Strong no-go theorem for Gaussian quantum bit commitment

Abstract

Unconditionally secure bit commitment is forbidden by quantum mechanics. We extend this no-go theorem to continuous-variable protocols where both players are restricted to use Gaussian states and operations, which is a reasonable assumption in current-state optical implementations. Our Gaussian no-go theorem also provides a natural counter-example to a conjecture that quantum mechanics can be rederived from the assumption that key distribution is allowed while bit commitment is forbidden in Nature.

4 pages. v2: We discuss the implications of this theorem on the Brassard-Fuchs conjecture and the CBH theorem

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• Non-Gaussian operations on bosonic modes of light: Photon-added Gaussian channels
• Non-Gaussian entangled states and quantum teleportation of Schrödinger-cat states
• Quantum uncertainty relation saturated by the eigenstates of the harmonic oscillator
• Quantum key distribution based on orthogonal states allows secure quantum bit commitment
• Quantum Protocols within Spekkens' Toy Model
• Generation of picosecond pulsed coherent state superpositions
• Estimation of squeezing in a nonlinear quadrature of a mechanical oscillator
• Gaussian intrinsic entanglement
• Quantum bit commitment under Gaussian constraints
• Quantum Hypergraph States in Continuous Variables
• Interconversion of pure Gaussian states using non-Gaussian operations
• Gaussian intrinsic entanglement: An entanglement quantifier based on secret correlations
• Can relativistic bit commitment lead to secure quantum oblivious transfer?
• Unconditionally secure quantum bit commitment based on the uncertainty principle
• An optical implementation of quantum bit commitment using infinite-dimensional systems
• Adaptive Non-Gaussian Quantum State Engineering
• Nonexistence of a universal quantum machine to examine the precision of unknown quantum states
• Detecting nonclassicality and non-Gaussianity of a coherent superposed quantum state
• Cryptanalysis and improvement of Wu-Cai-Wu-Zhang's quantum private comparison protocol