Locking classical information

Abstract

It is known that the maximum classical mutual information that can be achieved between measurements on a pair of quantum systems can drastically underestimate the quantum mutual information between those systems. In this article, we quantify this distinction between classical and quantum information by demonstrating that after removing a logarithmic-sized quantum system from one half of a pair of perfectly correlated bitstrings, even the most sensitive pair of measurements might only yield outcomes essentially independent of each other. This effect is a form of information locking but the definition we use is strictly stronger than those used previously. Moreover, we find that this property is generic, in the sense that it occurs when removing a random subsystem. As such, the effect might be relevant to statistical mechanics or black hole physics. Previous work on information locking had always assumed a uniform message. In this article, we assume only a min-entropy bound on the message and also explore the effect of entanglement. We find that classical information is strongly locked almost until it can be completely decoded. As a cryptographic application of these results, we exhibit a quantum key distribution protocol that is "secure" if the eavesdropper's information about the secret key is measured using the accessible information but in which leakage of even a logarithmic number of key bits compromises the secrecy of all the others.

arXiv comment32 pages, 2 figures

References in corpus (23)

• Introducing Quantum Discord
• Simple Proof of Security of the BB84 Quantum Key Distribution Protocol
• Classical, quantum and total correlations
• Unconditional Security Of Quantum Key Distribution Over Arbitrarily Long Distances
• Black holes as mirrors: quantum information in random subsystems
• Fast Scramblers
• Quantum Data Hiding
• Randomizing quantum states: Constructions and applications
• The mother of all protocols: Restructuring quantum information's family tree
• Continuity of quantum conditional information
• Locking classical correlation in quantum states
• Quantum Darwinism: Entanglement, branches, and the emergent classicality of redundantly stored quantum information
• Distinguishability and Accessible Information in Quantum Theory
• Distinguishability of quantum states under restricted families of measurements with an application to quantum data hiding
• Locking of accessible information and implications for the security of quantum cryptography
• Information locking in black holes
• Possibility, Impossibility and Cheat-Sensitivity of Quantum Bit String Commitment
• Almost Certain Escape from Black Holes
• Entangled black holes as ciphers of hidden information
• Multiparty data hiding of quantum information
• Security of quantum key distribution from generalised entropy accumulation
• Security of quantum bit string commitment depends on the information measure
• Hiding Quantum Data

Cited by in corpus (20)

• Entropic Uncertainty Relations and their Applications
• Quantum-memory-assisted entropic uncertainty relations
• A Quantum Enigma Machine: Experimentally Demonstrating Quantum Data Locking
• From Low-Distortion Norm Embeddings to Explicit Uncertainty Relations and Efficient Information Locking
• Quantum-locked key distribution at nearly the classical capacity rate
• Robust quantum data locking from phase modulation
• Experimental quantum data locking
• Asymptotic entropic uncertainty relations
• Quantum cryptography beyond key distribution: theory and experiment
• Quantum data locking for high-rate private communication
• Identification Via Quantum Channels
• Sampling and scrambling on a chain of superconducting qubits
• Essential lack of security proof in quantum key distribution
• Continuous-variable quantum enigma machines for long-distance key distribution
• Photonic quantum data locking
• On the spectral gap of random quantum channels
• Locally restricted measurements on a multipartite quantum system: data hiding is generic
• Metric and classical fidelity uncertainty relations for random unitary matrices
• Fault tolerant quantum data locking
• Security of Quantum Key Distribution