Toward Heisenberg-Limited Spectroscopy with Multiparticle Entangled States

Leibfried, D.; Barrett, M. D.; Schaetz, Tobias; Britton, J.; Chiaverini, John; Itano, Wayne M.; Jost, John D.; Langer, C.; Wineland, David J.

doi:10.1126/science.1097576

Cited by 622 publications

(635 citation statements)

References 24 publications

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“…It means that for SSS, its fluctuation of the collective angular momentum is squeezed in one direction and inflated in the another direction, and the fluctuation in the squeezed direction is smaller than the sub-short limit. It is believed that spin squeezing which is aroused from quantum correlation effect among individual particles, is closely related to multipartite entanglement [9,11,16,41]. One of the main applications of the SSSs is used to reduce quantum noise and increase the signal-to-noise ratio in spectroscopy [10,11,42,43].…”

Section: Spin Squeezingmentioning

confidence: 99%

“…Equation (1) shows that a quantum state with the APEP-enhancing must be entangled. Besides entangled states, it has been theoretically and experimentally demonstrated that spin squeezed states (SSSs) can also be used to improve the accuracy of estimation [8,9,10,11,12,13,14,15,16,17,18,19]. The concept of SSSs was first established by Kitagawa and Ueda [9].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Quantum Fisher information and spin squeezing in one-axis twisting model

Zhong¹,

Liu²,

Ma³

et al. 2014

Chinese Phys. B

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Abstract. We consider the quantum Fisher information and spin squeezing in oneaxis twisting model with a coherent spin state |θ 0 , φ 0 . We analytically discuss the dependence of the two parameters: spin squeezing parameter ξ 2 K and the average parameter estimation precision χ 2 on the polar angle θ 0 and the azimuth angle φ 0 . Moreover, we discuss the effects of the collisional dephasing on the dynamics of the two parameters. In this case, the analytical solution of ξ 2 K is also obtained.

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Section: Spin Squeezingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Quantum Fisher information and spin squeezing in one-axis twisting model

Zhong¹,

Liu²,

Ma³

et al. 2014

Chinese Phys. B

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“…In the atomic literature, where |a and |b refer to different atomic levels, |ψ (N) 0 often is referred to as "spin-squeezed state" [42,43] or "Schrödinger-cat state" [44][45][46]. It has been experimentally demonstrated using trapped ions [44][45][46][47], Bose-Einstein condensates [48], macroscopic atomic ensembles [49], and NMR [50]. 5 The map Φx is called programmable if one can express it in terms of a constant interaction with an external ancillary system B whose initial state encodes the dependence on the parameter x, i.e.…”

Section: Quantum Parameter Estimation For Channelsmentioning

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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“…Starting with two-qubit gate operations [2,3], long lived two-qubit entanglement [4,5,6], teleportation experiments [7,8], and different sorts of multi-qubit entangled states [9,10,4,11], the record for qubit-entanglement is currently presented in a 6-qubit cat state and a 8-qubit W-state [12,13]. Future improvement is expected using the technique of segmented linear Paul traps which allow to shuttle ions from a "processor" unit to a "memory" section [14].…”

Section: Introductionmentioning

confidence: 99%

Optimization of segmented linear Paul traps and transport of stored particles

Schulz

Poschinger

Singer³

et al. 2006

Fortschritte der Physik

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Single ions held in linear Paul traps are promising candidates for a future quantum computer. Here, we discuss a two-layer microstructured segmented linear ion trap. The radial and axial potentials are obtained from numeric field simulations and the geometry of the trap is optimized. As the trap electrodes are segmented in the axial direction, the trap allows the transport of ions between different spatial regions. Starting with realistic numerically obtained axial potentials, we optimize the transport of an ion such that the motional degrees of freedom are not excited, even though the transport speed far exceeds the adiabatic regime. In our optimization we achieve a transport within roughly two oscillation periods in the axial trap potential compared to typical adiabatic transports that take of the order 10 2 oscillations. Furthermore heating due to quantum mechanical effects is estimated and suppression strategies are proposed.

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Toward Heisenberg-Limited Spectroscopy with Multiparticle Entangled States

Cited by 622 publications

References 24 publications

Quantum Fisher information and spin squeezing in one-axis twisting model

Quantum Fisher information and spin squeezing in one-axis twisting model

Advances in quantum metrology

Optimization of segmented linear Paul traps and transport of stored particles

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