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Maximal privacy without coherence.

Debbie Leung1, Ke Li2, Graeme Smith3

  • 1Institute for Quantum Computing, University of Waterloo, Waterloo N2L 3G1, Ontario, Canada.

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This summary is machine-generated.

Quantum channels can transmit private classical information even when they are too noisy for reliable quantum information transfer. This study introduces channels that maximize private capacity while minimizing quantum capacity, revealing insights into quantum privacy.

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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.