Maximal Privacy Without Coherence

Abstract

Privacy lies at the fundament of quantum mechanics. A coherently transmitted quantum state is inherently private. Remarkably, coherent quantum communication is not a prerequisite for privacy: there are quantum channels that are too noisy to transmit any quantum information reliably that can nevertheless send private classical information. Here, we ask how much private classical information a channel can transmit if it has little quantum capacity. We present a class of channels N_d with input dimension d^2, quantum capacity Q(N_d) <= 1, and private capacity P(N_d) = log d. These channels asymptotically saturate an interesting inequality P(N) <= (log d_A + Q(N))/2 for any channel N with input dimension d_A, and capture the essence of privacy stripped of the confounding influence of coherence.

6 pages. Proof of Eq.(13) slightly revised

References in corpus (5)

• A Sharp Fannes-type Inequality for the von Neumann Entropy
• The private classical capacity with a symmetric side channel and its application to quantum cryptography
• Extensive nonadditivity of privacy
• Can non-private channels transmit quantum information?
• Highly Entangled States With Almost No Secrecy

Cited by in corpus (15)

• Semidefinite programming strong converse bounds for classical capacity
• Dephrasure channel and superadditivity of coherent information
• Extracting quantum coherence via steering
• Quantum and private capacities of low-noise channels
• Generic nonadditivity of quantum capacity in simple channels
• The platypus of the quantum channel zoo
• Bounding quantum capacities via partial orders and complementarity
• Quantum resource theory of coding for error correction
• Maximum privacy without coherence, zero-error
• Hybrid quantum network design against unauthorized secret-key generation, and its memory cost
• Allowing leakage can increase quantum transmission
• Noise is resource-contextual in quantum communication
• Information storage and transmission under Markovian noise
• An additive refinement of quantum channel capacities
• Simultaneous superadditivity of the direct and complementary channel capacities