# Correcting quantum channels by measuring the environment

@article{Hayden2005CorrectingQC, title={Correcting quantum channels by measuring the environment}, author={Patrick M. Hayden and Christopher King}, journal={Quantum Inf. Comput.}, year={2005}, volume={5}, pages={156-160} }

The corrected capacity of a quantum channel is defined as the best one-shot capacity that can be obtained by measuring the environment and using the result to correct the output of the channel. It is shown that (i) all qubit channels have corrected capacity log 2, (ii) a product of N qubit channels has corrected capacity N log 2, and (iii) all channels have corrected capacity at least log 2. The question is posed of finding the channel with smallest corrected capacity in any dimension d.

## 38 Citations

### Environment-assisted quantum-information correction for continuous variables

- Computer Science, Physics
- 2010

This article investigates continuous-variable quantum information, and proposes a simple environmental measurement that under certain circumstances fully restores the quantum information of the signal state although the state is not reconstructed with unit fidelity.

### On environment-assisted capacities of a quantum channel

- Computer Science
- 2015

It is shown that entanglement plays a crucial role in this problem of quantum and classical communication, and interesting phenomenon like super-activation, super-additivity and non-zero lower bounds for the classical capacity with conferencing encoders are found.

### Recovering quantum information through partial access to the environment

- Computer Science
- 2011

This work investigates the possibility of correcting errors occurring on a multipartite system through a feedback mechanism that acquires information through partial access to the environment and applies a partial control scheme of this type to the depolarizing and correlated errors.

### On environment-assisted capacities of quantum channels

- Computer Science
- 2005

It is shown that a lower bound on the environment-assisted classical capacity is always half the logarithm of the input space dimension, and a few techniques are developed to prove the existence of channels which meet this lower bound up to terms of much smaller order, even when PPT decoding measurements are allowed.

### Capacities of Gaussian Quantum Channels With Passive Environment Assistance

- Computer ScienceIEEE Transactions on Information Theory
- 2022

An uncertainty-type relation between the classical capacities of the sender and the helper is derived, showing a lower bound on the sum of the two capacities, which is used to lower bound the classical information transmission rate in the scenario of classical communication between sender and helper.

### Classical capacities of quantum channels with environment assistance

- Computer ScienceProbl. Inf. Transm.
- 2016

This work defines and study the classical capacity of a unitary interaction with helper, in two variants: one where the helper can only prepare separable states across many channel uses, and one without this restriction.

### Entanglement and Approximate Quantum Error Correction

- Physics, Philosophy
- 2008

It is shown that, if the loss of entanglement is small, then approximate quantum error correction is possible, thereby generalizing what happens for coherent information. The result is obtained for…

### Quantum Broadcast Channels with Cooperating Decoders: An Information-Theoretic Perspective on Quantum Repeaters

- Computer Science2021 IEEE International Symposium on Information Theory (ISIT)
- 2021

It is shown that as opposed to the MAC with entangled encoders, entanglement between decoders does not increase the classical communication rates for the broadcast dual.

### The Quantum Multiple-Access Channel With Cribbing Encoders

- Computer ScienceIEEE Transactions on Information Theory
- 2022

A MAC model with noisy cribbing is introduced, whereby Transmitter 2 performs a measurement on a system that is entangled with Transmitter 1, and a regularized capacity characterization is established for robust cribbing, i.e. when the cribbing system contains all the information of the channel input.

### Reliably distinguishing states in qutrit channels using one-way LOCC

- Computer Science
- 2005

We present numerical evidence showing that any three-dimensional subspace of C^3 \otimes C^n has an orthonormal basis which can be reliably distinguished using one-way LOCC, where a measurement is…

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