Towards minimal self-testing of qubit states and measurements in prepare-and-measure scenarios

• URL: http://arxiv.org/abs/2406.08661v1
• Date: Wed, 12 Jun 2024 21:47:19 GMT
• Title: Towards minimal self-testing of qubit states and measurements in prepare-and-measure scenarios
• Authors: Gábor Drótos, Károly F. Pál, Abdelmalek Taoutioui, Tamás Vértesi,
• Abstract summary: 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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Self-testing is a promising approach to certifying quantum states or measurements. Originally, it relied solely on the outcome statistics of the measurements involved in a device-independent (DI) setup. Extra physical assumptions about the system make the setup semi-DI. In the latter approach, we consider a prepare-and-measure scenario in which the dimension of the mediating particle is assumed to be two. In a setup involving four (three) preparations and three (two) projective measurements in addition to the target, we exemplify how to self-test any four- (three-) outcome extremal positive operator-valued measure using a linear witness. One of our constructions also achieves self-testing of any number of states with the help of as many projective measurements as the dimensionality of the space spanned by the corresponding Bloch vectors. These constructions are conjectured to be minimal in terms of the number of preparations and measurements required. In addition, we implement one of our prepare-and-measure constructions on IBM and IonQ quantum processors and certify the existence of a complex qubit Hilbert space based on the data obtained from these experiments.

Related papers

• 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)
• A universal scheme to self-test any quantum state and extremal measurement [41.94295877935867]
  quantum network considered in this work is the simple star network, which is implementable using current technologies. For our purposes, we also construct a scheme that can be used to self-test the two-dimensional tomographically complete set of measurements with an arbitrary number of parties.
  arXiv  Detail & Related papers  (2023-12-07T16:20:28Z)
• Self-testing of semisymmetric informationally complete measurements in a qubit prepare-and-measure scenario [0.0]
  Self-testing is a powerful method for certifying quantum systems. In this study, we focus on the self-testing of a specific type of non-projective qubit measurements. Our results pave the way towards self-testing any extremal qubit POVM within a potentially minimal PM scenario.
  arXiv  Detail & Related papers  (2023-06-12T17:15:56Z)
• Evolution of many-body systems under ancilla quantum measurements [58.720142291102135]
  We study the concept of implementing quantum measurements by coupling a many-body lattice system to an ancillary degree of freedom. We find evidence of a disentangling-entangling measurement-induced transition as was previously observed in more abstract models.
  arXiv  Detail & Related papers  (2023-03-13T13:06:40Z)
• Certification of the maximally entangled state using non-projective measurements [0.0]
  We consider the one-sided device-independent POV (1) scenario, and propose a self-testing scheme for the two-qubit maximally entangled state using non-projective measurements. We also analyse the robustness of our scheme against white noise.
  arXiv  Detail & Related papers  (2022-10-25T15:35:29Z)
• Experimentally determining the incompatibility of two qubit measurements [55.41644538483948]
  We describe and realize an experimental procedure for assessing the incompatibility of two qubit measurements. We demonstrate this fact in an optical setup, where the qubit states are encoded into the photons' polarization degrees of freedom.
  arXiv  Detail & Related papers  (2021-12-15T19:01:44Z)
• Minimal scheme for certifying three-outcome qubit measurements in the prepare-and-measure scenario [0.0]
  The number of outcomes is a defining property of a quantum measurement. The certification of this property is possible in a semi-device-independent way.
  arXiv  Detail & Related papers  (2021-05-20T17:39:46Z)
• 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)
• A universal scheme for robust self-testing in the prepare-and-measure scenario [0.0]
  We consider the problem of certification of arbitrary ensembles of pure states and projective measurements. We propose a universal and intuitive scheme based on establishing perfect correlations between target states and suitably-chosen projective measurements.
  arXiv  Detail & Related papers  (2020-03-02T17:06:06Z)
• 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)
• Direct estimation of quantum coherence by collective measurements [54.97898890263183]
  We introduce a collective measurement scheme for estimating the amount of coherence in quantum states. Our scheme outperforms other estimation methods based on tomography or adaptive measurements. We show that our method is accessible with today's technology by implementing it experimentally with photons.
  arXiv  Detail & Related papers  (2020-01-06T03:50:42Z)

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.