Spin operator, Bell nonlocality and Tsirelson bound in quantum-gravity induced minimal-length quantum mechanics

Abstract

Different approaches to quantum gravity converge in predicting the existence of a minimal scale of length. This raises the fundamental question as to whether and how an intrinsic limit to spatial resolution can affect quantum mechanical observables associated to internal degrees of freedom. We answer this question in general terms by showing that the spin operator acquires a momentum-dependent contribution in quantum mechanics equipped with a minimal length. Among other consequences, this modification induces a form of quantum nonlocality stronger than the one arising in ordinary quantum mechanics. In particular, we show that violations of the Bell inequality can exceed the maximum value allowed in ordinary quantum mechanics, the so-called Tsirelson bound, by a positive-valued function of the momentum operator. We introduce possible experimental settings based on neutron interferometry and quantum contextuality, and we provide preliminary estimates on the values of the physical parameters needed for actual laboratory implementations.

References in corpus (39)

• Bell nonlocality
• Hilbert Space Representation of the Minimal Length Uncertainty Relation
• Quantum gravity and minimum length
• Cool horizons for entangled black holes
• Lorentz invariance with an invariant energy scale
• A Generalized Uncertainty Principle in Quantum Gravity
• Generalized Uncertainty Principle in Quantum Gravity from Micro-Black Hole Gedanken Experiment
• A Spin Entanglement Witness for Quantum Gravity
• Information Causality as a Physical Principle
• Gravitationally-induced entanglement between two massive particles is sufficient evidence of quantum effects in gravity
• Quantum Spacetime Phenomenology
• Universality of Quantum Gravity Corrections
• The algebraic structure of the generalized uncertainty principle
• On Gravity and the Uncertainty Principle
• A proposal for testing Quantum Gravity in the lab
• Quantum Mechanics as Quantum Measure Theory
• Quantum-corrected black hole thermodynamics to all orders in the Planck length
• A Higher Order GUP with Minimal Length Uncertainty and Maximal Momentum
• No quantum advantage for nonlocal computation
• String theories with deformed energy momentum relations, and a possible non-tachyonic bosonic string
• Generalized Uncertainty Principle, Classical Mechanics, and General Relativity
• Quantum gravitational decoherence from fluctuating minimal length and deformation parameter at the Planck scale
• Challenge to Macroscopic Probes of Quantum Spacetime Based on Noncommutative Geometry
• Relative locality and the soccer ball problem
• Generalized uncertainty principles and quantum field theory
• The deformation parameter of the generalized uncertainty principle
• Generalized Uncertainty Principle and Angular Momentum
• Spacetime with zero point length is two-dimensional at the Planck scale
• Planck scale Corrections to the Harmonic Oscillator, Coherent and Squeezed States
• On Quantum Gravity Tests with Composite Particles
• Generalized uncertainty principle or curved momentum space?
• On the quasi-position representation in theories with a minimal length
• Unveiling contextual realities by microscopically entangling a neutron
• Quantum-optical tests of Planck-scale physics
• Gravitationally induced uncertainty relations in curved backgrounds
• On the (2+1)-dimensional Dirac equation in a constant magnetic field with a minimal length uncertainty
• A histories perspective on characterising quantum non-locality
• An Operator Analysis of Contextuality Witness Measurements for Multimode-Entangled Single Neutron Interferometry
• Neutron State Entanglement with Overlapping Paths

Cited by in corpus (8)

• 30 years in: Quo vadis generalized uncertainty principle?
• The minimal length: a cut-off in disguise?
• Quantum-spacetime effects on nonrelativistic Schrödinger evolution
• Coherent states for generalized uncertainty relations as Tsallis probability amplitudes: new route to non-extensive thermostatistics
• Momentum gauge fields from curved momentum space through Kaluza-Klein reduction
• Tests of macrorealism in meson oscillation physics
• The shadows of quantum gravity on Bell's inequality
• Finite geometry and black hole stability: Embedding discrete space into classical manifolds