Coherence and asymmetry cannot be broadcast

Abstract

In the presence of conservation laws, superpositions of eigenstates of the corresponding conserved quantities cannot be generated by quantum dynamics. Thus, any such coherence represents a potentially valuable resource of asymmetry, which can be used, for example, to enhance the precision of quantum metrology or to enable state transitions in quantum thermodynamics. Here we ask if such superpositions, already present in a reference system, can be broadcast to other systems, thereby distributing asymmetry indefinitely at the expense of creating correlations. We prove a no-go theorem showing that this is forbidden by quantum mechanics in every finite-dimensional system. In doing so we also answer some open questions in the quantum information literature concerning the sharing of timing information of a clock and the possibility of catalysis in quantum thermodynamics. We also prove that even weaker forms of broadcasting, of which Aberg's `catalytic coherence' is a particular example, can only occur in the presence of infinite-dimensional reference systems. Our results set fundamental limits to the creation and manipulation of quantum coherence and shed light on the possibilities and limitations of quantum reference frames to act catalytically without being degraded.

arXiv comment5+5 pages, 1 figure, close to published version

References in corpus (38)

• Quantum Coherence as a Resource
• Reference frames, superselection rules, and quantum information
• Fundamental limitations for quantum and nano thermodynamics
• Description of quantum coherence in thermodynamic processes requires constraints beyond free energy
• The second laws of quantum thermodynamics
• Noncommuting mixed states cannot be broadcast
• Quantum cloning
• Optimal Cloning of Pure States
• Catalytic Coherence
• No-local-broadcasting theorem for quantum correlations
• Structure of states which satisfy strong subadditivity of quantum entropy with equality
• Entanglement-assisted local manipulation of pure quantum states
• How to quantify coherence: Distinguishing speakable and unspeakable notions
• Extending Noether's theorem by quantifying the asymmetry of quantum states
• The extraction of work from quantum coherence
• Quantum speed limits, coherence and asymmetry
• Measuring the quality of a quantum reference frame: the relative entropy of frameness
• Optimal Cloning of Pure States, Judging Single Clones
• Embezzling Entangled Quantum States
• Gibbs-Preserving Maps outperform Thermal Operations in the quantum regime
• Correlating thermal machines and the second law at the nanoscale
• Degradation of a quantum reference frame
• Creation of superposition of unknown quantum states
• Catalytic coherence transformations
• A no-broadcasting theorem for quantum asymmetry and coherence and a trade-off relation for approximate broadcasting
• Clock-Driven Quantum Thermal Engines
• Fundamental work cost of quantum processes
• Autonomous thermal machine for amplification and control of energetic coherence
• Markovian evolution of quantum coherence under symmetric dynamics
• Extracting work from quantum systems
• The thermodynamic cost of reliability and low temperatures: Tightening Landauer's principle and the Second Law
• The Wigner-Yanase entropy is not subadditive
• Is coherence catalytic?
• Broadcasting Quantum Coherence via Cloning
• Perfect Embezzlement of Entanglement
• Degradation of a quantum directional reference frame as a random walk
• Global and local gauge symmetries beyond Lagrangian formulations
• Decomposition of time-covariant operations on quantum systems with continuous and/or discrete energy spectrum

Cited by in corpus (47)

• An introductory review of the resource theory approach to thermodynamics
• Quantum thermodynamics of correlated-catalytic state conversion at small-scale
• A no-broadcasting theorem for quantum asymmetry and coherence and a trade-off relation for approximate broadcasting
• Catalytic Transformations of Pure Entangled States
• Catalysis of entanglement and other quantum resources
• Quantum reference frame transformations as symmetries and the paradox of the third particle
• Optimizing autonomous thermal machines powered by energetic coherence
• Correlation in Catalysts Enables Arbitrary Manipulation of Quantum Coherence
• Non-Abelian Quantum Transport and Thermosqueezing Effects
• Operational definition of the temperature of a quantum state
• Quantifying quantum coherence of optical cat states
• All states are universal catalysts in quantum thermodynamics
• Enhanced steady-state coherence via repeated system-bath interactions
• Internal quantum reference frames for finite Abelian groups
• Coherence cost for violating conservation laws
• Quantum Thermodynamics and Quantum Coherence Engines
• Fundamental limits on anomalous energy flows in correlated quantum systems
• Amplifying asymmetry with correlated catalysts
• One-shot Coherence Distillation with Catalysts
• Macroscopic Thermodynamic Reversibility in Quantum Many-Body Systems
• Cloning of Quantum Entanglement
• Arbitrary Amplification of Quantum Coherence in Asymptotic and Catalytic Transformation
• Coherence and complementarity based on modified generalized skew information
• Assisted harvesting and catalysis of coherence from scalar fields
• Average skew information-based coherence and its typicality for random quantum states
• Second law of thermodynamics for batteries with vacuum state
• Skew information-based coherence generating power of quantum channels
• Structured quantum collision models: generating coherence with thermal resources
• Geometry of skew information-based quantum coherence
• Coherence manipulation in asymmetry and thermodynamics
• Covariant catalysis requires correlations and good quantum reference frames degrade little
• Entanglement catalysis for quantum states and noisy channels
• Fisher information matrix as a resource measure in resource theory of asymmetry with general connected Lie group symmetry
• Broadcasting of quantum correlations in qubit-qudit systems
• Quantum catalysis in cavity quantum electrodynamics
• Catalytic transformations for thermal operations
• Perspective-neutral approach to quantum frame covariance for general symmetry groups
• Impossibility of creating a superposition of unknown quantum states
• Coherence-variance uncertainty relation and coherence cost for quantum measurement under conservation laws
• Faithful extraction of quantum coherence
• Quantum thermodynamics with coherence: Covariant Gibbs-preserving operation is characterized by the free energy
• Communication with Quantum Catalysts
• Catalytic Activation of Bell Nonlocality
• Finite-size catalysis in quantum resource theories
• Unspeakable Coherence Concentration
• Quantum geometric tensor determines the pure-state i.i.d. conversion rate in the resource theory of asymmetry for any compact Lie group
• Operational Interpretation of Quantum Fisher Information in Quantum Thermodynamics