# Quantum Reverse Shannon Theorem

@article{Bennett2009QuantumRS, title={Quantum Reverse Shannon Theorem}, author={Charles H. Bennett and Igor Devetak and Aram Wettroth Harrow and Peter W. Shor and Andreas J. Winter}, journal={ArXiv}, year={2009}, volume={abs/0912.5537} }

Dual to the usual noisy channel coding problem, where a noisy (classical or quantum) channel is used to simulate a noiseless one, reverse Shannon theorems concern the use of noiseless channels to simulate noisy ones, and more generally the use of one noisy channel to simulate another. For channels of nonzero capacity, this simulation is always possible, but for it to be efficient, auxiliary resources of the proper kind and amount are generally required. In the classical case, shared randomness…

## 60 Citations

Entanglement cost of quantum channels

- Computer Science2012 IEEE International Symposium on Information Theory Proceedings
- 2012

Here, it is shown that any coding scheme that sends quantum information through a quantum channel at a rate larger than the entanglement cost of the channel has an exponentially small fidelity.

Identifying the Information Gain of a Quantum Measurement

- Computer ScienceIEEE Transactions on Information Theory
- 2014

We show that quantum-to-classical channels, i.e., quantum measurements, can be asymptotically simulated by an amount of classical communication equal to the quantum mutual information of the…

Trading classical communication, quantum communication, and entanglement in quantum Shannon theory

- Computer ScienceIEEE Transactions on Information Theory
- 2010

A “unit-resource” capacity theorem is proved that applies to the scenario where only the above three noiseless resources are available for consumption or generation, and the optimal strategy mixes the three fundamental protocols of teleportation, superdense coding, and entanglement distribution.

Strong converse for entanglement-assisted capacity

- Computer Science2014 IEEE International Symposium on Information Theory
- 2014

The proof here demonstrates the extent to which the Arimoto approach can be helpful in proving strong converse theorems, it provides an operational relevance for the multiplicativity result of Devetak et al., and it adds to the growing body of evidence that the sandwiched Rényi relative entropy is the correct quantum generalization of the classical concept for all α > 1.

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

- Computer ScienceIEEE Transactions on Information Theory
- 2016

An upper bound on the feedback-assisted zero-error capacity is presented, motivated by a conjecture originally made by Shannon and proved later by Ahlswede, and it is demonstrated that this bound to have many good properties, including being additive and given by a minimax formula.

Unification of quantum information theory

- Computer Science
- 2006

The mother protocol described here is easily transformed into the so-called "father" protocol, demonstrating that the division of single-sender/single-receiver protocols into two families was unnecessary: all protocols in the family are children of the mother.

Lower Bound on Expected Communication Cost of Quantum Huffman Coding

- Computer ScienceTQC
- 2016

This work considers the case in which the message can have a variable length and the goal is to minimize its expected length, and shows that there is no one-shot scheme which is able to match this rate, even if interactive communication is allowed.

Zero-Error Channel Capacity and Simulation Assisted by Non-Local Correlations

- Computer ScienceIEEE Transactions on Information Theory
- 2011

The theory of zero-error communication is re-examined in the broader setting of using one classical channel to simulate another exactly in the presence of various classes of nonsignalling correlations between sender and receiver, finding that entanglement can assist in zero- error communication.

Second-order coding rates for entanglement-assisted communication

- Computer Science2015 IEEE International Symposium on Information Theory (ISIT)
- 2015

It is proved that the Gaussian approximation for a second-order coding rate is achievable for all quantum channels and defines a quantum generalization of the mutual information variance of a channel in the entanglement-assisted setting.

Quantum Rate-Distortion Coding With Auxiliary Resources

- Computer ScienceIEEE Transactions on Information Theory
- 2013

The result here is that the regularized entanglement of formation characterizes the quantum rate-distortion function, extending earlier work of Devetak and Berger and combining this bound with theEntanglement-assisted bound from their prior work to obtain the best known bounds on the quantum Rate-Distortion function for an isotropic qubit source.