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/0211136 · Journal of Physics A Mathematical and General

A note on quantum entropy inequalities and channel capacities

Heng Fan

Published Nov 18, 2003• 8 citations
arXivHTMLPDF

Abstract

Quantum entropy inequalities are studied. Some quantum entropy inequalities are obtained by several methods. For an entanglement breaking channel, we show that the entanglement-assisted classical capacity is upper bounded by log d . A relationship between entanglement-assisted and one-shot unassisted capacities is obtained. This relationship shows the entanglement-assisted channel capacity is upper bounded by the sum of log d and the one-shot unassisted classical capacity.

DOI
10.1088/0305-4470/36/48/010

Related papers

Remarks on the classical capacity of quantum channel

Alexander Semenovich Holevo

A direct proof of the relation between the one-shot classical capacity and the minimal output entropy for covariant quantum channels is suggested. The structure of covariant channels is described in some detail. A simple proof of a general inequality for entanglement-assisted classical capacity is given.

arXiv:quant-ph/0212025•Dec 4, 2002•50 citations

Entropy Bound for the Classical Capacity of a Quantum Channel Assisted by Classical Feedback

Dawei Ding, Yihui Quek, Peter W. Shor +1 more

We prove that the classical capacity of an arbitrary quantum channel assisted by a free classical feedback channel is bounded from above by the maximum average output entropy of the quantum channel. As a consequence of this bound, we conclude that a classical feedback channel does not improve the classical capacity of a quantum erasure channel, and by taking into account energy constraints, we conclude the same for a pure-loss bosonic channel. The method for establishing the aforementioned entropy bound involves identifying an information measure having two key properties: 1) it does not increase under a one-way local operations and classical communication channel from the receiver to the sender and 2) a quantum channel from sender to receiver cannot increase the information measure by more than the maximum output entropy of the channel. This information measure can be understood as the sum of two terms, with one corresponding to classical correlation and the other to entanglement.

arXiv:1902.02490•IEEE International Symposium on Information Theory (ISIT)•Jul 1, 2019•3 citations

Capacities of Gaussian classical-quantum channels

Alexander Semenovich Holevo

In the present paper we introduce and study Bosonic Gaussian classical-quantum (c-q) channels; the embedding of the classical input into quantum is always possible and therefore the classical entanglement-assisted capacity Ceaunder appropriate input constraint is well defined. We prove a general property of entropy increase for weak complementary channel, that implies the equality C = Cea(where C is the unassisted capacity) for certain class of c-q Gaussian channels under appropriate energy-type constraint. On the other hand, we show by explicit example that the inequality Ceais not unusual for constrained c-q Gaussian channel.

IEEE International Symposium on Information Theory (ISIT)•Jul 1, 2013•0 citations

Gaussian classical-quantum channels: gain of entanglement-assistance

Alexander Semenovich Holevo

In the present paper we introduce and study Bosonic Gaussian classical-quantum (c-q) channels; the embedding of the classical input into quantum is always possible and therefore the classical entanglement-assisted capacity C_{ea} under appropriate input constraint is well defined. We prove a general property of entropy increase for weak complementary channel, that implies the equality C_{ea}=C (where C is the unassisted capacity) for certain class of c-q Gaussian channel under appropriate energy-type constraint. On the other hand, we show by explicit example that the inequality C

arXiv:1211.4774•Nov 20, 2012•2 citations

The quantum capacity with symmetric side channels

Graeme Smith, John A. Smolin, Andreas Winter

We present an upper bound for the quantum channel capacity that is both additive and convex. Our bound can be interpreted as the capacity of a channel for high-fidelity quantum communication when assisted by a family of channels that have no capacity on their own. This family of assistance channels, which we call symmetric side channels, consists of all channels mapping symmetrically to their output and environment. The bound seems to be quite tight, and for degradable quantum channels it coincides with the unassisted channel capacity. Using this symmetric side channel capacity, we find new upper bounds on the capacity of the depolarizing channel. We also briefly indicate an analogous notion for distilling entanglement using the same class of (one-way) channels, yielding one of the few entanglement measures that is monotonic under local operations with oneway classical communication (1-LOCC), but not under the more general class of local operations with classical communication (LOCC).

•Jul 5, 2006•46 citations

Gaussian classical-quantum channels: Gain from entanglement-assistance

Alexander Semenovich Holevo

In the present paper we introduce and study Bosonic Gaussian classical-quantum (c-q) channels; embedding of the classical input in quantum input is always possible, and therefore the classical entanglement-assisted capacity C ea under an appropriate input constraint is well defined. We prove the general property of entropy increase for a weak complementary channel, which implies the equality C = C ea (where C is the unassisted capacity) for a certain class of c-q Gaussian channels under an appropriate energy-type constraint. On the other hand, we show by an explicit example that the inequality C < C ea is not unusual for constrained c-q Gaussian channel.

Problems of Information Transmission•Jan 1, 2014•2 citations
Quantum entropy inequalities are studied. Some quantum entropy inequalities are obtained by several methods. For an entanglement breaking channel, we show that the entanglement-assisted classical capacity is upper bounded by log d . A relationship between entanglement-assisted and one-shot unassisted capacities is obtained. This relationship shows the entanglement-assisted channel capacity is upper bounded by the sum of log d and the one-shot unassisted classical capacity.
We prove that the classical capacity of an arbitrary quantum channel assisted by a free classical feedback channel is bounded from above by the maximum average output entropy of the quantum channel. As a consequence of this bound, we conclude that a classical feedback channel does not improve the classical capacity of a quantum erasure channel, and by taking into account energy constraints, we conclude the same for a pure-loss bosonic channel. The method for establishing the aforementioned entropy bound involves identifying an information measure having two key properties: 1) it does not increase under a one-way local operations and classical communication channel from the receiver to the sender and 2) a quantum channel from sender to receiver cannot increase the information measure by more than the maximum output entropy of the channel. This information measure can be understood as the sum of two terms, with one corresponding to classical correlation and the other to entanglement.
In the present paper we introduce and study Bosonic Gaussian classical-quantum (c-q) channels; the embedding of the classical input into quantum is always possible and therefore the classical entanglement-assisted capacity Ceaunder appropriate input constraint is well defined. We prove a general property of entropy increase for weak complementary channel, that implies the equality C = Cea(where C is the unassisted capacity) for certain class of c-q Gaussian channels under appropriate energy-type constraint. On the other hand, we show by explicit example that the inequality Ceais not unusual for constrained c-q Gaussian channel.
In the present paper we introduce and study Bosonic Gaussian classical-quantum (c-q) channels; the embedding of the classical input into quantum is always possible and therefore the classical entanglement-assisted capacity C_{ea} under appropriate input constraint is well defined. We prove a general property of entropy increase for weak complementary channel, that implies the equality C_{ea}=C (where C is the unassisted capacity) for certain class of c-q Gaussian channel under appropriate energy-type constraint. On the other hand, we show by explicit example that the inequality C
We present an upper bound for the quantum channel capacity that is both additive and convex. Our bound can be interpreted as the capacity of a channel for high-fidelity quantum communication when assisted by a family of channels that have no capacity on their own. This family of assistance channels, which we call symmetric side channels, consists of all channels mapping symmetrically to their output and environment. The bound seems to be quite tight, and for degradable quantum channels it coincides with the unassisted channel capacity. Using this symmetric side channel capacity, we find new upper bounds on the capacity of the depolarizing channel. We also briefly indicate an analogous notion for distilling entanglement using the same class of (one-way) channels, yielding one of the few entanglement measures that is monotonic under local operations with oneway classical communication (1-LOCC), but not under the more general class of local operations with classical communication (LOCC).
In the present paper we introduce and study Bosonic Gaussian classical-quantum (c-q) channels; embedding of the classical input in quantum input is always possible, and therefore the classical entanglement-assisted capacity C ea under an appropriate input constraint is well defined. We prove the general property of entropy increase for a weak complementary channel, which implies the equality C = C ea (where C is the unassisted capacity) for a certain class of c-q Gaussian channels under an appropriate energy-type constraint. On the other hand, we show by an explicit example that the inequality C < C ea is not unusual for constrained c-q Gaussian channel.