Separation of measurement uncertainty into quantum and classical parts based on Kirkwood-Dirac quasiprobability and generalized entropy
arXiv:2412.10619 · doi:10.1088/1751-8121/ad8993
Abstract
Measurement in quantum mechanics is notoriously unpredictable. The uncertainty in quantum measurement can arise from the noncommutativity between the state and the measurement basis which is intrinsically quantum, but it may also be of classical origin due to the agent's ignorance. It is of fundamental as well as practical importance to cleanly separate the two contributions which can be directly accessed using laboratory operations. Here, we propose two ways of decomposition of the total measurement uncertainty additively into quantum and classical parts. In the two decompositions, the total uncertainty of a measurement described by a POVM (positive-operator-valued measure) over a quantum state is quantified respectively by two generalized nonadditive entropies of the measurement outcomes; the quantum parts are identified, respectively, by the nonreality and the nonclassicality | which captures simultaneously both the nonreality and negativity | of the associated generalized Kirkwood-Dirac quasiprobability relative to the POVM of interest and a PVM (projection-valued measure) and maximized over all possible choices of the latter; and, the remaining uncertainties are identified as the classical parts. Both decompositions are shown to satisfy a few plausible requirements. The minimum of the total measurement uncertainties in the two decompositions over all POVM measurements are given by the impurity of the quantum state quantified by certain generalized quantum entropies, and are entirely classical. We argue that nonvanishing genuine quantum uncertainty in the two decompositions are sufficient and necessary to prove quantum contextuality via weak measurement with postselection. Finally, we suggest that the genuine quantum uncertainty is a manifestation of a specific measurement disturbance.
35 pages
References in corpus (16)
- Complex weak values in quantum measurement
- Negativity and contextuality are equivalent notions of nonclassicality
- Anomalous Weak Values Are Proofs of Contextuality
- Non-equilibrium quantum fluctuations of work
- Quantum theory of successive projective measurements
- Negative quasiprobabilities enhance phase estimation in quantum-optics experiment
- Quantifying quantum coherence via nonreal Kirkwood-Dirac quasiprobability
- Kirkwood-Dirac quasiprobability approach to the statistics of incompatible observables
- Quantum circuits for measuring weak values, Kirkwood--Dirac quasiprobability distributions, and state spectra
- Quasiprobabilities in quantum thermodynamics and many-body systems
- Projective measurements can probe non-classical work extraction and time-correlations
- Operational interpretation and estimation of quantum trace-norm asymmetry based on weak value measurement and some bounds
- Quantum coherence as asymmetry from complex weak values
- General quantum correlation from nonreal values of Kirkwood-Dirac quasiprobability over orthonormal product bases
- Asymmetry and tighter uncertainty relations for Rényi entropies via quantum-classical decompositions of resource measures
- Dimension-independent weak value estimation via controlled SWAP operations