Quasi-probability distributions for observables in dynamic systems
arXiv:1702.00998 · doi:10.22331/q-2017-10-12-32
Abstract
We develop a general framework to investigate fluctuations of non-commuting observables. To this end, we consider the Keldysh quasi-probability distribution (KQPD). This distribution provides a measurement-independent description of the observables of interest and their time-evolution. Nevertheless, positive probability distributions for measurement outcomes can be obtained from the KQPD by taking into account the effect of measurement back-action and imprecision. Negativity in the KQPD can be linked to an interference effect and acts as an indicator for non-classical behavior. Notable examples of the KQPD are the Wigner function and the full counting statistics, both of which have been used extensively to describe systems in the absence as well as in the presence of a measurement apparatus. Here we discuss the KQPD and its moments in detail and connect it to various time-dependent problems including weak values, fluctuating work, and Leggett-Garg inequalities. Our results are illustrated using the simple example of two subsequent, non-commuting spin measurements.
Accepted in Quantum
References in corpus (17)
- Fluctuation theorems: Work is not an observable
- Reconstruction of non-classical cavity field states with snapshots of their decoherence
- Negativity and contextuality are equivalent notions of nonclassicality
- Weak values and the Leggett-Garg inequality in solid-state qubits
- Anomalous Weak Values Are Proofs of Contextuality
- Mapping the optimal route between two quantum states
- Weak Values are Interference Phenomena
- Frame representations of quantum mechanics and the necessity of negativity in quasi-probability representations
- Framed Hilbert space: hanging the quasi-probability pictures of quantum theory
- Nonclassical correlation properties of radiation fields
- Efficient simulation scheme for a class of quantum optics experiments with non-negative Wigner representation
- Signatures of quantum behavior in single-qubit weak measurements
- Probing Quantum Interference Effects in the Work Distribution
- Quasiprobabilistic Interpretation of Weak measurements in Mesoscopic Junctions
- Weak values are universal in von Neumann measurements
- Strong correspondence principle for joint measurement of conjugate observables
- Time-dependent quantum correlations in phase space
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- Quasiprobability distributions for quantum-optical coherence and beyond
- Experimentally reducing the quantum measurement back-action in work distributions by a collective measurement
- (Non) equilibrium dynamics: a (broken) symmetry of the Keldysh generating functional
- Probabilistically Violating the First Law of Thermodynamics in a Quantum Heat Engine
- Detecting violations of macrorealism when the original Leggett-Garg inequalities are satisfied
- Minimizing back-action through entangled measurements
- Interferometry of quantum correlation functions to access quasiprobability distribution of work
- Spectral characterization of non-Gaussian quantum noise: Keldysh approach and application to photon shot noise
- The First Law of Quantum Field Thermodynamics
- Certifying Non-Classical Behavior for Negative Keldysh Quasi-Probabilities
- Leggett-Garg inequalities for quantum fluctuating work
- Energy conservation and fluctuation theorem are incompatible for quantum work
- Identifying weak values with intrinsic dynamical properties in Modal theories
- Quantum speed limit for Kirkwood-Dirac quasiprobabilities
- Objectivity of classical quantum stochastic processes
- Non-equilibrium Dynamics of Renyi Entropy for Bosonic Many-Particle Systems
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- Complex counterpart of variance in quantum measurements for pre- and post-selected systems
- Ancilla-assisted measurement of quantum work
- Quantum Fluctuations of Entropy Production for Fermionic Systems in Landauer-Buttiker State
- Quasiprobability distributions with weak measurements
- Energy densities in quantum mechanics
- Wigner-function formalism for the detection of single microwave pulses in a resonator-coupled double quantum dot
- Probability vector representation of the Schrödinger equation and Leggett-Garg-type experiments
- Quantum Non-Demolition Measurements and Leggett-Garg inequality
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