Equivalence relations for the classical capacity of single-mode Gaussian quantum channels

Area of Science:

• Quantum Information Theory
• Quantum Communication Channels
• Quantum Optics

Background:

• Gaussian quantum channels are fundamental in quantum information processing.
• Understanding their properties, like classical capacity, is crucial for quantum communication.
• Previous methods for calculating capacity were complex for arbitrary channels.

Purpose of the Study:

• To establish an equivalence between arbitrary single-mode Gaussian quantum channels and a simplified fiducial channel.
• To provide a practical method for calculating the energy-constrained classical capacity of these channels.
• To derive an analytical expression for the Gaussian classical capacity and bound its deviation from the classical capacity.

Main Methods:

• Mathematical proof of channel equivalence using quantum channel theory.
• Characterization of the fiducial channel using standard quantum optical components.
• Analysis of channel additivity properties to derive capacity expressions.
• Derivation of upper bounds for the classical capacity.

Main Results:

• An arbitrary single-mode Gaussian quantum channel is shown to be equivalent to a specific fiducial channel combined with unitary operations.
• The energy-constrained classical capacity can be calculated using this simpler fiducial channel, realizable with beam splitters and squeezers.
• An analytical expression for the Gaussian classical capacity is derived for a large parameter domain.
• It is proven that the classical capacity is at most 1/ln2 bits greater than the Gaussian classical capacity.

Conclusions:

• The equivalence simplifies the study and practical implementation of single-mode Gaussian quantum channels.
• The fiducial channel provides a computationally tractable approach to determining classical capacity.
• The derived analytical expressions and bounds offer valuable insights into the limits of quantum communication over Gaussian channels.