Quantum State Smoothing

Guevara, Ivonne; Wiseman, Howard Mark

doi:10.1103/physrevlett.115.180407

Cited by 59 publications

(131 citation statements)

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“…That is, a smoothed estimate made from incomplete data taken only by the first observer can be a better fit to the unknown data of the second observer than even the pure causal qubit state that uses all available data. Notably, this last result improves upon a recent proposal [46] that constructs a "smoothed quantum state" to estimate the observations made by an unknown second observer, since that method can never outperform the most pure causal state that uses all collected data. The conclusions of our study are consistent with prior work concerned with time-symmetric quantum state estimates, such as the two-state-vector formalism [37,47,48], quantum smoothing [49][50][51][52], bidirectional quantum states [53], and past quantum states [54][55][56][57].…”

supporting

confidence: 56%

“…To emphasize the significance of this result, we note that a similar situation to scenario (B) has been discussed by Guevara and Wiseman [46], who conclude that using an entire collected measurement record allows one to construct a "smoothed state" ρ S that is closer in fidelity to the (typically pure) maximally informative state ρ rz,p, rx,p known to an omniscient observer O than the (mixed) state ρ rz,p constructed from the incomplete information known to Z. The surprising extension to this result that we show here is that the informationally incomplete smoothed estimate x Z S can outperform even the best expectation value x known to the omniscient observer O. Evidently, the omniscient state ρ rz,p, rx,p is not informationally complete when it comes to the content of the collected readout.…”

Section: Smoothed Estimates By An Ignorant Third Partymentioning

confidence: 79%

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Past observable dynamics of a continuously monitored qubit

García-Pintos

Dressel

2017

Phys. Rev. A

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Monitoring a quantum observable continuously in time produces a stochastic measurement record that noisily tracks the observable. For a classical process such noise may be reduced to recover an average signal by minimizing the mean squared error between the noisy record and a smooth dynamical estimate. We show that for a monitored qubit this usual procedure returns unusual results. While the record seems centered on the expectation value of the observable during causal generation, examining the collected past record reveals that it better approximates a moving-mean Gaussian stochastic process centered at a distinct (smoothed) observable estimate. We show that this shifted mean converges to the real part of a generalized weak value in the time-continuous limit without additional postselection. We verify that this smoothed estimate minimizes the mean squared error even for individual measurement realizations. We go on to show that if a second observable is weakly monitored concurrently, then that second record is consistent with the smoothed estimate of the second observable based solely on the information contained in the first observable record. Moreover, we show that such a smoothed estimate made from incomplete information can still outperform estimates made using full knowledge of the causal quantum state.Over the past decade, time-continuous quantum measurements [1-9] of superconducting qubits (such as transmons [10]) have become an important and increasingly well-controlled component of emerging quantum computing technology . Indeed, the primary method for extracting information from a superconducting transmon is to dispersively couple it to a pumped microwave resonator, then amplify and mix the leaked microwave field with a local oscillator to perform a homodyne measurement of the traveling field, which produces a stochastic time-dependent voltage that encodes information about the transmon energy basis [33][34][35]. Understanding what information is contained in the resulting stochastic readout is thus an essential theoretical issue.In simple terms, a continuous measurement can be understood as a sequence of weak measurements [36,37] on the qubit. In the superconducting case, each temporal segment of the steady-state traveling coherent microwave field acts as an independent and approximately Gaussian meter that becomes entangled with the qubit and later measured [35]. During the measurement of the field, the finite bandwidth of the circuitry typically discretizes the field into time bins of size dt. Provided that dt is longer than the correlation timescale of the traveling field, the statistics of the averaged homodyne voltage collected in each independent time bin are approximately Gaussian, producing a discrete temporal sequence of Gaussian-distributed measurement results {r j } with a wide variance that inversely depends upon the time step size dt. All information about the qubit must be extracted by processing this stochastic time series.For convenience, this time series is traditionally interpolated ...

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confidence: 56%

Section: Smoothed Estimates By An Ignorant Third Partymentioning

confidence: 79%

Past observable dynamics of a continuously monitored qubit

García-Pintos

Dressel

2017

Phys. Rev. A

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“…is the probability of the outcome α which is determined by the Bayesian inference based on the continuous monitoring results after t m in a single realization [70], which is called retrodiction [71] or retrofiltering [72]. A bad retrodiction ensues from a quantum rare event.…”

Section: Fig 3: (Color Online) (A)mentioning

confidence: 99%

Quantum-trajectory thermodynamics with discrete feedback control

2016

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We employ the quantum jump trajectory approach to construct a systematic framework to study the thermodynamics at the trajectory level in a nonequilibrium open quantum system under discrete feedback control. Within this framework, we derive quantum versions of the generalized Jarzynski equalities, which are demonstrated in an isolated pseudospin system and a coherently driven twolevel open quantum system. Due to quantum coherence and measurement backaction, a fundamental distinction from the classical generalized Jarzynski equalities emerges in the quantum versions, which is characterized by a large negative information gain reflecting genuinely quantum rare events. A possible experimental scheme to test our findings in superconducting qubits is discussed.

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“…an estimated state that is Hermitian, positive semi-definite, and thus satisfies the Heisenberg uncertainty principle. This deficiency was removed recently in [29], which proposed quantum state smoothing, whereby a smoothed quantum state is introduced as a convex average of all possible true but unknown states weighted with a classical smoothed PDF. This allows one to assign a quantum state in the usual sense to a system of interest, conditioned on measurement records both prior and posterior to the estimation time.…”

Section: Introductionmentioning

confidence: 99%

Quantum state smoothing: why the types of observed and unobserved measurements matter

2019

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We investigate the estimation technique called quantum state smoothing introduced in (Guevara and Wiseman 2015 Phys. Rev. Lett. 115 180407), which offers a valid quantum state estimate for a partially monitored system, conditioned on the observed record both prior and posterior to an estimation time. The technique was shown to give a better estimate of the underlying true quantum states than the usual quantum filtering approach. However, the improvement in estimation fidelity, originally examined for a resonantly driven qubit coupled to two vacuum baths, was also shown to vary depending on the types of detection used for the qubit's fluorescence. In this work, we analyse this variation in a systematic way for the first time. We first define smoothing power using an average purity recovery and a relative average purity recovery, of smoothing over filtering. Then, we explore the power for various combinations of fluorescence detection for both observed and unobserved channels. We next propose a method to explain the variation of the smoothing power, based on multitime correlation strength between fluorescence detection records. The method gives a prediction of smoothing power for different combinations, which is remarkably successful in comparison with numerically simulated qubit trajectories. Gesellschaft which is a function of time difference τ and is symmetric under the interchange of the records, i.e.3 ss ss ss 2 using the steady-state correlators defined in equation (21)- (22). We note that the first argument,definition is the record that appear twice in the correlator. Thus we now have correlators in equations (23) and (26) defined with unit-less measurement results and can capture solely the correlation between any two records. We show in figures 4(a) and (b) the two-time and threetime correlators for all combinations of records JK and J d M , as functions of τ. There are only two out of six of the two-time correlators that are zero:  [ ] J J d , d X N 2 , and  [ ] J J d , d X Y 2 . For the three-time correlators, there are three out of nine, i.e.    [ ] [ ] [ ] in equation (23) are shown as functions of τ. The non-vanishing correlators are for the following:in equation (26) are shown as functions of τ, where  is chosen to be one Rabi period. The colour legend is read in the same way as in figure 3, but with dK and dM, representing any two types of records. The values of correlators here are used for the analysis in table 1. Time τ is presented in units of the Rabi period T Ω =2π/Ω. Therefore, we instead focus on a parameter-independent feature, which is the vanishing or non-vanishing property of the correlators. Some correlators, such as, are zero regardless of the values of  and τ. Those that do not vanish identically are non-zero for almost all values of  and τ.In order to predict the power of quantum state smoothing offered by different measurement unravelling combinations, we propose the following principles. Firstly, the stronger the correlation, the better the smoothing power. We quantify ...

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Quantum State Smoothing

Cited by 59 publications

References 51 publications

Past observable dynamics of a continuously monitored qubit

Past observable dynamics of a continuously monitored qubit

Quantum-trajectory thermodynamics with discrete feedback control

Quantum state smoothing: why the types of observed and unobserved measurements matter

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