Determination of All Unknown Pure Quantum States with Two Observables

• URL: http://arxiv.org/abs/2108.05752v4
• Date: Fri, 9 Aug 2024 03:50:38 GMT
• Title: Determination of All Unknown Pure Quantum States with Two Observables
• Authors: Yu Wang,
• Abstract summary: Efficiently extracting information from pure quantum states using minimal observables on the main system is a longstanding and fundamental issue in quantum information theory. We show that two orthogonal bases are capable of effectively filtering up to $2d-1$ finite candidates by disregarding a measure-zero set. We also show that almost all pure qudits can be uniquely determined by adaptively incorporating a POVM in the middle, followed by measuring the complementary observable.
• Score: 3.19428095493284
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Efficiently extracting information from pure quantum states using minimal observables on the main system is a longstanding and fundamental issue in quantum information theory. Despite the inability of probability distributions of position and momentum to uniquely specify a wavefunction, Peres conjectured a discrete version wherein two complementary observables, analogous to position and momentum and realized as projective measurements onto orthogonal bases, can determine all pure qudits up to a finite set of ambiguities. Subsequent findings revealed the impossibility of uniquely determining $d$-dimenisonal pure states even when neglecting a measure-zero set with any two orthogonal bases, and Peres's conjecture is also correct for $d=3$ but not for $d=4$. In this study, we show that two orthogonal bases are capable of effectively filtering up to $2^{d-1}$ finite candidates by disregarding a measure-zero set, without involving complex numbers in the bases' coefficients. Additionally, drawing inspiration from sequential measurements to directly calculate the target coefficients of the wavefunction using two complementary observables, we show that almost all pure qudits can be uniquely determined by adaptively incorporating a POVM in the middle, followed by measuring the complementary observable.

Related papers

• Direct Measurement of Density Matrices via Dense Dual Bases [8.502021723268465]
  We introduce a novel set of (2d) observables specifically designed to enable the complete characterization of any (d)-dimensional quantum state. We show that direct measurement of density matrix elements is feasible without auxiliary systems, with any element extractable using only three selected observables. This significantly reduces the number of unitary operations compared to compressed sensing with Pauli observables.
  arXiv  Detail & Related papers  (2024-09-05T11:36:54Z)
• Interferometry of quantum correlation functions to access quasiprobability distribution of work [0.0]
  We use an interferometric scheme aided by an auxiliary system to reconstruct the Kirkwood-Dirac quasiprobability distribution. Our results clarify the physical meaning of the work quasiprobability distribution in the context of quantum thermodynamics.
  arXiv  Detail & Related papers  (2024-05-31T17:32:02Z)
• 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)
• Form of Contextuality Predicting Probabilistic Equivalence between Two Sets of Three Mutually Noncommuting Observables [0.0]
  We introduce a contextual quantum system comprising mutually complementary observables organized into two or more collections of pseudocontexts with the same probability sums of outcomes. These pseudocontexts constitute non-orthogonal bases within the Hilbert space, featuring a state-independent sum of probabilities. The measurement contextuality in this setup arises from the quantum realizations of the hypergraph, which adhere to a specific bound on the linear combination of probabilities.
  arXiv  Detail & Related papers  (2023-09-22T08:51:34Z)
• A Universal Quantum Certainty Relation for Arbitrary Number of Observables [0.0]
  We derive by lattice theory a universal quantum certainty relation for arbitrary $M$ observables in $N$-dimensional system. We find that one cannot prepare a quantum state with PDVs of incompatible observables spreading out arbitrarily.
  arXiv  Detail & Related papers  (2023-08-10T16:44:10Z)
• 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)
• Quantum Measurements in the Light of Quantum State Estimation [0.0]
  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.
  arXiv  Detail & Related papers  (2021-11-04T13:00:11Z)
• Reachable sets for two-level open quantum systems driven by coherent and incoherent controls [77.34726150561087]
  We study controllability in the set of all density matrices for a two-level open quantum system driven by coherent and incoherent controls. For two coherent controls, the system is shown to be completely controllable in the set of all density matrices.
  arXiv  Detail & Related papers  (2021-09-09T16:14:23Z)
• Observation-dependent suppression and enhancement of two-photon coincidences by tailored losses [68.8204255655161]
  Hong-Ou-Mandel (HOM) effect can lead to a perfect suppression of two-particle coincidences between the output ports of a balanced beam splitter. In this work, we demonstrate experimentally that the two-particle coincidence statistics of two bosons can instead be seamlessly tuned to substantial enhancement. Our findings reveal a new approach to harnessing non-Hermitian settings for the manipulation of multi-particle quantum states.
  arXiv  Detail & Related papers  (2021-05-12T06:47:35Z)
• Quantum indistinguishability through exchangeable desirable gambles [69.62715388742298]
  Two particles are identical if all their intrinsic properties, such as spin and charge, are the same. Quantum mechanics is seen as a normative and algorithmic theory guiding an agent to assess her subjective beliefs represented as (coherent) sets of gambles. We show how sets of exchangeable observables (gambles) may be updated after a measurement and discuss the issue of defining entanglement for indistinguishable particle systems.
  arXiv  Detail & Related papers  (2021-05-10T13:11:59Z)
• Symmetric distinguishability as a quantum resource [21.071072991369824]
  We develop a resource theory of symmetric distinguishability, the fundamental objects of which are elementary quantum information sources. We study the resource theory for two different classes of free operations: $(i)$ $rmCPTP_A$, which consists of quantum channels acting only on $A$, and $(ii)$ conditional doubly (CDS) maps acting on $XA$.
  arXiv  Detail & Related papers  (2021-02-24T19:05:02Z)

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.