The No-Broadcasting Theorem and its Classical Counterpart

Abstract

Although it is widely accepted that `no-broadcasting' -- the nonclonability of quantum information -- is a fundamental principle of quantum mechanics, an impossibility theorem for the broadcasting of general density matrices has not yet been formulated. In this paper, we present a general proof for the no-broadcasting theorem, which applies to arbitrary density matrices. The proof relies on entropic considerations, and as such can also be directly linked to its classical counterpart, which applies to probabilistic distributions of statistical ensembles.

4 pages

References in corpus (12)

• Quantum Copying: Beyond the No-Cloning Theorem
• Optimal Quantum Cloning Machines
• Noncommuting mixed states cannot be broadcast
• Quantum information can be negative
• Quantum State Disturbance vs. Information Gain: Uncertainty Relations for Quantum Information
• A generalized no-broadcasting theorem
• Inequalities for Quantum Entropy: A Review with Conditions for Equality
• Quantum Approach to a Derivation of the Second Law of Thermodynamics
• No-cloning of Orthogonal States in Composite Systems
• Common origin of no-cloning and no-deleting principles - Conservation of information
• Information theoretic approach to single-particle and two-particle interference in multi-path interferometers
• Local Hidden Variables Underpinning of Entanglement and Teleportation

Cited by in corpus (25)

• Monogamy of quantum correlations - a review
• Quantum Cloning Machines and the Applications
• Masking quantum information is impossible
• Linear Assignment Maps for Correlated System-Environment States
• $k$-Uniform states and quantum information masking
• Complete characterization of qubit masking
• Probabilistic and Approximate Masking of Quantum Information
• Photonic implementation of quantum information masking
• Virtual quantum broadcasting
• Information-theoretic limitations on approximate quantum cloning and broadcasting
• Quantum multipartite maskers vs quantum error-correcting codes
• Quantum information masking of an arbitrary qudit can be realized in multipartite lower dimensional systems
• Activation of Nonmonogamous Multipartite Quantum States
• The masking condition for quantum state in two-dimensional Hilbert space
• Quantum information masking basing on quantum teleportation
• Anyonic quantum multipartite maskers in the Kitaev model
• Restrictions on shareability of classical correlations for random multipartite quantum states
• Orthogonality Broadcasting and Quantum Position Verification
• Masking quantum information encoded in pure and mixed states
• Detection of quantum information masking via machine learning
• Quantum Channel Masking
• No-local-broadcasting theorem for non-signalling behaviours and assemblages
• Entanglement is indispensable for masking arbitrary set of quantum states
• Thermodynamic Constraints on Information Transmission in Quantum Ensembles
• Masking quantum information into a tripartite syste