Exact signal correlators in continuous quantum measurements

Tilloy, Antoine

doi:10.1103/physreva.98.010104

Cited by 16 publications

(11 citation statements)

References 41 publications

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“…(86) regarding that a(t) = z(t)/β, U (t 2 , t 1 )A = G(t 2 − t 1 )A, and U (t 1 , 0)ρ 0 = ρ 0 for ρ 0 in equilibrium. Very recently, expressions for higher order moments were also found for applications in qubit measurements and the parameter estimation of quantum system while no expressions for cumulants or higher order spectra were derived 61,62 .…”

Section: Multi-time Moments Of Z(t)mentioning

confidence: 99%

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Higher-order moments, cumulants, and spectra of continuous quantum noise measurements

Hägele

Schefczik

2018

Phys. Rev. B

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We present general quantum mechanical expressions for higher order moments, cumulants, and spectra of continuously measured quantum systems with applications in spin noise spectroscopy, quantum transport, and measurement theory in general. Starting from the so-called stochastic master equation of continuous measurement theory, we find that the leading orders of the fluctuating detector output z(t) with respect to the measurement strength β are a white shot noise background, a constant measurement offset, and the leading order quantum noise of the measured operator A. Starting from quantum expressions for the multi-time moments z(tn) · · · z(t1) we derive three-and four-time cumulants that are valid in all orders of β covering the full regime between the weak and strong measurement limit (Zeno-limit). Intriguingly, quantum expressions for the cumulants were found that exhibit the same simple structure as those for the moments after introduction of only a slightly modified system propagator. Very compact expressions for the cumulant-based third and fourth order spectra (bispectrum and trispectrum) follow naturally. We illustrate the usefulness of higher order spectra by treating a real world two-spin system with strong hyperfine interaction. Moreover, spin noise spectroscopy is shown to have the potential for investigating the transition from weak measurements to the famous quantum Zeno regime for realistic probe laser intensities.

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Section: Multi-time Moments Of Z(t)mentioning

confidence: 99%

“…Moreover, a cumulant like C 3 (z(t 1 ), z(t 2 ), z(t 3 )) is strictly zero if any two of the arguments are uncorrelated. In contrast, the moment z(t 1 )z(t 2 )z(t 3 ) can still be non-zero although such a quantity is sometimes referred to as a "correlator" 62 .…”

Section: Multi-time Cumulants C3 and C4mentioning

confidence: 99%

Higher-order moments, cumulants, and spectra of continuous quantum noise measurements

Hägele

Schefczik

2018

Phys. Rev. B

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“…which can be exponentially small as we increase the integration time parameter T c since SNR ∝ T c , for sufficiently large T c , see Eq. (65). Furthermore, the probability that ∆C(t) ≥ Θ 2 − Θ 1 is time-independent and can be obtained from Eq.…”

Section: Small Tc Limitmentioning

confidence: 99%

Bacon-Shor code with continuous measurement of noncommuting operators

et al. 2017

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We analyze the continuous operation of the nine-qubit error correcting Bacon-Shor code with all noncommuting gauge operators measured at the same time. The error syndromes are continuously monitored using cross-correlations of sets of three measurement signals. We calculate the logical error rates due to X, Y and Z errors in the physical qubits and compare the continuous implementation with the discrete operation of the code. We find that both modes of operation exhibit similar performances when the measurement strength from continuous measurements is sufficiently strong. We also estimate the value of the crossover error rate of the physical qubits, below which continuous error correction gives smaller logical error rates. Continuous operation has the advantage of passive monitoring of errors and avoids the need for additional circuits involving ancilla qubits.

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“…So far, many reliable control methods have been developed, including adiabatic control, optimal control, Lyapunov control, and so on. Among them, the measurement‐based control methods are of prominent importance, such as the methods based on nondemolition measurements, projective measurements, and partial measurements . They are widespread in fabricating and designing experimental technologies for quantum system manipulations and metrology applications …”

Section: Introductionmentioning

confidence: 99%

Manipulation of Multi‐Level Quantum Systems via Unsharp Measurements and Feedback Operations

et al. 2019

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In this paper, we propose a scheme to eliminate the influence of noises on system dynamics, by means of a sequential unsharp measurements and unitary feedback operations. The unsharp measurements are carried out periodically during system evolution, while the feedback operations are well designed based on the eigenstates of the density matrices of the exact (noiseless) dynamical states and its corresponding post-measurement states. For illustrative examples, we show that the dynamical trajectory errors caused by both static and non-static noises are successfully eliminated in typical two-level and multi-level systems, i.e., the high-fidelity quantum dynamics can be maintained. Furthermore, we discuss the influence of noise strength and measurement strength on the degree of precise quantum control. Crucially, the measurement-feedback scheme is quite universal in that it can be applied to precise quantum control for any dimension systems. Thus, it naturally finds extensive applications in quantum information processing.

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Exact signal correlators in continuous quantum measurements

Cited by 16 publications

References 41 publications

Higher-order moments, cumulants, and spectra of continuous quantum noise measurements

Higher-order moments, cumulants, and spectra of continuous quantum noise measurements

Bacon-Shor code with continuous measurement of noncommuting operators

Manipulation of Multi‐Level Quantum Systems via Unsharp Measurements and Feedback Operations

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