Quantum Measurements in the Light of Quantum State Estimation

• URL: http://arxiv.org/abs/2111.02841v2
• Date: Mon, 3 Oct 2022 09:49:15 GMT
• Title: Quantum Measurements in the Light of Quantum State Estimation
• Authors: Huangjun Zhu
• Abstract summary: We show that rank-1 projective measurements are uniquely determined by their information-extraction capabilities. We also offer a new perspective for understanding noncommutativity and incompatibility from tomographic performances.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Starting from a simple estimation problem, here we propose a general approach for decoding quantum measurements from the perspective of information extraction. By virtue of the estimation fidelity only, we provide surprisingly simple characterizations of rank-1 projective measurements, mutually unbiased measurements, and symmetric informationally complete measurements. Notably, our conclusions do not rely on any assumption on the rank, purity, or the number of measurement outcomes, and we do not need bases to start with. Our work demonstrates that all these elementary quantum measurements are uniquely determined by their information-extraction capabilities, which are not even anticipated before. In addition, we offer a new perspective for understanding noncommutativity and incompatibility from tomographic performances, which also leads to a universal criterion for detecting quantum incompatibility. Furthermore, we show that the estimation fidelity can be used to distinguish inequivalent mutually unbiased bases and symmetric informationally complete measurements. In the course of study, we introduce the concept of (weighted complex projective) $1/2$-designs and show that all $1/2$-designs are tied to symmetric informationally complete measurements, and vice versa.

Related papers

• Informationally overcomplete measurements from generalized equiangular tight frames [0.0]
  We introduce a class of informationally overcomplete POVMs that are generated by equiangular tight frames of arbitrary rank. Our results show benefits of considering a single informationally overcomplete measurement over informationally complete collections of POVMs.
  arXiv  Detail & Related papers  (2024-05-01T15:07:32Z)
• Enhanced Entanglement in the Measurement-Altered Quantum Ising Chain [46.99825956909532]
  Local quantum measurements do not simply disentangle degrees of freedom, but may actually strengthen the entanglement in the system. This paper explores how a finite density of local measurement modifies a given state's entanglement structure.
  arXiv  Detail & Related papers  (2023-10-04T09:51:00Z)
• 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)
• Simulability of high-dimensional quantum measurements [0.0]
  We demand that the statistics obtained from $mathcalM$ and an arbitrary quantum state $rho$ are recovered exactly by first compressing $rho$ into a lower dimensional space. A full quantum compression is possible, if and only if the set $mathcalM$ is jointly measurable. We analytically construct optimal simulation models for all projective measurements subjected to white noise or losses.
  arXiv  Detail & Related papers  (2022-02-25T21:22:29Z)
• 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)
• Relating measurement disturbance, information and orthogonality [0.38073142980732994]
  In the general theory of quantum measurement, one associates a positive semidefinite operator on a $d$-dimensional Hilbert space to each of the $n$ possible outcomes of an arbitrary measurement. This restriction allows us to more precisely state the quantum adage: information gain of a system is always accompanied by unavoidable disturbance. We identify symmetric informationally complete quantum measurements as the unique quantum analogs of a perfectly informative and nondisturbing classical ideal measurement.
  arXiv  Detail & Related papers  (2021-05-05T14:19:40Z)
• Quantifying coherence of quantum measurements [0.0]
  We show that any statistical distance can be adopted to define a coherence monotone of measurement. We specifically introduce a coherence monotone of measurement in terms of off-diagonal elements of Positive-Operator-Valued Measure (POVM) components.
  arXiv  Detail & Related papers  (2020-08-10T09:57:28Z)
• Entropic Uncertainty Relations and the Quantum-to-Classical transition [77.34726150561087]
  We aim to shed some light on the quantum-to-classical transition as seen through the analysis of uncertainty relations. We employ entropic uncertainty relations to show that it is only by the inclusion of imprecision in our model of macroscopic measurements that we can prepare a system with two simultaneously well-defined quantities.
  arXiv  Detail & Related papers  (2020-03-04T14:01:17Z)
• 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)
• Dissipative Adiabatic Measurements: Beating the Quantum Cram\'{e}r-Rao Bound [0.0]
  It is challenged only recently that the precision attainable in any measurement of a physical parameter is fundamentally limited by the quantum Cram'er-Rao Bound (QCRB) Here, we propose an innovative measurement scheme called it dissipative adiabatic measurement and theoretically show that it can beat the QCRB.
  arXiv  Detail & Related papers  (2020-02-03T03:47:55Z)
• 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.