Heisenberg scaling with weak measurement: a quantum state discrimination point of view

Jordan, Andrew N.; Tollaksen, Jeff; Troupe, James E.; Dressel, Justin; Aharonov, Yakir

doi:10.1007/s40509-015-0036-8

Cited by 31 publications

(31 citation statements)

References 23 publications

(52 reference statements)

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“…In a single shot measurement a quantum-limited detector induces a stochastic evolution of the system without any decoherence, and therefore a pure state remains as such during the measurement 2,7,8 ; decoherence appears only as a result of averaging over the detectors's outcome. This observation is at the basis of a number of techniques for quantum devices control 2,9,10 , precision measurement [11][12][13] , and quantum information processing [14][15][16][17] . The experimental implementation of these techniques besides quantum optics 2 has been initiated in superconducting qubits where feedback loops 18 and single trajectories mapping 19 have been reported.…”

Section: Introductionmentioning

confidence: 96%

Effect of interactions on quantum-limited detectors

et al. 2017

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We consider the effect of electron-electron interactions on a voltage biased quantum point contact in the tunneling regime used as a detector of a nearby qubit. We model the leads of the quantum point contact as Luttinger liquids, incorporate the effects of finite temperature and analyze the detection-induced decoherence rate and the detector efficiency, Q. We find that interactions generically reduce the induced decoherence along with the detector's efficiency, and strongly affect the relative strength of the decoherence induced by tunneling and that induced by interactions with the local density. With increasing interaction strength, the regime of quantum-limited detection (Q → 1) is shifted to increasingly lower temperatures or higher bias voltages respectively. For small to moderate interaction strengths, Q is a monotonously decreasing function of temperature as in the non-interacting case. Surprisingly, for sufficiently strong interactions we identify an intermediate temperature regime where the efficiency of the detector increases with rising temperature.

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Section: Introductionmentioning

confidence: 96%

Effect of interactions on quantum-limited detectors

et al. 2017

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“…Note this result also implies that when we introduce any imperfection at all, the scaling will always be standard quantum limit in the asymptotic limit of large ν (but with a small prefactor). This conclusions applies generically to added dephasing imperfections in Heisenberg scaling schemes [23][24][25].…”

Section: Small ν Scalingmentioning

confidence: 60%

Precision optical displacement measurements using biphotons

Lyons¹,

Pang²,

Kwiat³

et al. 2016

Phys. Rev. A

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We propose and examine the use of biphoton pairs, such as those created in parametric down conversion or four-wave mixing, to enhance the precision and the resolution of measuring optical displacements by position-sensitive detection. We show that the precision of measuring a small optical beam displacement with this method can be significantly enhanced by the correlation between the two photons, given the same optical mode. The improvement is largest if the correlations between the photons are strong, and falls off as the biphoton correlation weakens. More surprisingly, we find that the smallest resolvable parameter of a simple split detector scales as the inverse of the number of biphotons for small biphoton number ("Heisenberg scaling"), because the Fisher information diverges as the parameter to be estimated decreases in value. One usually sees this scaling only for systems with many entangled degrees of freedom. We discuss the transition for the split-detection scheme to the standard quantum limit scaling for imperfect correlations as the biphoton number is increased. An analysis of an N -pixel detector is also given to investigate the benefit of using a higher resolution detector. The physical limit of these metrology schemes is determined by the uncertainty in the birth zone of the biphoton in the nonlinear crystal.

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“…Refs. [13,24] argue that time-correlated noise, for example, renders the optimal estimator impractical due to computational complexity. This is not, by itself, a compelling argument for employing weak values, however: one must show that the entire weak value protocol, including the post processing, is not outperformed by a suitable benchmark strategy.…”

Section: Suboptimal Estimation Strategiesmentioning

confidence: 99%

Weak-value amplification: state of play

Knee¹,

Combes²,

Ferrie³

et al. 2016

Quantum Measurements and Quantum Metrology

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Weak values arise in quantum theory when the result of a weak measurement is conditioned on a subsequent strong measurement. The majority of the trials are discarded, leaving only very few successful events. Intriguingly those can display a substantial signal ampli cation. This raises the question of whether weak values carry potential to improve the performance of quantum sensors, and indeed a number of impressive experimental results suggested this may be the case. By contrast, recent theoretical studies have found the opposite: using weak-values to obtain an ampli cation generally worsens metrological performance. This survey summarises the implications of those studies, which call for a reappraisal of weak values' utility and for further work to reconcile theory and experiment. Weak measurements vs. weak valuesA quantum weak measurement is a procedure whereby only a little bit of information about a quantum system is obtained; as a consequence, the system is only disturbed a little. This is in contrast to the usual strong measurements, which give a lot of information but in ict a large disturbance on the system. Imagine the needle on a poor-quality analogue voltmeter, which twitches or de ects in response to an electrical signal. In a weak measurement, the amount of deection is only loosely correlated with the true voltagebecause the needle also twitches about randomly. The expected value of the de ection, however, is precisely the true voltage.Physically, a weak measurement can be implemented by introducing a weak interaction between the system of interest and an ancillary meter degree of freedom [1,2]. Consider the following interaction Hamiltonian between system and meter:where g is a scalar quantity, A is the operator associated with the relevant system observable, and P is an operator e ecting a shift of the meter variable. The dynamics induced by this Hamiltonian (we assume it is switched on and o again instantaneously) will build up correlations between the system and meter. The degree of correlations, or the 'measurement strength' can be controlled for example by changing g; with strong and weak limits being attained when g → ∞ and g → , respectively. Owing to these correlations, a subsequent measurement on the meter alone may reveal information about the system. The back-action imparted to the system can be understood by examining the e ective measurement operators of the system (sometimes called POVM, or positive operator values measure elements [3]): strong measurement operators are projective, giving maximal information but also imparting the largest back-action. Intermediate strength measurements impart less back-action but give less information. In the limit of a vanishing interaction, the POVM elements become proportional to the identity matrix, and no measurement is performed at all. As long as a measurement of some nite strength is performed, however, the average de ection will reveal the true voltage with increasing precision. Weak measurements have become part of the standard too...

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Heisenberg scaling with weak measurement: a quantum state discrimination point of view

Cited by 31 publications

References 23 publications

Effect of interactions on quantum-limited detectors

Effect of interactions on quantum-limited detectors

Precision optical displacement measurements using biphotons

Weak-value amplification: state of play

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