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

arXiv:quant-ph/0209076 · IEEE Transactions on Information Theory

Quantum Feedback Channels

Garry Bowen

Published Sep 28, 2004• 45 citations
arXivHTMLPDF

Abstract

In Shannon information theory, the capacity of a memoryless communication channel cannot be increased by the use of feedback. In quantum information theory, the no-cloning theorem means that noiseless copying and feedback of quantum information cannot be achieved. In this correspondence, quantum feedback is defined as the unlimited use of a noiseless quantum channel from receiver to sender. Given such quantum feedback, it is shown to provide no increase in the entanglement-assisted capacities of a memoryless quantum channel, in direct analogy to the classical case. It is also shown that in various cases of nonassisted capacities, feedback may increase the capacity of memoryless quantum channels.

DOI
10.1109/tit.2004.834749

Related papers

On Feedback and the Classical Capacity of a Noisy Quantum Channel

Garry Bowen, Rajagopal Nagarajan

In Shannon information theory, the capacity of a memoryless communication channel cannot be increased by the use of feedback from receiver to sender. In this correspondence, the use of classical feedback is shown to provide no increase in the unassisted classical capacity of a memoryless quantum channel when feedback is used across nonentangled input states, or when the channel is an entanglement-breaking channel. This gives a generalization of the Shannon theory for certain classes of feedback protocols when transmitting through noisy quantum communication channels.

IEEE Transactions on Information Theory•Jan 1, 2005•19 citations

On Feedback and the Classical Capacity of a Noisy Quantum Channel

Garry Bowen, Rajagopal Nagarajan

In Shannon information theory the capacity of a memoryless communication channel cannot be increased by the use of feedback from receiver to sender. In this paper the use of classical feedback is shown to provide no increase in the unassisted classical capacity of a memoryless quantum channel when feedback is used across non-entangled input states, or when the channel is an entanglement--breaking channel. This gives a generalization of the Shannon theory for certain classes of feedback protocols when transmitting through noisy quantum communication channels.

arXiv:quant-ph/0305176•May 29, 2003•4 citations

On feedback and the classical capacity of a noisy quantum channel

Garry Bowen, Rajagopal Nagarajan

In Shannon information theory the capacity of a memoryless communication channel cannot be increased by the use of feedback. The use of classical feedback is shown to provide no increase in the classical capacity of a memoryless quantum channel when feedback is used across nonentangled input states, or when the channel is an entanglement-breaking channel

IEEE International Symposium on Information Theory (ISIT)•Dec 23, 2004•1 citation

Classical feedback for quantum channels

Andrew Skeen

We investigate whether the use of a noiseless, classical feedback channel will increase the capacity of a quantum discrete memoryless channel to transmit classical information. This problem has been previously analyzed by Bowen and Nagarajan for the case of protocols restricted to product input states. They showed that feedback did not increase the information capacity. In this paper we introduce a quantum analogue of classical causality and prove a capacity theorem (in regularized form) for the transmission of classical information.

arXiv:quant-ph/0409207•Sep 29, 2004•0 citations

On Zero-Error Communication via Quantum Channels in the Presence of Noiseless Feedback

Runyao Duan, Simone Severini B, Andreas Winter

We initiate the study of zero-error communication via quantum channels when the receiver and the sender have at their disposal a noiseless feedback channel of unlimited quantum capacity, generalizing Shannon's zero-error communication theory with instantaneous feedback. We first show that this capacity is only a function of the linear span of Choi-Kraus operators of the channel, which generalizes the bipartite equivocation graph of a classical channel, and which we dub non-commutative bipartite graph. Then, we go on to show that the feedback-assisted capacity is non-zero (allowing for a constant amount of activating noiseless communication) if and only if the non-commutative bipartite graph is non-trivial, and give a number of equivalent characterizations. This result involves a far-reaching extension of the conclusive exclusion of quantum states. We then present an upper bound on the feedback-assisted zero-error capacity, motivated by a conjecture originally made by Shannon and proved later by Ahlswede. We demonstrate that this bound to have many good properties, including being additive and given by a minimax formula. We also prove a coding theorem showing that this quantity is the entanglement-assisted capacity against an adversarially chosen channel from the set of all channels with the same Choi-Kraus span, which can also be interpreted as the feedback-assisted unambiguous capacity. The proof relies on a generalization of the Postselection Lemma (de Finetti reduction) that allows to reflect additional constraints, and which we believe to be of independent interest. This capacity is a relaxation of the feedback-assisted zero-error capacity; however, we have to leave open the question of whether they coincide in general. We illustrate our ideas with a number of examples, including classical-quantum channels and Weyl diagonal channels, and close with an extensive discussion of open questions.

arXiv:1502.02987•IEEE Transactions on Information Theory•May 3, 2016•19 citations

Some Effects of Classical Feedback on the Classical Capacity of a Memoryless Quantum Channel

G.V. Klimovitch

Classical feedback is defined here as the knowledge by the transmitter of the quantum state of the qubit received by the receiver. Such classical feedback doubles capacities of certain memoryless quantum channels without preexisting entanglement between transmitter and receiver. The increase in capacity, which is absent on classical memoryless channels, occurs because we can transform an entangled qubit pair into any other entangled state by applying a unitary operator to only one of the qubits.

arXiv:quant-ph/0403211•Mar 29, 2004•0 citations
In Shannon information theory, the capacity of a memoryless communication channel cannot be increased by the use of feedback. In quantum information theory, the no-cloning theorem means that noiseless copying and feedback of quantum information cannot be achieved. In this correspondence, quantum feedback is defined as the unlimited use of a noiseless quantum channel from receiver to sender. Given such quantum feedback, it is shown to provide no increase in the entanglement-assisted capacities of a memoryless quantum channel, in direct analogy to the classical case. It is also shown that in various cases of nonassisted capacities, feedback may increase the capacity of memoryless quantum channels.
In Shannon information theory, the capacity of a memoryless communication channel cannot be increased by the use of feedback from receiver to sender. In this correspondence, the use of classical feedback is shown to provide no increase in the unassisted classical capacity of a memoryless quantum channel when feedback is used across nonentangled input states, or when the channel is an entanglement-breaking channel. This gives a generalization of the Shannon theory for certain classes of feedback protocols when transmitting through noisy quantum communication channels.
In Shannon information theory the capacity of a memoryless communication channel cannot be increased by the use of feedback from receiver to sender. In this paper the use of classical feedback is shown to provide no increase in the unassisted classical capacity of a memoryless quantum channel when feedback is used across non-entangled input states, or when the channel is an entanglement--breaking channel. This gives a generalization of the Shannon theory for certain classes of feedback protocols when transmitting through noisy quantum communication channels.
We investigate whether the use of a noiseless, classical feedback channel will increase the capacity of a quantum discrete memoryless channel to transmit classical information. This problem has been previously analyzed by Bowen and Nagarajan for the case of protocols restricted to product input states. They showed that feedback did not increase the information capacity. In this paper we introduce a quantum analogue of classical causality and prove a capacity theorem (in regularized form) for the transmission of classical information.
We initiate the study of zero-error communication via quantum channels when the receiver and the sender have at their disposal a noiseless feedback channel of unlimited quantum capacity, generalizing Shannon's zero-error communication theory with instantaneous feedback. We first show that this capacity is only a function of the linear span of Choi-Kraus operators of the channel, which generalizes the bipartite equivocation graph of a classical channel, and which we dub non-commutative bipartite graph. Then, we go on to show that the feedback-assisted capacity is non-zero (allowing for a constant amount of activating noiseless communication) if and only if the non-commutative bipartite graph is non-trivial, and give a number of equivalent characterizations. This result involves a far-reaching extension of the conclusive exclusion of quantum states. We then present an upper bound on the feedback-assisted zero-error capacity, motivated by a conjecture originally made by Shannon and proved later by Ahlswede. We demonstrate that this bound to have many good properties, including being additive and given by a minimax formula. We also prove a coding theorem showing that this quantity is the entanglement-assisted capacity against an adversarially chosen channel from the set of all channels with the same Choi-Kraus span, which can also be interpreted as the feedback-assisted unambiguous capacity. The proof relies on a generalization of the Postselection Lemma (de Finetti reduction) that allows to reflect additional constraints, and which we believe to be of independent interest. This capacity is a relaxation of the feedback-assisted zero-error capacity; however, we have to leave open the question of whether they coincide in general. We illustrate our ideas with a number of examples, including classical-quantum channels and Weyl diagonal channels, and close with an extensive discussion of open questions.