Time-Reversal and Super-Resolving Phase Measurements

Resch, K. J.; Pregnell, Kenneth Lyell; Prevedel, Robert; Gilchrist, Alexei; Pryde, Geoff J.; O'Brien, Jeremy L.; White, A. G.

doi:10.1103/physrevlett.98.223601

Cited by 260 publications

(208 citation statements)

References 38 publications

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“…The basic idea is to employ retrodiction [77,78]: once a highresolution quantum state has been detected at the output, one can interpret the whole experiment as having employed such a state since the input. This is a consequence of the fact that the wave-function collapse can be placed at an arbitrary time between probe preparation and measurement [77,79].…”

Section: Filtering Protocolsmentioning

confidence: 99%

Advances in quantum metrology

2011

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In classical estimation theory, the central limit theorem implies that the statistical error in a measurement outcome can be reduced by an amount proportional to n −1/2 by repeating the measures n times and then averaging. Using quantum effects, such as entanglement, it is often possible to do better, decreasing the error by an amount proportional to n −1 . Quantum metrology is the study of those quantum techniques that allow one to gain advantages over purely classical approaches.In this review, we analyze some of the most promising recent developments in this research field. Specifically, we deal with the developments of the theory and point out some of the new experiments. Then we look at one of the main new trends of the field, the analysis of how the theory must take into account the presence of noise and experimental imperfections.Any measurement consists in three parts: the preparation of a probe, its interaction with the system to be measured, and the probe readout. This process is often plagued by statistical or systematic errors. The source of the former can be accidental (e.g. deriving from an insufficient control of the probes or of the measured system) or fundamental (e.g. deriving from the Heisenberg uncertainty relations). Whatever their origin, we can reduce their effect by repeating the measurement and averaging the resulting outcomes. This is a consequence of the central-limit theorem: given a large number n of independent measurement results (each having a standard deviation ∆σ), their average will converge to a Gaussian distribution with standard deviation ∆σ/ √ n, so that the error scales as n −1/2 . In quantum mechanics this behavior is referred to as "standard quantum limit" (SQL) and is associated with procedures which do not fully exploit the quantum nature of the system under investigation 1 . Notably it is possible to do better when one employs quantum effects, such as entanglement among the probing devices employed for the measurements, e.g. see Refs. [1][2][3][4][5][6]. Consequently, the SQL is not a fundamental quantum mechanical bound as it can be surpassed by using "non-classical" strategies. Nonetheless, through Heisenberg-like uncertainty relations, quantum mechanics still sets ultimate limits in precision which are typically referred to as "Heisenberg bounds". In Fig. 1 we present a simple example which may be useful to un-1 In quantum optics, the n −1/2 scaling is also indicated as "shot noise", since it is connected to the discrete nature of the radiation that can be heard as "shots" in a photon counter operating in Geiger mode.derstand the quantum enhancement. Part of the emerging field of quantum technology [7], quantum metrology studies these bounds and the (quantum) strategies which allows us to attain them. More generally it deals with measurement and discrimination procedures that receive some kind of enhancement (in precision, efficiency, simplicity of implementation, etc.) through the use of quantum effects. This paper aims to review some of the most recent developmen...

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Section: Filtering Protocolsmentioning

confidence: 99%

Advances in quantum metrology

2011

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“…These states are extremely difficult to generate. Measurement schemes with counted photons or ions have been performed with N ≤ 6 [6,7,8,9,10,11,12,13,14,15], but few have surpassed the standard quantum limit [12,14] and none have shown Heisenberg-limited scaling. Here we demonstrate experimentally a Heisenberg-limited phase estimation procedure.…”

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confidence: 99%

Entanglement-free Heisenberg-limited phase estimation

Higgins

Berry

Bartlett

et al. 2007

Nature

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602

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Measurement underpins all quantitative science. A key example is the measurement of optical phase, used in length metrology and many other applications. Advances in precision measurement have consistently led to important scientific discoveries. At the fundamental level, measurement precision is limited by the number N of quantum resources (such as photons) that are used. Standard measurement schemes, using each resource independently, lead to a phase uncertainty that scales as 1/ √ N -known as the standard quantum limit. However, it has long been conjectured [1,2] that it should be possible to achieve a precision limited only by the Heisenberg uncertainty principle, dramatically improving the scaling to 1/N [3]. It is commonly thought that achieving this improvement requires the use of exotic quantum entangled states, such as the NOON state [4,5]. These states are extremely difficult to generate. Measurement schemes with counted photons or ions have been performed with N ≤ 6 [6, 7, 8, 9, 10, 11, 12, 13, 14, 15], but few have surpassed the standard quantum limit [12,14] and none have shown Heisenberg-limited scaling. Here we demonstrate experimentally a Heisenberg-limited phase estimation procedure. We replace entangled input states with multiple applications of the phase shift on unentangled single-photon states. We generalize Kitaev's phase estimation algorithm [16] using adaptive measurement theory [17,18,19,20] to achieve a standard deviation scaling at the Heisenberg limit. For the largest number of resources used (N = 378), we estimate an unknown phase with a variance more than 10 dB below the standard quantum limit; achieving this variance would require more than 4,000 resources using standard interferometry. Our results represent a drastic reduction in the complexity of achieving quantumenhanced measurement precision.Phase estimation is a ubiquitous measurement primitive, used for precision measurement of length, displacement, speed, optical properties, and much more. Recent work in quantum interferometry has focused on nphoton NOON states [5,6,7,8,9,10,11,12,21], (|n |0 + |0 |n ) / √ 2, expressed in terms of number states of the two arms of the interferometer. With this state, an improved phase sensitivity results from a decrease in the phase period from 2π to 2π/n. We achieve improved phase sensitivity more simply using an insight from quantum computing. We apply Kitaev's phase estimation algorithm [16,22] to quantum interferometry, wherein the entangled input state is replaced by multiple passes through the phase shift. The idea of using multi-pass protocols to gain a quantum advantage was proposed for the problem of aligning spatial reference frames [23], and further developed in relation to clock synchronization [24] and phase estimation [25,26].The conceptual circuit for Kitaev's phase estimation algorithm is shown in Fig. 1a. The algorithm yields, with K + 1 bits of precision, an estimate φ est of a classical phase parameter φ, where e iφ is an eigenvalue of a unitary operator U . It requires us t...

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“…The field operator for detector D is same as Eq. (16). As in Sect.IIC, the four-photon coincidence rate is related to the correlation function in Eq.…”

Section: Multi-mode Analysismentioning

confidence: 99%

“…The NOON-state projection measurement scheme was first proposed by Sun et al [15] and realized by Resch et al [16] for six-photon case and by Sun et al [17] for the four-photon case. Since it is based on a multi-photon interference effect, it was recently used to demonstrate the temporal distinguishability of an N-photon state [29,30].…”

Section: A Principle Of Experimentsmentioning

confidence: 99%

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Demonstration of the three-photon de Broglie wavelength by projection measurement

et al. 2008

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Two schemes of projection measurement are realized experimentally to demonstrate the de Broglie wavelength of three photons without the need for a maximally entangled three-photon state (the NOON state). The first scheme is based on the proposal by Wang and Kobayashi (Phys. Rev. A 71, 021802) that utilizes a couple of asymmetric beam splitters while the second one applies the general method of NOON state projection measurement to three-photon case. Quantum interference of three photons is responsible for projecting out the unwanted states, leaving only the NOON state contribution in these schemes of projection measurement.

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Time-Reversal and Super-Resolving Phase Measurements

Cited by 260 publications

References 38 publications

Advances in quantum metrology

Advances in quantum metrology

Entanglement-free Heisenberg-limited phase estimation

Demonstration of the three-photon de Broglie wavelength by projection measurement

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