Time correlators from deferred measurements

Oehri, David; Lebedev, A. V.; Lesovik, G. B.; Blatter, G.

doi:10.1103/physrevb.93.045308

Cited by 7 publications

(17 citation statements)

References 35 publications

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“…Recent quasiprobability advances involve out-of-time ordering, including in correlation functions [124][125][126][127][128]. Merging these works with the OTOC framework offers an opportunity for further research (Sec.…”

Section: Theoretical Study Ofãρmentioning

confidence: 99%

Quasiprobability behind the out-of-time-ordered correlator

2018

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Two topics, evolving rapidly in separate fields, were combined recently: The out-of-time-ordered correlator (OTOC) signals quantum-information scrambling in many-body systems. The Kirkwood-Dirac (KD) quasiprobability represents operators in quantum optics. The OTOC was shown to equal a moment of a summed quasiprobability [Yunger Halpern, Phys. Rev. A 95, 012120 (2017)]. That quasiprobability, we argue, is an extension of the KD distribution. We explore the quasiprobability's structure from experimental, numerical, and theoretical perspectives. First, we simplify and analyze Yunger Halpern's weak-measurement and interference protocols for measuring the OTOC and its quasiprobability. We decrease, exponentially in system size, the number of trials required to infer the OTOC from weak measurements. We also construct a circuit for implementing the weak-measurement scheme. Next, we calculate the quasiprobability (after coarse-graining) numerically and analytically: We simulate a transverse-field Ising model first. Then, we calculate the quasiprobability averaged over random circuits, which model chaotic dynamics. The quasiprobability, we find, distinguishes chaotic from integrable regimes. We observe nonclassical behaviors:The quasiprobability typically has negative components. It becomes nonreal in some regimes. The onset of scrambling breaks a symmetry that bifurcates the quasiprobability, as in classical-chaos pitchforks. Finally, we present mathematical properties. We define an extended KD quasiprobability that generalizes the KD distribution. The quasiprobability obeys a Bayes-type theorem, for example, that exponentially decreases the memory required to calculate weak values, in certain cases. A time-ordered correlator analogous to the OTOC, insensitive to quantum-information scrambling, depends on a quasiprobability closer to a classical probability. This work not only illuminates the OTOC's underpinnings, but also generalizes quasiprobability theory and motivates immediate-future weak-measurement challenges.2. Bayes-type theorem and retrodiction with the KD quasiprobability chain example. Discrete systems are governed by quasiprobabilities, which resemble probabilities. Continuous systems are governed by quasiprobability densities, which resemble probability densities. Our quasiprobabilities can be replaced with quasiprobability densities, and our sums can be replaced with integrals, in, e.g., quantum field theory.

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Section: Theoretical Study Ofãρmentioning

confidence: 99%

Quasiprobability behind the out-of-time-ordered correlator

2018

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“…For a = x, y, the above is achieved when the system rotation axis is orthogonal to the az plane, while for a = z no system rotation is needed since A i = σ z i is already fulfilled by the TPM coupling. The same is true for the ancilla rotation when measuring (20) with a = x, y whereas for a = z no rotation is needed since B = σ z already fulfills condition (19). Estimators (22) are obtained for a = x, y by rotating the ancilla parallel to the a-axis, while for a = z a rotation around the x axis is necessary.…”

Section: Appendix E: Derivation Of the Cnimpmentioning

confidence: 87%

“…Physically relevant states satisfying this condition are, for instance, spin coherent states, or equal superpositions where c ma = 1/ √ 2s + 1 for all m a ∈ S . We choose the latter for our derivation, noting that other choices only lead to modified prefactors f (1) , f (2) in (20) and (22).…”

Section: Noninvasive Measurement Protocolmentioning

confidence: 99%

Noninvasive measurement of dynamic correlation functions

et al. 2017

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The measurement of dynamic correlation functions of quantum systems is complicated by measurement backaction. To facilitate such measurements we introduce a protocol, based on weak ancilla-system couplings, that is applicable to arbitrary (pseudo)spin systems and arbitrary equilibrium or nonequilibrium initial states. Different choices of the coupling operator give access to the real and imaginary parts of the dynamic correlation function. This protocol reduces disturbances due to the early time measurements to a minimum, and we quantify the deviation of the measured correlation functions from the theoretical, unitarily-evolved ones. Implementations of the protocol in trapped ions and other experimental platforms are discussed. For spin-1/2 models and single-site observables we prove that measurement backaction can be avoided altogether, allowing for the use of ancilla-free protocols.

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“…Discussions on quantum measurement in electronic transport systems involve both the von Neumann projecton postulate and detector's backaction on the system 52,53 . In Refs.…”

Section: Introductionmentioning

confidence: 99%

Short-time dynamics of molecular junctions after projective measurement

Tang¹,

Xing

Wang³

2017

Phys. Rev. B

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In this work, we study the short time dynamics of a molecular junction described by AndersonHolstein model using full-counting statistics after projective measurement. The coupling between the central quantum dot (QD) and two leads was turned on at remote past and the system is evolved to steady state at time t = 0, when we perform the projective measurement in one of the lead. Generating function for the charge transfer is expressed as a Fredholm determinant in terms of Keldysh nonequilibrium Green's function in the time domain. It is found that the current is not constant at short times indicating that the measurement does perturb the system. We numerically compare the current behaviors after the projective measurement with those in the transient regime where the subsystems are connected at t = 0. The universal scaling for high-order cumulants is observed for the case with zero QD occupation due to the unidirectional transport at short times. The influences of electron-phonon interaction on short time dynamics of electric current, shot noise and differential conductance are analyzed.

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Time correlators from deferred measurements

Cited by 7 publications

References 35 publications

Quasiprobability behind the out-of-time-ordered correlator

Quasiprobability behind the out-of-time-ordered correlator

Noninvasive measurement of dynamic correlation functions

Short-time dynamics of molecular junctions after projective measurement

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