Entropic singularities give rise to quantum transmission

Area of Science:

• Quantum Information Science
• Quantum Communication
• Quantum Channel Theory

Background:

• Understanding the limits of quantum information transmission through noisy quantum channels is crucial for quantum technology development.
• Non-additivity, a phenomenon where quantum channels transmit more information than expected, has been primarily observed in highly noisy channels.
• The precise conditions and mechanisms underlying non-additivity, especially in less noisy scenarios, remained largely unexplored.

Purpose of the Study:

• To investigate the occurrence of non-additivity in low-noise quantum channels.
• To develop a general theorem for the positivity of a quantum channel's coherent information.
• To establish a simple dimensional test for a quantum channel's capacity and solve an open problem regarding qubit channels.

Main Methods:

• Introduction and analysis of logarithmic singularities in the von-Neumann entropy.
• Linking these singularities to quantum transmission, specifically to the positivity and non-additivity of coherent information.
• Development of a general theorem on the positivity of coherent information and its corollary for channel capacity testing.

Main Results:

• Demonstrated non-additivity in a simple, low-noise quantum channel, challenging previous assumptions.
• Proved a general theorem concerning the positivity of a channel's coherent information.
• Established a simple dimensional test for quantum channel capacity, characterizing qubit channels with non-zero complementary capacity and identifying channels that can assist in quantum information transmission.

Conclusions:

• Logarithmic singularities in von-Neumann entropy are identified as a key mechanism responsible for the positivity and non-additivity of coherent information.
• The findings provide new insights into the fundamental limits and capabilities of quantum information transmission.
• The developed theoretical framework and tests offer practical tools for characterizing and utilizing quantum channels in future quantum technologies.