Observable measure of quantum coherence in finite dimensional systems

Abstract

Quantum coherence is the key resource for quantum technology, with applications in quantum optics, information processing, metrology and cryptography. Yet, there is no universally efficient method for quantifying coherence either in theoretical or in experimental practice. I introduce a framework for measuring quantum coherence in finite dimensional systems. I define a theoretical measure which satisfies the reliability criteria established in the context of quantum resource theories. Then, I present an experimental scheme implementable with current technology which evaluates the quantum coherence of an unknown state of a d-dimensional system by performing two programmable measurements on an ancillary qubit, in place of the $O(d^2)$ direct measurements required by full state reconstruction. The result yields a benchmark for monitoring quantum effects in complex systems, e.g. certifying non-classicality in quantum communication and simulation protocols and probing the quantum behaviour of biological complexes.

5+2 pages, close to published version

References in corpus (11)

• Quantum Non-Markovianity: Characterization, Quantification and Detection
• Reference frames, superselection rules, and quantum information
• Complete experimental toolbox for alignment-free quantum communication
• Witnessing Quantum Coherence: from solid-state to biological systems
• Measuring the quality of a quantum reference frame: the relative entropy of frameness
• Metric adjusted skew information
• Entanglement constrained by superselection rules
• The WAY theorem and the quantum resource theory of asymmetry
• Measuring bipartite quantum correlations of an unknown state
• A measurement scheme for purity based on two two-body gates
• Information geometry of density matrices and state estimation

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• Maximally coherent mixed states: Complementarity between maximal coherence and mixedness
• Geometric lower bound for a quantum coherence measure
• Quantifying quantum coherence via nonreal Kirkwood-Dirac quasiprobability
• Factorization and Criticality in the Anisotropic XY Chain via Correlations
• Criticality and factorization in the Heisenberg chain with Dzyaloshinskii-Moriya interaction
• Quantum Simulation of single-qubit thermometry using linear optics
• Maximum coherence in the optimal basis
• Detecting macroscopic quantum coherence with a cavity optomechanical system
• Uncertainty Relations for Quantum Coherence
• Estimation on geometric measure of quantum coherence
• Ultrafast dynamics of photoinduced charge separation
• The Wigner-Yanase information can increase under phase sensitive incoherent operations
• Coherence breaking channels and coherence sudden death
• Enhancing coherence of a state by stochastic strictly incoherent operations
• The dynamic behaviors of local quantum uncertainty for three-qubit X states under decoherence channels
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• Inhibiting decoherence of two-level atom in thermal bath by presence of boundaries
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• Maximum Relative Entropy of Coherence for Quantum Channels
• Bosonic and fermionic coherence of N-partite states in the background of a dilaton black hole
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• Remote Creation of Quantum Coherence
• Factorization, coherence and asymmetry in the Heisenberg spin-1/2 XXZ chain a transverse magnetic field and with Dzyaloshinskii-Moriya interaction
• Quantum coherence generating power, maximally abelian subalgebras, and Grassmannian Geometry
• Duality relation between coherence and path information in the presence of quantum memory
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• Geometry of skew information-based quantum coherence
• The influence of the Earth's curved spacetime on Gaussian quantum coherence
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• The $n$-th decay rate of coherence for Bell-diagonal states under quantum channels
• Protecting coherence in the non-Hermitian two-level system
• Teleportation based detection of quantum critical points using small spin chains
• Quantum speed limits based on Jensen-Shannon and Jeffreys divergences for general physical processes
• Dynamics of quantum Fisher and Wigner-Yanase skew information following a noisy quench
• Probing phase transitions in non-Hermitian systems with quantum entanglement
• Classifying coherence with a finite set of witnesses
• Imaginarity as a Resource within Quantum Coherence: Geometric Decomposition and Operational Conversion
• Phase-sensitive superposition of quantum states
• Quantum speed limit for observables from quantum asymmetry
• Experimental demonstration of complementarity relations between quantum steering criteria
• Direct estimation of quantum coherence by collective measurements
• Universal decay of quantumness for photonic qubits carrying orbital angular momentum through atmospheric turbulence
• Universal trade-off relation between coherence and intrinsic concurrence for two-qubit states
• Coherence Concurrence for X States
• Dark state population determines magnetic sensitivity in radical pair magnetoreception model
• Quantum partial coherence measures constructed from Fisher information