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

@article{Ding2019EntropyBF, title={Entropy Bound for the Classical Capacity of a Quantum Channel Assisted by Classical Feedback}, author={Dawei Ding and Yihui Quek and Peter W. Shor and Mark M. Wilde}, journal={2019 IEEE International Symposium on Information Theory (ISIT)}, year={2019}, pages={250-254} }

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…

## Figures from this paper

## 3 Citations

Bounding the forward classical capacity of bipartite quantum channels

- Computer ScienceArXiv
- 2020

The reduced measures are upper bounds on the classical capacity of a point-to-point quantum channel assisted by a classical feedback channel and can be computed by semi-definite programming.

Capacity of Quantum Private Information Retrieval With Multiple Servers

- Computer ScienceIEEE Transactions on Information Theory
- 2021

It is proved that the QPIR capacity with multiple servers is 1 regardless of the number of servers and files and the strong converse bound is derived concisely without using any secrecy condition.

Capacity of Quantum Private Information Retrieval with Multiple Servers

- Computer Science2019 IEEE International Symposium on Information Theory (ISIT)
- 2019

It is proved that the QPIR capacity with multiple servers is 1 regardless of the number of servers and files, and a rate-one protocol which can be implemented by using only two servers is proposed which outperforms its classical counterpart in the sense of capacity, server secrecy, and upload cost.

## References

SHOWING 1-10 OF 21 REFERENCES

The private classical capacity and quantum capacity of a quantum channel

- Physics, Computer ScienceIEEE Transactions on Information Theory
- 2005

Motivated by the work of Schumacher and Westmoreland on quantum privacy and quantum coherence, parallels between private classical information and quantum information are exploited to obtain an expression for the capacity of a quantum channel for generating pure bipartite entanglement.

Entanglement-assisted capacity of a quantum channel and the reverse Shannon theorem

- Computer ScienceIEEE Trans. Inf. Theory
- 2002

In the classical analog of entanglement-assisted communication - communication over a discrete memoryless channel (DMC) between parties who share prior random information - 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.

Strong Converse for the Feedback-Assisted Classical Capacity of Entanglement-Breaking Channels

- Computer ScienceProbl. Inf. Transm.
- 2018

It is proved that a strong converse theorem holds for the classical capacity of an entanglement-breaking channel even when it is assisted by a classical feedback link from the receiver to the transmitter, provided that the transmitter does not use entangled encoding schemes.

Entanglement-Assisted Classical Capacity of Noisy Quantum Channels

- Computer Science, PhysicsPhysical Review Letters
- 1999

It is obtained that exact expressions for the entanglement-assisted capacity of depolarizing and erasure channels in d dimensions are obtained.

Quantum feedback channels

- Computer ScienceIEEE Transactions on Information Theory
- 2004

It is shown to provide no increase in the entanglement-assisted capacities of a memoryless quantum channel, in direct analogy to the classical case, and it is also shown that in various cases of nonassisted capacities, feedback may increase the capacity ofMemoryless quantum channels.

The Squashed Entanglement of a Quantum Channel

- PhysicsIEEE Transactions on Information Theory
- 2014

A new subadditivity inequality for the original squashedEntanglement measure of Christandl and Winter leads to the conclusion that the squashed entanglement of a quantum channel is an additive function of a tensor product of any two quantum channels.

Strong Converse Exponents for a Quantum Channel Discrimination Problem and Quantum-Feedback-Assisted Communication

- Computer ScienceArXiv
- 2014

It is shown that the most general adaptive discrimination strategies provide no asymptotic advantage over non-adaptive tensor-power strategies in this channel discrimination setting, and a strong converse theorem is established for the quantum-feedback-assisted capacity of a channel.

The Quantum Reverse Shannon Theorem and Resource Tradeoffs for Simulating Quantum Channels

- Computer ScienceIEEE Transactions on Information Theory
- 2014

The amounts of communication and auxiliary resources needed in both the classical and quantum cases, the tradeoffs among them, and the loss of simulation efficiency when auxiliary resources are absent or insufficient are established.

Inequalities and separations among assisted capacities of quantum channels.

- HistoryPhysical review letters
- 2006

A hierarchy of capacity inequalities and open questions is given of quantum channels whose classical and quantum capacities, when assisted by classical feedback, exceed their unassisted classical Holevo capacity.

Amortized entanglement of a quantum channel and approximately teleportation-simulable channels

- Computer ScienceArXiv
- 2017

Many of the concepts in the paper are generalized to the setting of general resource theories, defining the amortized resourcefulness of a channel and the notion of ν-freely-simulable channels, connecting these concepts in an operational way as well.