# Reversibility conditions for quantum channels and their applications

@article{Shirokov2012ReversibilityCF, title={Reversibility conditions for quantum channels and their applications}, author={Maksim E. Shirokov}, journal={arXiv: Quantum Physics}, year={2012} }

A necessary condition for reversibility (sufficiency) of a quantum channel with respect to complete families of states with bounded rank is obtained. A full description (up to isometrical equivalence) of all quantum channels reversible with respect to orthogonal and nonorthogonal complete families of pure states is given. Some applications in quantum information theory are considered.
The main results can be formulated in terms of the operator algebras theory (as conditions for reversibility… Expand

#### 9 Citations

Reversibility of a quantum channel: general conditions and their applications to Bosonic linear channels

- Mathematics, Physics
- 2012

The method of complementary channel for analysis of reversibility (sufficiency) of a quantum channel with respect to families of input states (pure states for the most part) are considered and… Expand

On the entanglement-assisted classical capacity of infinite-dimensional quantum channels

- Mathematics, Physics
- 2012

The coding theorem for the entanglement-assisted communication via infinite-dimensional quantum channel with linear constraint is extended to a natural degree of generality. Relations between the… Expand

Criteria for equality in two entropic inequalities

- Mathematics
- 2014

We obtain a simple criterion for local equality between the con- strained Holevo capacity and the quantum mutual information of a quan- tum channel. This shows that the set of all states for which… Expand

On the Energy-Constrained Diamond Norm and Its Application in Quantum Information Theory

- Mathematics, Computer Science
- Probl. Inf. Transm.
- 2018

It is proved that any norm from this family generates strong (pointwise) convergence on the set of all quantum channels, which is more adequate for describing variations of infinite-dimensional channels than the diamond norm topology. Expand

A criterion for coincidence of the entanglement-assisted classical capacity and the Holevo capacity of a quantum channel

- Mathematics, Physics
- 2012

It is easy to show coincidence of the entanglement-assisted classical capacity and the Holevo capacity for any c-q channel between finite dimensional quantum systems. In this paper we prove the… Expand

Energy-Constrained Private and Quantum Capacities of Quantum Channels

- Computer Science, Physics
- IEEE Transactions on Information Theory
- 2018

It is shown how the regularized, energy-constrained coherent information is equal to the capacity for the first two tasks and is an achievable rate for the latter two tasks, whenever the energy observable satisfies the Gibbs condition of having a well-defined thermal state for all temperatures and the channel satisfies a finite output-entropy condition. Expand

Критерии равенства в двух энтропийных неравенствах@@@Criteria for equality in two entropic inequalities

- Physics, Mathematics
- 2014

A simple criterion for local equality between the constrained Holevo capacity and the quantum mutual information of a quantum channel is obtained. It implies that the set of all states for which this… Expand

Physical Implementability of Quantum Maps and Its Application in Error Mitigation

- Computer Science
- ArXiv
- 2020

This work decomposes a target quantum map into a linear combination of physically implementable operations and introduces the physical implementability measure as the least amount of negative portion that the quasiprobability must pertain, which is efficiently computable by semidefinite programs and proves several properties of this measure, such as faithfulness, additivity, and unitary invariance. Expand

Physical Implementability of Linear Maps and Its Application in Error Mitigation

- Physics, Computer Science
- 2020

This work decomposes a target linear map into a linear combination of physically implementable operations and introduces the physical implementability measure as the least amount of negative portion that the quasiprobability must pertain, which directly quantifies the cost of simulating a given map using physical implementable quantum operations. Expand

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