Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

On the Capacities of Bipartite Hamiltonians and

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

Published Jan 1, 2003• 0 citations
OpenAlex

Abstract

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.

Related papers

On the capacities of bipartite Hamiltonians and unitary gates

C. H. Bennett, Aram W. Harrow, Debbie Leung +1 more

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.

•Jan 1, 2002•95 citations

On the capacities of bipartite hamiltonians and unitary gates

C.H. Bennett, Aram W. Harrow, Debbie Leung +1 more

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.

arXiv:quant-ph/0205057•IEEE Transactions on Information Theory•Jul 23, 2003•135 citations

Two-way quantum communication channels

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

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.

•Jan 1, 2005•16 citations

TWO-WAY QUANTUM COMMUNICATION CHANNELS

Andrew M. Childs, Debbie Leung, HOI-KWONG LO

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.

arXiv:quant-ph/0506039•International Journal of Quantum Information•Feb 1, 2006•19 citations

Lower bounds for communication capacities of two-qudit unitary operations

Dominic William Berry

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.

arXiv:0704.2066•Physical Review A•Dec 6, 2007•4 citations

Entanglement and secret-key-agreement capacities of bipartite quantum interactions and read-only memory devices

Siddhartha Das, Stefan Bäuml, Mark M. Wilde

A bipartite quantum interaction corresponds to the most general quantum interaction that can occur between two quantum systems in the presence of a bath. In this work, we determine bounds on the capacities of bipartite interactions for entanglement generation and secret-key agreement between two quantum systems. Our upper bound on the entanglement generation capacity of a bipartite quantum interaction is given by a quantity called the bidirectional max-Rains information. Our upper bound on the secret-key-agreement capacity of a bipartite quantum interaction is given by a related quantity called the bidirectional max-relative entropy of entanglement. We also derive tighter upper bounds on the capacities of bipartite interactions obeying certain symmetries. Observing that reading of a memory device is a particular kind of bipartite quantum interaction, we leverage our bounds from the bidirectional setting to deliver bounds on the capacity of a task that we introduce, called private reading of a wiretap memory cell. Given a set of point-to-point quantum wiretap channels, the goal of private reading is for an encoder to form codewords from these channels, in order to establish a secret key with a party who controls one input and one output of the channels, while a passive eavesdropper has access to one output of the channels. We derive both lower and upper bounds on the private reading capacities of a wiretap memory cell. We then extend these results to determine achievable rates for the generation of entanglement between two distant parties who have coherent access to a controlled point-to-point channel, which is a particular kind of bipartite interaction.

arXiv:1712.00827•Physical Review A•Jan 27, 2020•39 citations
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 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 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.
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.
A bipartite quantum interaction corresponds to the most general quantum interaction that can occur between two quantum systems in the presence of a bath. In this work, we determine bounds on the capacities of bipartite interactions for entanglement generation and secret-key agreement between two quantum systems. Our upper bound on the entanglement generation capacity of a bipartite quantum interaction is given by a quantity called the bidirectional max-Rains information. Our upper bound on the secret-key-agreement capacity of a bipartite quantum interaction is given by a related quantity called the bidirectional max-relative entropy of entanglement. We also derive tighter upper bounds on the capacities of bipartite interactions obeying certain symmetries. Observing that reading of a memory device is a particular kind of bipartite quantum interaction, we leverage our bounds from the bidirectional setting to deliver bounds on the capacity of a task that we introduce, called private reading of a wiretap memory cell. Given a set of point-to-point quantum wiretap channels, the goal of private reading is for an encoder to form codewords from these channels, in order to establish a secret key with a party who controls one input and one output of the channels, while a passive eavesdropper has access to one output of the channels. We derive both lower and upper bounds on the private reading capacities of a wiretap memory cell. We then extend these results to determine achievable rates for the generation of entanglement between two distant parties who have coherent access to a controlled point-to-point channel, which is a particular kind of bipartite interaction.