• Corpus ID: 4852725

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}
}
  • P. Hayden, C. King
  • Published 3 September 2004
  • Computer Science
  • Quantum Inf. Comput.
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. 

Environment-assisted quantum-information correction for continuous variables

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

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

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

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

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

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

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

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

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

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

References

SHOWING 1-7 OF 7 REFERENCES

On quantum error-correction by classical feedback in discrete time

This work considers the problem of correcting the errors incurred from sending quantum information through a noisy quantum environment by using classical information obtained from a measurement on the environment, and finds optimal feedback maximizing the channel fidelity.

Information-theoretic approach to quantum error correction and reversible measurement

Quantum operations provide a general description of the state changes allowed by quantum mechanics. The reversal of quantum operations is important for quantum error–correcting codes, teleportation

Coding Theorems for Quantum Channels

An emphasis is made on recent results, such as general quantum coding theorems including cases of infinite (possibly continuous) alphabets and constrained inputs, reliability function for pure state channels and quantum Gaussian channel.

Local distinguishability of multipartite orthogonal quantum states

The protocol outlined is both completely reliable and completely general; it will correctly distinguish any two orthogonal states 100% of the time.

Inversion of quantum jumps in quantum optical systems under continuous observation.

Conditions for invertibility of quantum jumps in systems that decay by emission of quanta into a continuously monitored reservoir are formulated and proposed using techniques from cavity quantum electrodynamics and ion trapping.

Bayesian feedback versus Markovian feedback in a two-level atom

We compare two different approaches to the control of the dynamics of a continuously monitored open quantum system. The first is Markovian feedback, as introduced in quantum optics by Wiseman and

Matrix Analysis " Section 2.2, Exercise 3

  • Matrix Analysis " Section 2.2, Exercise 3
  • 1985