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On the capacities of bipartite Hamiltonians and unitary gates

C. H. Bennett, Aram W. Harrow, Debbie Leung, John A. Smolin

Published Jan 1, 2002• 95 citations
OpenAlex

Abstract

We consider interactions as bidirectional channels, and investigate the capacities for interaction Hamiltonians and nonlocal unitary gates to generate entanglement and transmit classical information. We give analytic expressions for the entanglement generating capacity and entanglement-assisted 1-way classical communication capacity of interactions, and show that these quantities are additive, so that the asymptotic capacities equal the corresponding 1-shot capacities. We give bounds on other capacities and discuss their additivity, along with other open questions.

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We consider interactions as bidirectional channels, and investigate the capacities for interaction Hamiltonians and nonlocal unitary gates to generate entanglement and transmit classical information. We give analytic expressions for the entanglement generating capacity and entanglement-assisted 1-way classical communication capacity of interactions, and show that these quantities are additive, so that the asymptotic capacities equal the corresponding 1-shot capacities. We give bounds on other capacities and discuss their additivity, along with other open questions.
We consider interactions as bidirectional channels. We investigate the capacities for interaction Hamiltonians and nonlocal unitary gates to generate entanglement and transmit classical information. We give analytic expressions for the entanglement generating capacity and entanglement-assisted one-way classical communication capacity of interactions, and show that these quantities are additive, so that the asymptotic capacities equal the corresponding 1-shot capacities. We give general bounds on other capacities, discuss some examples, and conclude with some open questions.
We consider interactions as bidirectional channels. We investigate the capacities for interaction Hamiltonians and non- local unitary gates to generate entanglement and transmit clas- sical information. We give analytic expressions for the entangle- ment generating capacity and entanglement-assisted one-way clas- sical communication capacity of interactions, and show that these quantities are additive, so that the asymptotic capacities equal the corresponding -shot capacities. We give general bounds on other capacities, discuss some examples, and conclude with some open questions.
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 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.
It is known that entangling capacities of bipartite unitary operations may be used to place upper bounds on communication capacities. Here we present alternative definitions of entangling capacities for unitary operations and use them to place lower bounds on the communication capacities of arbitrary bipartite unitaries. Thus entangling capacities may be used to place both upper and lower bounds on the communication capacities for arbitrary bipartite unitaries, allowing them to be more easily estimated. We elucidate the connection between these results and the standard formula for the entanglement assisted capacity of channels. In addition, we present more general methods for producing ensembles for communication from initial states for entanglement creation, and thereby derive sufficient conditions such that the usual forms of entangling capacity provide lower bounds on communication capacities.
Two-qubit operations may be characterized by their capacities for communication, both with and without free entanglement, and their capacity for creating entanglement. We establish a set of inequalities that give an ordering to the capacities of two-qubit unitary operations. Specifically, we show that the capacities for entanglement creation and bidirectional communication without entanglement assistance are at least as great as half the bidirectional communication capacity with entanglement assistance. In addition, we show that the bidirectional communication that can be performed using an ensemble may be increased via a two-qubit unitary operation by twice the operation's capacity for entanglement.