Detecting coherence with respect to general quantum measurements

Abstract

Quantum coherence is a crucial resource in quantum resource theory. Previous study mainly focused on standard coherence under a complete orthogonal reference basis. The standard coherence has recently been extended to general positive-operator-valued measure (POVM)-based coherence, including block coherence as a special case. Therefore, it is necessary to construct block coherence and POVM-based coherence witnesses to detect them. In this work, we present witnesses for block coherence and POVM-based coherence, and obtain the necessary and sufficient conditions for arbitrary block coherence and POVM-based coherence witnesses. We also discuss possible realizations of some block coherence and POVM-based coherence witnesses in experiments, and present examples of measuring block coherence witnesses based on real experimental data. Furthermore, an application of block coherence witnesses has been presented in a quantum parameter estimation task with a degenerate Hamiltonian, and one can estimate the unknown parameter by measuring our block coherence witnesses if the input state is block coherent. Lase but not least, we prove that the quantum Fisher information of any block incoherent state is equal to zero, which coincides with the result from measuring block coherence witnesses.

7 pages, 1 figure

References in corpus (18)

• Scalable multi-particle entanglement of trapped ions
• Quantum metrology from a quantum information science perspective
• Quantum Optical Metrology -- The Lowdown on High-N00N States
• Witnessing Quantum Coherence: from solid-state to biological systems
• Entanglement Theory and the Second Law of Thermodynamics
• Coherence measures with respect to general quantum measurements
• Constant of motion identifying excited-state quantum phases
• Detecting and estimating coherence based on coherence witnesses
• Quantitative Coherence Witness for Finite Dimensional States
• Control of Giant Topological Magnetic Moment and Valley Splitting in Trilayer Graphene
• Trapping Horizons of the Evolving Charged Wormhole and Black Bounce
• Simulating both parity sectors of the Hubbard Model with Tensor Networks
• Macroscopically degenerate localized zero-energy states of quasicrystalline bilayer systems in strong coupling limit
• Quantifying dynamical coherence with coherence measures
• Converting coherence based on positive-operator-valued measures into entanglement
• Tomographic Witnessing and Holographic Quantifying of Coherence
• Estimating coherence with respect to general quantum measurements
• Ultrafast excitation and topological soliton formation in incommensurate charge density wave states