Bounds on positive operator-valued measure based coherence of superposition

• URL: http://arxiv.org/abs/2305.06705v1
• Date: Thu, 11 May 2023 10:31:04 GMT
• Title: Bounds on positive operator-valued measure based coherence of superposition
• Authors: Meng-Li Guo, Jin-Min Liang, Bo Li, Shao-Ming Fei, and Zhi-Xi Wang
• Abstract summary: POVM-based coherence measures have been proposed with respect to the relative entropy of coherence. We derive analytically the lower and upper bounds on these POVM-based coherence of an arbitrary given superposed pure state. Our results can be used to estimate range of quantum coherence of superposed states.
• Score: 4.536603451832357
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantum coherence is a fundamental feature of quantum physics and plays a significant role in quantum information processing. By generalizing the resource theory of coherence from von Neumann measurements to positive operator-valued measures (POVMs), POVM-based coherence measures have been proposed with respect to the relative entropy of coherence, the $l_1$ norm of coherence, the robustness of coherence and the Tsallis relative entropy of coherence. We derive analytically the lower and upper bounds on these POVM-based coherence of an arbitrary given superposed pure state in terms of the POVM-based coherence of the states in superposition. Our results can be used to estimate range of quantum coherence of superposed states. Detailed examples are presented to verify our analytical bounds.

Related papers

• Quantum Implementation of Non-Positive-Operator-Valued Measurements in General Probabilistic Theories by Post-Selected POVMs [45.41082277680607]
  We deal with Non-Positive-Operator-Valued Measure (N-POVM) measurements in the framework of General Probabilistic Theories (GPTs) N-POVM measurements are not considered as implementable, but this paper gives a constructive way to implement N-POVM measurements by POVM measurements and post-selection in quantum theory.
  arXiv  Detail & Related papers  (2024-11-04T08:01:27Z)
• Coherence generation with Hamiltonians [44.99833362998488]
  We explore methods to generate quantum coherence through unitary evolutions. This quantity is defined as the maximum derivative of coherence that can be achieved by a Hamiltonian. We identify the quantum states that lead to the largest coherence derivative induced by the Hamiltonian.
  arXiv  Detail & Related papers  (2024-02-27T15:06:40Z)
• The relative entropy of coherence quantifies performance in Bayesian metrology [0.21111026813272177]
  We show how a coherence measure can be applied to an ensemble of states. We then prove that during parameter estimation, the ensemble relative entropy of coherence is equal to the difference between the information gained, and the optimal Holevo information.
  arXiv  Detail & Related papers  (2024-01-29T10:11:15Z)
• 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)
• A Quantum Optimal Control Problem with State Constrained Preserving Coherence [68.8204255655161]
  We consider a three-level $Lambda$-type atom subjected to Markovian decoherence characterized by non-unital decoherence channels. We formulate the quantum optimal control problem with state constraints where the decoherence level remains within a pre-defined bound.
  arXiv  Detail & Related papers  (2022-03-24T21:31:34Z)
• High Fidelity Quantum State Transfer by Pontryagin Maximum Principle [68.8204255655161]
  We address the problem of maximizing the fidelity in a quantum state transformation process satisfying the Liouville-von Neumann equation. By introducing fidelity as the performance index, we aim at maximizing the similarity of the final state density operator with the one of the desired target state.
  arXiv  Detail & Related papers  (2022-03-07T13:27:26Z)
• Quantifying dynamical coherence with coherence measures [2.446672595462589]
  Quantum coherence, like entanglement, is a fundamental resource in quantum information. It is difficult to define incoherent operations directly, without requiring incoherent states. We introduce an alternate definition of incoherent operations, induced via coherence measures, and quantify dynamical coherence.
  arXiv  Detail & Related papers  (2021-03-31T15:09:33Z)
• Coherence measures with respect to general quantum measurements [0.4588028371034407]
  We first establish an alternative framework for the block coherence and provide several block coherence measures. We then present several coherence measures with respect to POVM measurements, and prove a conjecture on the $l_1$-norm related POVM coherence measure.
  arXiv  Detail & Related papers  (2020-07-19T04:21:18Z)
• Anomalies of weight-based coherence measure and mixed maximally coherent states [6.292285191409447]
  We show that the weight-based coherence measure displays some unusual properties, in sharp contrast to other popular coherence quantifiers. We identify the existence of mixed maximally coherent states (MMCS) with respect to this coherence measure. We present several important families of MMCS by gaining insights from the numerical simulations.
  arXiv  Detail & Related papers  (2020-05-11T07:01:02Z)
• Quantum coherence and correlation measures based on affinity [1.3907460999698045]
  Coherence and correlation are key features of the quantum system. We identify an affinity-based metric to quantify closeness between two states. We propose a bipartite quantum correlation measure based on the affinity metric.
  arXiv  Detail & Related papers  (2020-03-29T17:03:52Z)
• 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.