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

2011/05/24 by Wojciech H. Zurek · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Amplitude #Classical mechanics #Geometry #Mathematical physics #Mathematics #Physics #Probability amplitude #Quantum #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum electrodynamics #Quantum entanglement #Quantum mechanics #Statistical physics #Sum rule in quantum mechanics #Symmetry (geometry) #Theoretical physics #cond-mat.stat-mech #math-ph #math.MP #quant-ph

paper · pdf · doi:10.1103/physrevlett.106.250402

published as Phys.Rev.Lett.106:250402,2011 · Submitted to Physical Review Letters

arxiv created 2011/05/24 · openalex publication_date 2011/06/22 · arxiv updated 2011/07/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Symmetry of entangled states under a swap of outcomes ("envariance") implies their equiprobability and leads to Born's rule pk =| ψk|(2). Here I show the converse: I demonstrate that the amplitude of a state given by a superposition of sequences of events that share the 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.

Citations

• Probabilities from Entanglement, Born's Rule from Envariance
• The Principles of Quantum Mechanics
• The EPR paradox, Bell’s inequality, and the question of locality
• Zur Quantenmechanik der Sto�vorg�nge
• The Quantum Postulate and the Recent Development of Atomic Theory1
• Quantum mechanics and reality
• Quantum probability law from ‘environment-assisted invariance’ in terms of pure-state twin unitaries
• On Zurek?s Derivation of the Born Rule
• "Relative State" Formulation of Quantum Mechanics
• Assumptions that imply quantum dynamics is linear
• Experimental motivation and empirical consistency in minimal no-collapse quantum mechanics
• Decoherence, einselection, and the quantum origins of the classical
• Context, spacetime loops and the interpretation of quantum mechanics
• Quantum entanglement
• Quantum Darwinism

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