Greenberger-Horne-Zeilinger test for multi-dimension and arbitrary time nodes entangled histories

Abstract

Based on the framework of consistent history theory, the quantum entangled history was proposed in 2015 and experimentally verified through temporal Greenberger-Horne-Zeilinger (GHZ) test with $3$ time nodes in 2016. In this paper, we extend the temporal GHZ test to arbitrary time nodes and even system dimensions. Then, we define a witness to distinguish between the quantum entangled histories and the classical histories. The minimums of the witness for the classical histories are calculated for arbitrary number of time nodes and the system dimensions $2$ and $\infty$. It is found that the minimums of the witness for the classical histories is always larger than the quantum entangled histories minimum $-1$. Only when both the number of time nodes and system dimensions approach to infinity, the minimum of the witness for classical and quantum entangled histories are identical.

16 pages, 1 figure. GHZ test for entangled histories with dimensions larger than 2 is added. The title is changed accordingly. Accepted for Science Bulletin

References in corpus (20)

• Experimental loophole-free violation of a Bell inequality using entangled electron spins separated by 1.3 km
• Significant-loophole-free test of Bell's theorem with entangled photons
• A strong loophole-free test of local realism
• Leggett-Garg Inequalities
• Experimental Test of Quantum Jarzynski Equality with a Trapped Ion System
• Large quantum superpositions of a levitated nanodiamond through spin-optomechanical coupling
• Violation of a temporal Bell inequality for single spins in solid by over 50 standard deviations
• Quantum superposition, entanglement, and state teleportation of a microorganism on an electromechanical oscillator
• Quantum correlations in the temporal CHSH scenario
• Greenberger-Horne-Zeilinger paradoxes for many qudits
• Quantum Entanglement in Time
• Greenberger-Horne-Zeilinger paradoxes from qudit graph states
• Entangled Histories
• Rotational covariance and GHZ contradictions for three or more particles of any dimension
• Greenberger-Horne-Zeilinger theorem for N qudits
• Multi-setting Greenberger-Horne-Zeilinger theorem
• Experimental Test of Entangled Histories
• Experimental Test of Irreducible Four-Qubit Greenberger-Horne-Zeilinger Paradox
• Bell Tests for Histories
• Temporal Observables and Entangled Histories

Cited by in corpus (2)

• Experimentally demonstrating indefinite causal order algorithms to solve the generalized Deutsch's problem
• Entanglement measures for two-particle quantum histories