Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Mathematical Techniques and Computational Mathematics

Maximal Violation of CHSH Inequality in a One-dimensional Quantum Harmonic Oscillator

Published Apr 22, 2024• 0 citations
Publisher

Abstract

It is shown that any eigenstate of quantum harmonic oscillator and the coherent state and the squeezed state displays quantum contextuality by the violation of a noncontextuality inequality
DOI
10.33140/jmtcm.03.04.06

Related papers

Quantum contextuality in a one-dimensional quantum harmonic oscillator

Hong-Yi Su, Jing‐Ling Chen, Chunfeng Wu +2 more

We investigate quantum contextuality of one-dimensional quantum harmonic oscillator. Through the violation of a noncontextuality inequality, any eigenstate of quantum harmonic oscillator and some typical continuous-variable states, such as the coherent state and the squeezed state, exhibit quantum contextuality. The state-independent demonstration of quantum contextuality in continuous-variable states is also demonstrated.

Physical Review A•May 29, 2012•10 citations

Investigation of quantum contextuality in a harmonic oscillator using an NMR quantum simulator

Hemant Katiyar, C. S. Sudheer Kumar, T. S. Mahesh

Often physical potentials are approximated to a harmonic potential so as to analytically solve the system dynamics. For example, the quantized electromagnetic field used to manipulate a qubit in cavity quantum electrodynamics, can be described using quantum harmonic oscillator (QHO). Hence it is important to know when a QHO behaves quantum mechanically and when classically. In this work, we encode the four lower-most eigenstates of the one dimensional-QHO(1D-QHO) onto the four Zeeman product states of a pair of spin-1/2 nuclei. Using the techniques of nuclear magnetic resonance (NMR) quantum information processing (QIP), we then demonstrate the strong violation of noncontextual hidden variable (NCHV) inequality, under specific experimental arrangements. We also experimentally investigate the weak violation of NCHV inequality by thermal equilibrium states in nuclear spins, thereby assessing their quantumness.

•Mar 19, 2015•1 citation

NMR investigation of contextuality in a quantum harmonic oscillator via pseudospin mapping

Hemant Katiyar, C. S. Sudheer Kumar, T. S. Mahesh

Physical potentials are routinely approximated to harmonic potentials. Hence it is important to know when a quantum harmonic oscillator (QHO) behaves quantum mechanically and when classically. Recently Su et al. ( Phys. Rev. A , 85 (2012) 052126) have theoretically shown that QHO exhibits quantum contextuality (QC) for a certain set of pseudospin observables. Here we encode the four eigenstates of a QHO onto four Zeeman product states of a pair of spin-(1/2) nuclei. Using the techniques of NMR quantum information processing, we then demonstrate the violation of both state-dependent and state-independent inequalities arising from the noncontextual hidden variable model.

arXiv:1503.05883•Europhysics Letters (EPL)•Jan 1, 2016•4 citations

Experimentally Testable State-Independent Violation of Bell-Type Inequalities for Quantum Contextuality

Adán Cabello

There are experimentally testable correlation Bell inequalities which are satisfied by any noncontextual theory but are violated by any quantum state. We discuss how to test one of them.

International Conference on Quantum, Nano and Micro Technologies (ICQNM)•Feb 1, 2009•0 citations

Experimental Test of High-Dimensional Quantum Contextuality Based on Contextuality Concentration

Zhenghao Liu, Hui-Xian Meng, Zhen‐Peng Xu +6 more

Contextuality is a distinctive feature of quantum theory and a fundamental resource for quantum computation. However, existing examples of contextuality in high-dimensional systems lack the necessary robustness required in experiments. Here, we address this problem by identifying a family of noncontextuality inequalities whose maximum quantum violation grows with the dimension of the system. At first glance, this contextuality is the single-system version of multipartite Bell nonlocality taken to an extreme form. What is interesting is that the single-system version achieves the same degree of contextuality but uses a Hilbert space of lower dimension. That is, contextuality "concentrates" as the degree of contextuality per dimension increases. We show the practicality of this result by presenting an experimental test of contextuality in a seven-dimensional system. By simulating sequences of quantum ideal measurements with destructive measurements and repreparation in an all-optical setup, we report a violation of 68.7 standard deviations of the simplest case of the noncontextuality inequalities identified. Our results advance the investigation of high-dimensional contextuality, its connection to the Clifford algebra, and its role in quantum computation.

arXiv:2209.02808•Physical Review Letters•Jun 13, 2023•8 citations

Experimentally Testable State-Independent Quantum Contextuality

Adán Cabello

We show that there are Bell-type inequalities for noncontextual theories that are violated by any quantum state. One of these inequalities between the correlations of compatible measurements is particularly suitable for testing this state-independent violation in an experiment.

arXiv:0808.2456•Physical Review Letters•Nov 19, 2008•407 citations
Often physical potentials are approximated to a harmonic potential so as to analytically solve the system dynamics. For example, the quantized electromagnetic field used to manipulate a qubit in cavity quantum electrodynamics, can be described using quantum harmonic oscillator (QHO). Hence it is important to know when a QHO behaves quantum mechanically and when classically. In this work, we encode the four lower-most eigenstates of the one dimensional-QHO(1D-QHO) onto the four Zeeman product states of a pair of spin-1/2 nuclei. Using the techniques of nuclear magnetic resonance (NMR) quantum information processing (QIP), we then demonstrate the strong violation of noncontextual hidden variable (NCHV) inequality, under specific experimental arrangements. We also experimentally investigate the weak violation of NCHV inequality by thermal equilibrium states in nuclear spins, thereby assessing their quantumness.
Physical potentials are routinely approximated to harmonic potentials. Hence it is important to know when a quantum harmonic oscillator (QHO) behaves quantum mechanically and when classically. Recently Su et al. ( Phys. Rev. A , 85 (2012) 052126) have theoretically shown that QHO exhibits quantum contextuality (QC) for a certain set of pseudospin observables. Here we encode the four eigenstates of a QHO onto four Zeeman product states of a pair of spin-(1/2) nuclei. Using the techniques of NMR quantum information processing, we then demonstrate the violation of both state-dependent and state-independent inequalities arising from the noncontextual hidden variable model.
Contextuality is a distinctive feature of quantum theory and a fundamental resource for quantum computation. However, existing examples of contextuality in high-dimensional systems lack the necessary robustness required in experiments. Here, we address this problem by identifying a family of noncontextuality inequalities whose maximum quantum violation grows with the dimension of the system. At first glance, this contextuality is the single-system version of multipartite Bell nonlocality taken to an extreme form. What is interesting is that the single-system version achieves the same degree of contextuality but uses a Hilbert space of lower dimension. That is, contextuality "concentrates" as the degree of contextuality per dimension increases. We show the practicality of this result by presenting an experimental test of contextuality in a seven-dimensional system. By simulating sequences of quantum ideal measurements with destructive measurements and repreparation in an all-optical setup, we report a violation of 68.7 standard deviations of the simplest case of the noncontextuality inequalities identified. Our results advance the investigation of high-dimensional contextuality, its connection to the Clifford algebra, and its role in quantum computation.