Constant-sized self-tests for maximally entangled states and single projective measurements

• URL: http://arxiv.org/abs/2306.13498v2
• Date: Fri, 15 Mar 2024 18:18:02 GMT
• Title: Constant-sized self-tests for maximally entangled states and single projective measurements
• Authors: Jurij Volčič,
• Abstract summary: Self-testing is a powerful certification of quantum systems relying on measured, classical statistics. This paper considers self-testing in bipartite Bell scenarios with small number of inputs and outputs, but with quantum states and measurements of arbitrarily large dimension.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Self-testing is a powerful certification of quantum systems relying on measured, classical statistics. This paper considers self-testing in bipartite Bell scenarios with small number of inputs and outputs, but with quantum states and measurements of arbitrarily large dimension. The contributions are twofold. Firstly, it is shown that every maximally entangled state can be self-tested with four binary measurements per party. This result extends the earlier work of Man\v{c}inska-Prakash-Schafhauser (2021), which applies to maximally entangled states of odd dimensions only. Secondly, it is shown that every single binary projective measurement can be self-tested with five binary measurements per party. A similar statement holds for self-testing of projective measurements with more than two outputs. These results are enabled by the representation theory of quadruples of projections that add to a scalar multiple of the identity. Structure of irreducible representations, analysis of their spectral features and post-hoc self-testing are the primary methods for constructing the new self-tests with small number of inputs and outputs.

Related papers

• Towards minimal self-testing of qubit states and measurements in prepare-and-measure scenarios [0.0]
  Self-testing is a promising approach to certifying quantum states or measurements. We show how to self-test any four- (three-) outcome extremal positive operator-valued measure using a linear witness. One of our constructions achieves self-testing of any number of states with the help of as many projective measurements.
  arXiv  Detail & Related papers  (2024-06-12T21:47:19Z)
• Measurement-Device-Independent Detection of Beyond-Quantum State [53.64687146666141]
  We propose a measurement-device-independent (MDI) test for beyond-quantum state detection. We discuss the importance of tomographic completeness of the input sets to the detection.
  arXiv  Detail & Related papers  (2023-12-11T06:40:13Z)
• Self-testing in prepare-and-measure scenarios and a robust version of Wigner's theorem [0.0]
  We consider communication scenarios where one party sends quantum states of known dimensionality $D$, prepared with an untrusted apparatus, to another, distant party. We prove that, for any ensemble of reference pure quantum states, there exists one such prepare-and-measure scenario and a linear functional $W$ on its observed measurement probabilities.
  arXiv  Detail & Related papers  (2023-06-01T14:27:24Z)
• All Real Projective Measurements Can be Self-tested [0.0]
  We show that every real projective measurement can be self-tested. We employ the idea that existing self-tests can be extended to verify additional untrusted measurements. We develop a new technique of iterative self-testing, which involves using post-hoc self-testing in a sequential manner.
  arXiv  Detail & Related papers  (2023-02-02T09:50:13Z)
• Validation tests of GBS quantum computers give evidence for quantum advantage with a decoherent target [62.997667081978825]
  We use positive-P phase-space simulations of grouped count probabilities as a fingerprint for verifying multi-mode data. We show how one can disprove faked data, and apply this to a classical count algorithm.
  arXiv  Detail & Related papers  (2022-11-07T12:00:45Z)
• Experimental demonstration of optimal unambiguous two-out-of-four quantum state elimination [52.77024349608834]
  A core principle of quantum theory is that non-orthogonal quantum states cannot be perfectly distinguished with single-shot measurements. Here we implement a quantum state elimination measurement which unambiguously rules out two of four pure, non-orthogonal quantum states.
  arXiv  Detail & Related papers  (2022-06-30T18:00:01Z)
• Self-testing of multipartite GHZ states of arbitrary local dimension with arbitrary number of measurements per party [0.0]
  Device independent certification schemes have gained a lot of interest lately. strongest form of device independent certification, known as self-testing, often requires for a Bell inequality to be maximally violated. We provide the first self-testing scheme for the multipartite Greenberger-Horne-Zeilinger (GHZ) states of arbitrary local dimension.
  arXiv  Detail & Related papers  (2021-12-20T21:26:52Z)
• On the properties of the asymptotic incompatibility measure in multiparameter quantum estimation [62.997667081978825]
  Incompatibility (AI) is a measure which quantifies the difference between the Holevo and the SLD scalar bounds. We show that the maximum amount of AI is attainable only for quantum statistical models characterized by a purity larger than $mu_sf min = 1/(d-1)$.
  arXiv  Detail & Related papers  (2021-07-28T15:16:37Z)
• Constant-sized robust self-tests for states and measurements of unbounded dimension [0.0]
  We show that correlations $p_n,x$ robustly self-test the underlying states and measurements. We are the first to exhibit a constant-sized self-test for measurements of unbounded dimension.
  arXiv  Detail & Related papers  (2021-03-02T14:02:17Z)
• On the optimal certification of von Neumann measurements [55.41644538483948]
  certification of quantum measurements can be viewed as the extension of quantum hypotheses testing. We show the connection between the certification of quantum channels or von Neumann measurements and the notion of $q$-numerical range.
  arXiv  Detail & Related papers  (2020-09-14T22:38:23Z)
• Quantum probes for universal gravity corrections [62.997667081978825]
  We review the concept of minimum length and show how it induces a perturbative term appearing in the Hamiltonian of any quantum system. We evaluate the Quantum Fisher Information in order to find the ultimate bounds to the precision of any estimation procedure. Our results show that quantum probes are convenient resources, providing potential enhancement in precision.
  arXiv  Detail & Related papers  (2020-02-13T19:35:07Z)

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.