Energy-Constrained LOCC-Assisted Quantum Capacity of the Bosonic Dephasing Channel

Area of Science:

• Quantum Information Theory
• Quantum Communication Channels
• Bosonic Systems

Background:

• The quantum capacity quantifies the maximum rate of high-quality quantum information transmission.
• Entanglement-assisted capacity and squashed entanglement are crucial for understanding channel capabilities.
• Energy constraints on input states add complexity to capacity calculations.

Purpose of the Study:

• To determine the LOCC-assisted quantum capacity of a bosonic dephasing channel under energy constraints.
• To establish and analyze upper and lower bounds for this capacity using squashed entanglement.
• To investigate the tightness of these bounds and the role of the dephasing parameter.

Main Methods:

• Focusing on energy-constrained squashed entanglement as an upper bound.
• Deriving an upper bound for squashed entanglement due to computational challenges.
• Proving the optimality of input states diagonal in the Fock basis.
• Analyzing specific squashing channels to derive explicit bounds.

Main Results:

• An upper bound for the energy-constrained squashed entanglement of the bosonic dephasing channel was derived.
• The optimal input state for this channel was identified as diagonal in the Fock basis.
• Explicit upper and lower bounds for the energy-constrained LOCC-assisted quantum capacity were obtained in terms of quantum capacity and noise parameters.

Conclusions:

• The derived bounds for the energy-constrained LOCC-assisted quantum capacity become tighter as the dephasing parameter increases.
• The study provides a refined understanding of quantum information transmission limits in noisy bosonic channels with energy restrictions.
• The findings contribute to the theoretical framework of quantum channel characterization and resource optimization.