Forgetfulness of continuous Markovian quantum channels

Abstract

The notion of forgetfulness, used in discrete quantum memory channels, is slightly weakened in order to be applied to the case of continuous channels. This is done in the context of quantum memory channels with Markovian noise. As a case study, we apply the notion of weak-forgetfulness to a bosonic memory channel with additive noise. A suitable encoding and decoding unitary transformation allows us to unravel the effects of the memory, hence the channel capacities can be computed using known results from the memoryless setting.

6 pages, 2 figures, comments are welcome. Minor corrections and acknoledgment added

References in corpus (7)

• Entanglement enhanced information transmission over a quantum channel with correlated noise
• Quantum Channels with Memory
• Quantum channels with a finite memory
• Coding Theorem for a Class of Quantum Channels with Long-Term Memory
• Quantum entanglement enhances the capacity of bosonic channels with memory
• Bounds on classical information capacities for a class of quantum memory channels
• Classical capacity of quantum channels with general Markovian correlated noise

Cited by in corpus (8)

• Quantum channels and memory effects
• Classical and quantum capacities of a fully correlated amplitude damping channel
• Capacity of a bosonic memory channel with Gauss-Markov noise
• Memory effects in attenuation and amplification quantum processes
• Gaussian capacity of the quantum bosonic channel with additive correlated Gaussian noise
• On the transitional behavior of quantum Gaussian memory channels
• Classical capacity of Gaussian thermal memory channels
• Removing correlations in signals transmitted over a quantum memory channel