Maximal privacy without coherence

Area of Science:

• Quantum Information Science
• Quantum Communication
• Information Theory

Background:

• Quantum mechanics inherently provides privacy for coherently transmitted quantum states.
• Surprisingly, privacy can be achieved even through noisy quantum channels incapable of reliable quantum information transmission.
• The relationship between a quantum channel's noise level and its capacity for transmitting private classical information requires further investigation.

Purpose of the Study:

• To quantify the amount of private classical information a quantum channel can transmit with limited quantum capacity.
• To explore the fundamental limits of privacy in quantum communication, independent of coherence.
• To investigate channels that exhibit high private capacity relative to their quantum capacity.

Main Methods:

• Introduction of a specific class of quantum channels, denoted as N(d), characterized by their input dimension.
• Analysis of the quantum capacity (Q(N(d))) and private capacity (P(N(d))) for these channels.
• Examination of how these channels relate to the inequality P(N) ≤ (1/2)[log d(A) + Q(N)].

Main Results:

• A class of channels N(d) was identified with quantum capacity Q(N(d)) ≤ 1.
• These channels demonstrate a private capacity P(N(d)) = log d, significantly high relative to their quantum capacity.
• The constructed channels asymptotically saturate the inequality P(N) ≤ (1/2)[log d(A) + Q(N)], highlighting a fundamental trade-off.

Conclusions:

• Quantum channels can be engineered to prioritize private classical information transmission over quantum information transfer.
• The findings reveal the essence of privacy in quantum communication, separable from the requirement of quantum coherence.
• This research provides a new perspective on quantum privacy by studying channels with minimal quantum capacity and maximal private capacity.