Cryptographic Distinguishability Measures for Quantum Mechanical States

Abstract

This paper, mostly expository in nature, surveys four measures of distinguishability for quantum-mechanical states. This is done from the point of view of the cryptographer with a particular eye on applications in quantum cryptography. Each of the measures considered is rooted in an analogous classical measure of distinguishability for probability distributions: namely, the probability of an identification error, the Kolmogorov distance, the Bhattacharyya coefficient, and the Shannon distinguishability (as defined through mutual information). These measures have a long history of use in statistical pattern recognition and classical cryptography. We obtain several inequalities that relate the quantum distinguishability measures to each other, one of which may be crucial for proving the security of quantum cryptographic key distribution. In another vein, these measures and their connecting inequalities are used to define a single notion of cryptographic exponential indistinguishability for two families of quantum states. This is a tool that may prove useful in the analysis of various quantum cryptographic protocols.

28 pages, 3 figures, minor typographical changes, submitted to IEEE Transactions on Information Theory

References in corpus (4)

• Distinguishability and Accessible Information in Quantum Theory
• The Ithaca Interpretation of Quantum Mechanics
• The Parity Bit in Quantum Cryptography
• Security of Quantum Key Distribution Against All Collective Attacks

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• Quantum conditional mutual information and approximate Markov chains
• General paradigm for distilling classical key from quantum states
• One-shot decoupling
• Simplified instantaneous non-local quantum computation with applications to position-based cryptography
• Renyi generalizations of the conditional quantum mutual information
• Fidelity of recovery, geometric squashed entanglement, and measurement recoverability
• Fundamental limits on quantum dynamics based on entropy change
• From Low-Distortion Norm Embeddings to Explicit Uncertainty Relations and Efficient Information Locking
• Tractable Simulation of Error Correction with Honest Approximations to Realistic Fault Models
• One-shot lossy quantum data compression
• Pretty good measures in quantum information theory
• Parallel approximation of min-max problems
• Superpolynomial speedups based on almost any quantum circuit
• Computational Distinguishability of Quantum Channels
• Performance of polar codes for quantum and private classical communication
• Reality, Causality, and Quantum Theory
• Quantum Commitments from Complexity Assumptions
• Optimal bounds for semi-honest quantum oblivious transfer
• A universal adiabatic quantum query algorithm