[Paper Review] Entanglement-assisted capacities of time-correlated amplitude-damping channel

Nigum Arshed, A. H. Toor|arXiv (Cornell University)|Jul 20, 2013

Chaos-based Image/Signal Encryption3 references7 citations

TL;DR

This paper investigates entanglement-assisted classical and quantum capacities of a time-correlated amplitude-damping channel, demonstrating that memory suppresses noise and enables non-zero information transmission even when the memoryless version has zero capacity. The capacities increase with memory, reaching a maximum for perfect memory channels.

ABSTRACT

We calculate the information capacities of a time-correlated amplitude-damping channel, provided the sender and receiver share prior entanglement. Our analytical results show that the noisy channel with zero capacity can transmit information if it has finite memory. The capacities increase as the memory increases attaining maximum value for perfect memory channel.

Motivation & Objective

• To analyze how channel memory affects the classical and quantum capacities of an amplitude-damping channel.
• To investigate the role of prior entanglement in enhancing information transmission over noisy quantum channels with memory.
• To determine the behavior of capacities under time-correlated noise, particularly in the limit of increasing memory.
• To derive analytical expressions for entanglement-assisted classical and quantum capacities under correlated noise.
• To examine the trade-off between shared entanglement and classical capacity in limited-entanglement scenarios.

Proposed method

• Model the time-correlated amplitude-damping channel using a Markovian noise process with memory parameter μ.
• Use Kraus operators to describe the channel evolution and compute the resulting density matrices for entangled input states.
• Calculate the entanglement-assisted classical capacity using the quantum mutual information formula: $ C_E = ext{max}_{ ho_s} ig[ S( ho_s) + S( ilde{ ho}) - S_e( ho_s) ig] $.
• Derive the limited-entanglement classical capacity $ C_E^{ ext{lim}} $ as a function of shared entanglement and memory, maximizing over input states and probabilities.
• Compute the quantum capacity via $ Q_E = C_E / 2 $, leveraging the duality of superdense coding and teleportation.
• Analyze the dependence of capacities on channel noise (χ) and memory (μ), including asymptotic limits such as μ = 1 (perfect memory).

Experimental results

Research questions

• RQ1 Can a time-correlated amplitude-damping channel with zero memoryless capacity transmit information when entanglement is shared?
• RQ2 How does increasing channel memory affect the entanglement-assisted classical and quantum capacities?
• RQ3 What is the behavior of the classical capacity when entanglement is limited, and how does it scale with shared entanglement?
• RQ4 Does the presence of memory suppress noise in such channels, enabling non-zero capacity even at high noise levels?
• RQ5 What is the maximum achievable capacity for a perfect memory channel, and under what input states is it attained?

Key findings

• The entanglement-assisted classical capacity $ C_E $ is non-zero even when the memoryless amplitude-damping channel has zero capacity, due to memory-induced noise suppression.
• The capacity increases monotonically with the memory parameter μ, reaching its maximum at μ = 1 (perfect memory channel).
• For maximally entangled input states (θ₁ = θ₂ = π/4), the limited-entanglement capacity $ C_E^{ ext{lim}} $ reduces to the full entanglement-assisted capacity $ C_E $, confirming maximal entanglement maximizes performance.
• The classical capacity for product states $ C_p^2 $ is non-zero for all μ > 0, even at maximum noise (χ = π/2), demonstrating that memory enables transmission where memoryless channels fail.
• The capacity under limited entanglement increases with both the amount of shared entanglement and the memory parameter μ, showing a dual enhancement effect.
• The maximum classical capacity for perfect memory (μ = 1) is achieved when input states are maximally entangled, confirming the optimality of Bell states in this context.