Quantum coherence as asymmetry from complex weak values

Abstract

Quantum coherence as an asymmetry relative to a translation group generated by a Hermitian operator, is a necessary resource for the quantum parameter estimation. On the other hand, the sensitivity of the parameter estimation is known to be related to the imaginary part of the weak value of the Hermitian operator generating the unitary imprinting of the parameter being estimated. This naturally suggests a question if one can use the imaginary part of the weak value to characterize the coherence as asymmetry. In this work, we show that the average absolute imaginary part of the weak value of the generator of the translation group, maximized over all possible projective measurement bases, can be used to quantify the coherence as asymmetry relative to the translation group, satisfying certain desirable requirements. We argue that the quantifier of coherence so defined, called TC (translationally-covariant) w-coherence, can be obtained experimentally using a hybrid quantum-classical circuit via the estimation of weak value combined with a classical optimization procedure. We obtain upper bounds of the TC w-coherence in terms of the quantum standard deviation, quantum Fisher information, and the imaginary part of the Kirkwood-Dirac quasiprobability. We further obtain a lower bound and derive a relation between the TC w-coherences relative to two generators of translation group taking a form analogous to the Kennard-Weyl-Robertson uncertainty relation.

arXiv comment31 pages, no figures

References in corpus (53)

• Advances in Quantum Metrology
• Variational Quantum Algorithms
• Quantifying Coherence
• Quantum Coherence as a Resource
• Operational Resource Theory of Coherence
• Description of quantum coherence in thermodynamic processes requires constraints beyond free energy
• Direct Measurement of the Quantum Wavefunction
• Colloquium: Understanding Quantum Weak Values: Basics and Applications
• Generalized uncertainty relations: Theory, examples, and Lorentz invariance
• Observable measure of quantum coherence in finite dimensional systems
• Catalytic Coherence
• Characterizing Nonclassical Correlations via Local Quantum Uncertainty
• Quantum coherence, time-translation symmetry and thermodynamics
• Converting Coherence to Quantum Correlations
• Complex weak values in quantum measurement
• How to quantify coherence: Distinguishing speakable and unspeakable notions
• Extending Noether's theorem by quantifying the asymmetry of quantum states
• Direct measurement of general quantum states using weak measurement
• Towards fully quantum second laws of thermodynamics: limitations on the evolution of quantum coherences
• Coherence as a resource in decision problems: The Deutsch-Jozsa algorithm and a variation
• Robustness of asymmetry and coherence of quantum states
• (Quantumness in the context of) Resource Theories
• Quantum speed limits, coherence and asymmetry
• Anomalous Weak Values Are Proofs of Contextuality
• A quantitative theory of coherent delocalization
• The theory of manipulations of pure state asymmetry: basic tools and equivalence classes of states under symmetric operations
• Weak Values, Quantum Trajectories, and the Stony-Brook Cavity QED experiment
• Non-equilibrium quantum fluctuations of work
• Quantifying Superposition
• Modes of asymmetry: the application of harmonic analysis to symmetric quantum dynamics and quantum reference frames
• The quasiprobability behind the out-of-time-ordered correlator
• A resource theory of superposition
• The significance of the imaginary part of the weak value
• Quantum Coherence Sets The Quantum Speed Limit For Mixed States
• Quantum fluctuation theorems, contextuality and work quasi-probabilities
• Quantum theory of successive projective measurements
• Out-of-Time-Ordered-Correlator Quasiprobabilities Robustly Witness Scrambling
• Strong measurements give a better direct measurement of the quantum wave function
• Resource theory of coherence based on positive-operator-valued measures
• Anomalous weak values and contextuality: robustness, tightness, and imaginary parts
• Certifying quantum signatures in thermodynamics and metrology via contextuality of quantum linear response
• A quasiprobability distribution for heat fluctuations in the quantum regime
• Practical measurement of joint weak values and their connection to the annihilation operator
• Uncertainty limits for quantum metrology obtained from the statistics of weak measurements
• Determination of weak values of quantum operators using only strong measurements
• Operational interpretation of coherence in quantum key distribution
• State estimation: direct state measurement vs. tomography
• Weak vs. approximate values in quantum state determination
• Optimal quantum operations at zero energy cost
• Reconstructing weak values without weak measurements
• Coherence as a resource for source-independent quantum random-number generation
• Wave-particle duality employing quantum coherence in superposition with non-orthogonal pointers
• Coherence quantifiers from the viewpoint of their decreases in the measurement process

Cited by in corpus (14)

• Properties and Applications of the Kirkwood-Dirac Distribution
• Unitary-invariant witnesses of quantum imaginarity
• Operational interpretation and estimation of quantum trace-norm asymmetry based on weak value measurement and some bounds
• Nonlocal Advantages of Quantum Imaginarity
• Quantifying imaginarity in terms of pure-state imaginarity
• General quantum correlation from nonreal values of Kirkwood-Dirac quasiprobability over orthonormal product bases
• Kirkwood-Dirac classical pure states
• Quantum entanglement as an extremal Kirkwood-Dirac nonreality
• Separation of measurement uncertainty into quantum and classical parts based on Kirkwood-Dirac quasiprobability and generalized entropy
• Imaginarity measures induced by real part states and the complementarity relations
• Probing Kirkwood-Dirac nonpositivity and its operational implications via moments
• Experimental certification of the nonlocal advantages of quantum imaginarity
• Quantum speed limit for observables from quantum asymmetry
• Measure of set imaginarity