Scalable Bell inequalities for graph states of arbitrary prime local dimension and self-testing

• URL: http://arxiv.org/abs/2212.07133v1
• Date: Wed, 14 Dec 2022 09:46:27 GMT
• Title: Scalable Bell inequalities for graph states of arbitrary prime local dimension and self-testing
• Authors: Rafael Santos, Debashis Saha, Flavio Baccari, Remigiusz Augusiak
• Abstract summary: Bell nonlocality -- the existence of quantum correlations that cannot be explained by classical means -- is one of the most striking features of quantum mechanics. This work provides a general construction of Bell inequalities maximally violated by graph states of any prime local dimension. We analytically determine their maximal quantum violation, a number of high relevance for device-independent applications of Bell inequalities.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Bell nonlocality -- the existence of quantum correlations that cannot be explained by classical means -- is certainly one of the most striking features of quantum mechanics. Its range of applications in device-independent protocols is constantly growing. Many relevant quantum features can be inferred from violations of Bell inequalities, including entanglement detection and quantification, and state certification applicable to systems of arbitrary number of particles. A complete characterisation of nonlocal correlations for many-body systems is, however, a computationally intractable problem. Even if one restricts the analysis to specific classes of states, no general method to tailor Bell inequalities to be violated by a given state is known. In this work we provide a general construction of Bell inequalities that are maximally violated by graph states of any prime local dimension. These form a broad class of multipartite quantum states that have many applications in quantum information, including quantum error correction. We analytically determine their maximal quantum violation, a number of high relevance for device-independent applications of Bell inequalities. Finally, we show that these inequalities can be used for self-testing of multi-qutrit graph states such as the well-known four-qutrit absolutely maximally entangled state AME(4,3).

Related papers

• Realizing fracton order from long-range quantum entanglement in programmable Rydberg atom arrays [45.19832622389592]
  Storing quantum information requires battling quantum decoherence, which results in a loss of information over time. To achieve error-resistant quantum memory, one would like to store the information in a quantum superposition of degenerate states engineered in such a way that local sources of noise cannot change one state into another. We show that this platform also allows to detect and correct certain types of errors en route to the goal of true error-resistant quantum memory.
  arXiv  Detail & Related papers  (2024-07-08T12:46:08Z)
• A computational test of quantum contextuality, and even simpler proofs of quantumness [43.25018099464869]
  We show that an arbitrary contextuality game can be compiled into an operational "test of contextuality" involving a single quantum device. Our work can be seen as using cryptography to enforce spatial separation within subsystems of a single quantum device.
  arXiv  Detail & Related papers  (2024-05-10T19:30:23Z)
• Bell inequalities with overlapping measurements [52.81011822909395]
  We study Bell inequalities where measurements of different parties can have overlap. This allows to accommodate problems in quantum information. The scenarios considered show an interesting behaviour with respect to Hilbert space dimension, overlap, and symmetry.
  arXiv  Detail & Related papers  (2023-03-03T18:11:05Z)
• Detection of Beyond-Quantum Non-locality based on Standard Local Quantum Observables [46.03321798937856]
  We show that device independent detection cannot distinguish beyond-quantum non-local states from standard quantum states. This paper gives a device dependent detection based on local observables to distinguish any beyond-quantum non-local state from all standard quantum states.
  arXiv  Detail & Related papers  (2023-01-10T20:19:34Z)
• Experimental violations of Leggett-Garg's inequalities on a quantum computer [77.34726150561087]
  We experimentally observe the violations of Leggett-Garg-Bell's inequalities on single and multi-qubit systems. Our analysis highlights the limits of nowadays quantum platforms, showing that the above-mentioned correlation functions deviate from theoretical prediction as the number of qubits and the depth of the circuit grow.
  arXiv  Detail & Related papers  (2021-09-06T14:35:15Z)
• Graph-Theoretic Framework for Self-Testing in Bell Scenarios [37.067444579637076]
  Quantum self-testing is the task of certifying quantum states and measurements using the output statistics solely. We present a new approach for quantum self-testing in Bell non-locality scenarios.
  arXiv  Detail & Related papers  (2021-04-27T08:15:01Z)
• Testing Scalable Bell Inequalities for Quantum Graph States on IBM Quantum Devices [6.070269792417041]
  Bell inequalities are useful for testing and verifying the quality of the quantum devices from their nonlocal quantum states and local measurements. We report violations of Bell inequalities on IBM Quantum devices based on the scalable and robust inequalities maximally violated by graph states.
  arXiv  Detail & Related papers  (2021-01-25T18:46:19Z)
• Class of Bell-Clauser-Horne inequalities for testing quantum nonlocality [11.367526341820643]
  We propose methods for the rearrangement and linear inequality to prove a large variety of Bell-CH inequalities. We also derive a set of Bell-CH inequalities by using these methods which can be violated in some quantum entangled states.
  arXiv  Detail & Related papers  (2021-01-07T08:25:21Z)
• Bell Non-Locality in Many Body Quantum Systems with Exponential Decay of Correlations [0.0]
  This paper uses Bell-inequalities as a tool to explore non-classical physical behaviours. We show that a large family of quantum many-body systems behave almost locally, violating Bell-inequalities (if so) only by a non-significant amount.
  arXiv  Detail & Related papers  (2020-06-09T22:41:44Z)
• Detecting many-body Bell non-locality by solving Ising models [0.0]
  We show that an arbitrary set of quantum data is compatible with a local theory, if not, it delivers a many-body Bell inequality violated by the quantum data. We use our approach to unveil new many-body Bell inequalities, violated by suitable measurements on paradigmatic quantum states.
  arXiv  Detail & Related papers  (2020-04-16T17:40:04Z)
• The Schmidt number of a quantum state cannot always be device-independently certified [0.0]
  We show that there exist quantum states, whose entanglement content, as measured by the Schmidt number, cannot be device-independently certified for all possible sequential measurements on any number of copies. While the bigger question: textitcan the presence of entanglement always be device-independently certified? remains open, we provide proof that quantifying entanglement device-independently is not always possible, even beyond the standard Bell scenario.
  arXiv  Detail & Related papers  (2020-03-31T13:28:07Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.