Entanglement Symmetry, Amplitudes, and Probabilities: Inverting Born's Rule

Abstract

Symmetry of entangled states under a swap of outcomes ("envariance") implies their equiprobability, and leads to Born's rule. Here I show that the amplitude of a state given by a superposition of sequences of events that share same total count (e.g., n detections of 0 and m of 1 in a spin 1/2 measurement) is proportional to the square root of the fraction - square root of the relative frequency - of all the equiprobable sequences of 0's and 1's with that n and m.

arXiv commentSubmitted to Physical Review Letters

References in corpus (16)

• Quantum entanglement
• Decoherence, einselection, and the quantum origins of the classical
• Decoherence, the measurement problem, and interpretations of quantum mechanics
• Quantum Darwinism
• Probabilities from Entanglement, Born's Rule from Envariance
• Environment - Assisted Invariance, Causality, and Probabilities in Quantum Physics
• Quantum origin of quantum jumps: Breaking of unitary symmetry induced by information transfer and the transition from quantum to classical
• On Zurek's derivation of the Born rule
• Experimental motivation and empirical consistency in minimal no-collapse quantum mechanics
• Assumptions that imply quantum dynamics is linear
• Macroscopic Observables
• The EPR paradox, Bell's inequality, and the question of locality
• Discreteness and the origin of probability in quantum mechanics
• Complete "Born's rule" from "environment-assisted invariance" in terms of pure-state twin unitaries
• Context, spacetime loops, and the interpretation of quantum mechanics
• Consistent histories of systems and measurements in spacetime

Cited by in corpus (18)

• Quantum Darwinism, Classical Reality, and the Randomness of Quantum Jumps
• Quantum discord cannot be shared
• The Objective Past of a Quantum Universe: Redundant Records of Consistent Histories
• Quantum Theory of the Classical: Einselection, Envariance, Quantum Darwinism and Extantons
• Quantum Theory of the Classical: Quantum Jumps, Born's Rule, and Objective Classical Reality via Quantum Darwinism
• Origin of probabilities and their application to the multiverse
• Demonstration of entanglement assisted invariance on IBM's Quantum Experience
• Wave-packet collapse and the core quantum postulates: Discreteness of quantum jumps from unitarity, repeatability, and actionable information
• Eliminating Ensembles from Equilibrium Statistical Physics: Maxwell's Demon, Szilard's Engine, and Thermodynamics via Entanglement
• Foundations of statistical mechanics from symmetries of entanglement
• Quantum probabilities from quantum entanglement: Experimentally unpacking the Born rule
• Born Rule and Noncontextual Probability
• Quantum Collapse and the Second Law of Thermodynamics
• Consistent theory for causal non-locality beyond Born's rule
• Derivation of the Born rule from the unitarity of quantum evolution
• The Born Rule and Time-Reversal Symmetry of Quantum Equations of Motion
• No-go theorem for environment-assisted invariance in non-unitary dynamics
• Modelling of consciousness and interpretation of quantum mechanics