Optimizing measurement strengths for qubit quasiprobabilities behind out-of-time-ordered correlators

Mohseninia, Razieh; Alonso, José Raúl González; Dressel, Justin

doi:10.1103/physreva.100.062336

Cited by 20 publications

(27 citation statements)

References 52 publications

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“…Unlike the Wigner functions, however, the Kirkwood–Dirac distribution is well-defined for discrete systems, even qubits. The Kirkwood–Dirac distribution has been used in the study of weak-value amplification 6 , 48 , 54 – 57 , information scrambling 6 , 52 , 53 , 58 , and direct measurements of quantum wavefunctions 59 – 61 . Moreover, negative and nonreal values of the distribution have been linked to nonclassical phenomena 6 , 48 , 52 , 53 .…”

Section: Resultsmentioning

confidence: 99%

Quantum advantage in postselected metrology

et al. 2020

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In every parameter-estimation experiment, the final measurement or the postprocessing incurs a cost. Postselection can improve the rate of Fisher information (the average information learned about an unknown parameter from a trial) to cost. We show that this improvement stems from the negativity of a particular quasiprobability distribution, a quantum extension of a probability distribution. In a classical theory, in which all observables commute, our quasiprobability distribution is real and nonnegative. In a quantummechanically noncommuting theory, nonclassicality manifests in negative or nonreal quasiprobabilities. Negative quasiprobabilities enable postselected experiments to outperform optimal postselection-free experiments: postselected quantum experiments can yield anomalously large information-cost rates. This advantage, we prove, is unrealizable in any classically commuting theory. Finally, we construct a preparation-and-postselection procedure that yields an arbitrarily large Fisher information. Our results establish the nonclassicality of a metrological advantage, leveraging our quasiprobability distribution as a mathematical tool.

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Section: Resultsmentioning

confidence: 99%

Quantum advantage in postselected metrology

et al. 2020

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“…(3) mk (t 1 , t 2 ), i.e., Equation (79) in Equation ( 78), and simplifying, the eigenstate representation of the micro-canonical correlator can be expressed as:…”

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confidence: 99%

The Generalized OTOC from Supersymmetric Quantum Mechanics—Study of Random Fluctuations from Eigenstate Representation of Correlation Functions

et al. 2020

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The concept of the out-of-time-ordered correlation (OTOC) function is treated as a very strong theoretical probe of quantum randomness, using which one can study both chaotic and non-chaotic phenomena in the context of quantum statistical mechanics. In this paper, we define a general class of OTOC, which can perfectly capture quantum randomness phenomena in a better way. Further, we demonstrate an equivalent formalism of computation using a general time-independent Hamiltonian having well-defined eigenstate representation for integrable Supersymmetric quantum systems. We found that one needs to consider two new correlators apart from the usual one to have a complete quantum description. To visualize the impact of the given formalism, we consider the two well-known models, viz. Harmonic Oscillator and one-dimensional potential well within the framework of Supersymmetry. For the Harmonic Oscillator case, we obtain similar periodic time dependence but dissimilar parameter dependences compared to the results obtained from both microcanonical and canonical ensembles in quantum mechanics without Supersymmetry. On the other hand, for the One-Dimensional PotentialWell problem, we found significantly different time scales and the other parameter dependence compared to the results obtained from non-Supersymmetric quantum mechanics. Finally, to establish the consistency of the prescribed formalism in the classical limit, we demonstrate the phase space averaged version of the classical version of OTOCs from a model-independent Hamiltonian, along with the previously mentioned well-cited models.

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“…In bridging entropic uncertainty relations with weak measurements and superconducting qubits, this Letter unites several subfields of quantum-information physics, which can benefit from the synergy introduced here. For example, in addition to the fundamental contribution to weak values mentioned above, this Letter paves the path toward detecting quantum chaos with weak measurements experimentally, being the first experiment to sprout from the considerable theoretical work on leveraging weak measurements to identify chaos [22,[30][31][32][33][34][35][36][37].…”

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confidence: 99%

“…Quantum information scrambles by spreading through many-body entanglement, during a nonclassical stage of equilibration [53][54][55][56]. The entropic uncertainty relation for quantum-information scrambling occupies a recent line of theoretical applications of weak measurements to scrambling [22,[30][31][32][33][34][35][36][37]. Our experiment is the first to arise from this theory.…”

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confidence: 99%