on the simultaneous forward and backward communication of classical messages. For the case in which the two parties share unlimited prior entanglement, we give inner and outer bounds on the achievable rate region that generalize classical results due to Shannon. In particular, using a protocol of Bennett, Harrow, Leung, and Smolin, we give a one-shot expression in terms of the Holevo information for the entanglement-assisted one-way capacity of a two-way quantum channel. As applications, we rederive two known additivity results for one-way channel capacities: the entanglement-assisted capacity of a general one-way channel, and the unassisted capacity of an entanglement-breaking one-way channel.
We consider quantum channels with one sender and two receivers, used in several different ways for the simultaneous transmission of independent messages. We begin by extending the technique of superposition coding to quantum channels with a classical input to give a general achievable region. We also give outer bounds to the capacity regions for various special cases from the classical literature and prove that superposition coding is optimal for a class of channels. We then consider extensions of superposition coding for channels with a quantum input, where some of the messages transmitted are quantum instead of classical, in the sense that the parties establish bipartite or tripartite GHZ entanglement. We conclude by using state merging to give achievable rates for establishing bipartite entanglement between different pair of parties with the assistance of free classical communication.
The entanglement-assisted classical capacity of a noisy quantum channel (C/sub E/) is the amount of information per channel use that can be sent over the channel in the limit of many uses of the channel, assuming that the sender and receiver have access to the resource of shared quantum entanglement, which may be used up by the communication protocol. We show that the capacity C/sub E/ is given by an expression parallel to that for the capacity of a purely classical channel: i.e., the maximum, over channel inputs /spl rho/, of the entropy of the channel input plus the entropy of the channel output minus their joint entropy, the latter being defined as the entropy of an entangled purification of /spl rho/ after half of it has passed through the channel. We calculate entanglement-assisted capacities for two interesting quantum channels, the qubit amplitude damping channel and the bosonic channel with amplification/attenuation and Gaussian noise. We discuss how many independent parameters are required to completely characterize the asymptotic behavior of a general quantum channel, alone or in the presence of ancillary resources such as prior entanglement. In the classical analog of entanglement-assisted communication - communication over a discrete memoryless channel (DMC) between parties who share prior random information - we show that one parameter is sufficient, i.e., that in the presence of prior shared random information, all DMCs of equal capacity can simulate one another with unit asymptotic efficiency.
A unitary interaction coupling two parties enables quantum or classical communication in both the forward and backward directions. Each communication capacity can be thought of as a tradeoff between the achievable rates of specific types of forward and backward communication. Our first result shows that for any bipartite unitary gate, bidirectional coherent classical communication is no more difficult than bidirectional classical communication --- they have the same achievable rate regions. Previously this result was known only for the unidirectional capacities (i.e., the boundaries of the tradeoff). We then relate the tradeoff for two-way coherent communication to the tradeoff for two-way quantum communication and the tradeoff for coherent communication in one direction and quantum communication in the other.
We present a communication protocol for the erasure channel assisted by backward classical communication, which achieves a significantly better rate than the best prior result. In addition, we prove an upper bound for the capacity of the channel. The upper bound is smaller than the capacity of the erasure channel when it is assisted by two-way classical communication. Thus, we prove the separation between quantum capacities assisted by backward classical communication and two-way classical communication.
Quantum mechanics allows operations to be in indefinite causal order, leading to advantages in computational and communication tasks. However, basic notions such as communication capacity have not yet been formalized. In light of this, through the process matrix formalism, we formulate different classical capacities for a bipartite quantum process. For one-way communication, we find that general quantum processes satisfy a generalization of the Holevo bound, i.e., we can send, at most, one bit per qubit. The result also holds for processes with indefinite causal order and with shared entanglement between the sender and the receiver. We further extend known bounds to classical channel capacities, showing that general processes cannot outperform causally separable ones. Next, we study bidirectional communication through a causally separable process. Our result shows that a bidirectional protocol cannot exceed the limit of a one-way communication protocol. Finally, we generalize this result to a multiparty broadcast communication protocol through a definite ordered process.