Many-particle interference to test Born's rule

Abstract

Born's rule, one of the cornerstones of quantum mechanics, relates detection probabilities to the modulus square of the wave function. Single-particle interference is accordingly limited to pairs of quantum paths and higher-order interferences are prohibited. Deviations from Born's law have been quantified via the Sorkin parameter which is proportional to the third-order term. We here extend this formalism to many-particle interferences and find that they exhibit a much richer structure. We demonstrate, in particular, that all interference terms of order $(2M+1)$ and greater vanish for $M$ particles. We further introduce a family of many-particle Sorkin parameters and show that they are exponentially more sensitive to deviations from Born's rule than their single-particle counterpart.

References in corpus (35)

• Advances in Quantum Metrology
• Multi-photon entanglement and interferometry
• Models of Wave-function Collapse, Underlying Theories, and Experimental Tests
• Quantum Theory of Probability and Decisions
• Testing the limits of quantum mechanical superpositions
• Quantum Mechanics as Quantum Measure Theory
• Camparison of the Hanbury Brown-Twiss effect for bosons and fermions
• Free fermion antibunching in a degenerate atomic Fermi gas released from an optical lattice
• Ruling Out Multi-Order Interference in Quantum Mechanics
• Environment - Assisted Invariance, Causality, and Probabilities in Quantum Physics
• An atomic Hong-Ou-Mandel experiment
• Distinguishability and many-particle interference
• Improved noninterferometric test of collapse models using ultracold cantilevers
• Non-classical paths in interference experiments
• Interference of Identical Particles from Entanglement to Boson-Sampling
• Observation of genuine three-photon interference
• Quantum Probability from Decision Theory?
• On Zurek's derivation of the Born rule
• Exotic Looped Trajectories of Photons in Three-Slit Interference
• Multiphoton interference in quantum Fourier transform circuits and applications to quantum metrology
• Directional superradiant emission from statistically independent incoherent non-classical and classical sources
• Testing Born's Rule in Quantum Mechanics for Three Mutually Exclusive Events
• Quantum Imaging with Incoherently Scattered Light from a Free-Electron Laser
• Born in an Infinite Universe: a Cosmological Interpretation of Quantum Mechanics
• Violations of the Born rule in cool state-dependent horizons
• The measurement postulates of quantum mechanics are operationally redundant
• Obtaining tight bounds on higher-order interferences with a 5-path interferometer
• Higher-order interference in extensions of quantum theory
• The Born Rule Dies
• Directional Dicke Subradiance with Nonclassical and Classical Light Sources
• High-Contrast Interference of Ultracold Fermions
• Classification of all alternatives to the Born rule in terms of informational properties
• Any modification of the Born rule leads to a violation of the purification and local tomography principles
• Hong-Ou-Mandel interference without beam splitters
• Consistent theory for causal non-locality beyond Born's rule

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• Derive the Born's rule from environment-induced stochastic dynamics of wave-functions in an open system
• Controlling and measuring a superposition of position and momentum
• The inconsistency of linear dynamics and Born's rule