Quantum resource covariance

Abstract

The developments of special relativity and quantum mechanics marked the beginning of the modern physics age. The former has taught us that while space and time are frame dependent notions, there is a quantity -- the space-time interval -- whose value all inertial observers agree upon. This reveals, so to speak, a genuine "fact" of the universe, a relativistic invariant. On the other hand, since the dawn of quantum mechanics, there is no consensus on what the theory is all about. The situation is admittedly subtler: quantum theory is grounded on a complex vector space and the very notions of observer and reference frame are controversial. Here we construct a theoretical framework within which a given combination of quantum resources is shown to be a Galilean invariant. To this end, we postulate a principle of relational symmetry between "the observer" and "the observed" and employ the notion of quantum reference frame. Unitary transformations then follow that allow us to perceive the physical resources seen from the viewpoint of any quantum system. Interestingly, we find that one needs more than quantum coherence and quantum correlations to prove quantum resources covariance. Finally, we show that the notion of physical reality implied by quantum mechanics is not absolute.

arXiv comment8 pages; 1 figure. Accepted for publication in Physical Review A. Comments are welcome!

References in corpus (72)

• Quantum entanglement
• Introducing Quantum Discord
• Quantifying Coherence
• Classical, quantum and total correlations
• Quantum Coherence as a Resource
• Relational Quantum Mechanics
• Quantum Resource Theories
• Measuring Quantum Coherence with Entanglement
• Reference frames, superselection rules, and quantum information
• Test of the Equivalence Principle Using a Rotating Torsion Balance
• On mutually unbiased bases
• Progress in Lunar Laser Ranging Tests of Relativistic Gravity
• Quantum Information and Relativity Theory
• Informational derivation of Quantum Theory
• Observable measure of quantum coherence in finite dimensional systems
• Quantum information can be negative
• Negative entropy and information in quantum mechanics
• The resource theory of quantum reference frames: manipulations and monotones
• The resource theory of informational nonequilibrium in thermodynamics
• Quantum Test of the Universality of Free Fall
• Global Quantum Discord in Multipartite Systems
• Quantum Entanglement of Moving Bodies
• A derivation of quantum theory from physical requirements
• Partial and Complete Observables for Hamiltonian Constrained Systems
• Quantum entropy and special relativity
• Quantum mechanics and the covariance of physical laws in quantum reference frames
• Partial and Complete Observables for Canonical General Relativity
• Quantum state merging and negative information
• Reversible transformations from pure to mixed states, and the unique measure of information
• Quantifying quantum resources with conic programming
• A change of perspective: switching quantum reference frames via a perspective-neutral framework
• All sets of incompatible measurements give an advantage in quantum state discrimination
• Testing the equivalence principle through freely falling quantum objects
• An effective approach to the problem of time
• Effective approach to the problem of time: general features and examples
• Quantum clocks and the temporal localisability of events in the presence of gravitating quantum systems
• Quantum Incompatibility Witnesses
• Quantum theory from questions
• Switching internal times and a new perspective on the 'wave function of the universe'
• Quantum communication using a bounded-size quantum reference frame
• Degradation of a quantum reference frame
• Noise Robustness of the Incompatibility of Quantum Measurements
• Physics within a quantum reference frame
• Comparing the degrees of incompatibility inherent in probabilistic physical theories
• A Complete Resource Theory of Quantum Incompatibility as Quantum Programmability
• Quantum reference frames for general symmetry groups
• Relativistic quantum reference frames: the operational meaning of spin
• Nonclassical correlations from randomly chosen local measurements
• Wave-particle duality: an information-based approach
• Quantum cryptography: key distribution and beyond
• Effective relational dynamics of a nonintegrable cosmological model
• A measure of physical reality
• Dynamics of a Quantum Reference Frame
• Quantum Temporal Superposition: the case of QFT
• Information-reality complementarity: The role of measurements and quantum reference frames
• State discrimination with post-measurement information and incompatibility of quantum measurements
• Toolbox for reconstructing quantum theory from rules on information acquisition
• Quantum reference frames and deformed symmetries
• Unruh effect for detectors in superposition of accelerations
• Nonanomalous measure of realism-based nonlocality
• Kinematics and dynamics in noninertial quantum frames of reference
• Galilei covariance and Einstein's equivalence principle in quantum reference frames
• Nonlocality, quantum correlations, and violations of classical realism in the dynamics of two noninteracting quantum walkers
• Quantum Reference Frames and Their Applications to Thermodynamics
• Hardy's paradox as a demonstration of quantum irrealism
• Resilience of realism-based nonlocality to local disturbance
• Information-based approach towards a unified resource theory
• Tripartite realism-based quantum nonlocality
• Can quantum probes satisfy the weak equivalence principle?
• Quantifying continuous-variable realism
• Quantum Incompatibility of a Physical Context
• Entanglement detection with bounded reference frames

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• Internal quantum reference frames for finite Abelian groups
• The sum of entanglement and subsystem coherence is invariant under quantum reference frame transformations
• Perspective-neutral approach to quantum frame covariance for general symmetry groups
• Predictability as a quantum resource
• Genuine multipartite entanglement and quantum coherence in an electron-positron system: Relativistic covariance
• Quantum observable's reality erasure with spacelike-separated operations
• Searching for a physical description relative to a quantum system
• Correlating Local Quantum Reality with Causally Disconnected Choices
• Two-time quantities as elements of physical reality
• Information leak and incompatibility of physical context: A modified approach