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Monte Carlo simulation of a noisy quantum channel with memory
Ismail Akhalwaya1, Mervlyn Moodley2, Francesco Petruccione2,3
1Department of Pure and Applied Mathematics, University of Johannesburg, Auckland Park Kingsway Campus, Johannesburg 2092, South Africa.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 14, 2015
Summary
This study calculates the classical capacity of quantum channels with correlated noise using a Metropolis-Hastings Monte Carlo method. The findings confirm previous results with higher precision, exploring the impact of memory on channel capacity.
Area of Science:
- Quantum information theory
- Quantum communication
Background:
- Classical capacity is understood for quantum channels with uncorrelated noise.
- Correlated noise in quantum channels presents open questions regarding classical capacity.
Purpose of the Study:
- To calculate the classical capacity of a forgetful quantum channel with correlated noise.
- To explore the effects of memory on channel capacity.
Main Methods:
- Numerical calculation of output entropy using a Metropolis-Hastings Monte Carlo approach.
- Parallel implementation and optimization of the Monte Carlo algorithm.
- Analysis of a forgetful channel constructed by Markov switching between two depolarizing channels.
Main Results:
- The classical capacity of the specified quantum channel was numerically calculated.
- The performance of the Metropolis-Hastings algorithm was studied and optimized.
- Previous results were confirmed to higher precision, with explored effects of memory.
Conclusions:
- The study provides a precise numerical calculation of classical capacity for a quantum channel with correlated noise.
- The Metropolis-Hastings Monte Carlo method is effective for calculating channel entropy and capacity.
- Memory effects in quantum channels significantly influence their classical capacity.
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