Heisenberg-limited interferometry with pair coherent states and parity measurements

Gerry, Christopher C.; Mimih, Jihane

doi:10.1103/physreva.82.013831

Cited by 73 publications

(60 citation statements)

References 33 publications

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“…However, one might think of instead employing interferometric protocols, related to the ones put forward in Refs. [31][32][33] for superpositions of coherent states, in order to exploit the enhanced precision scaling.…”

Section: Measurement Schemesmentioning

confidence: 99%

Dynamical phase transitions as a resource for quantum enhanced metrology

et al. 2016

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We consider the general problem of estimating an unknown control parameter of an open quantum system. We establish a direct relation between the evolution of both system and environment and the precision with which the parameter can be estimated. We show that when the open quantum system undergoes a first-order dynamical phase transition the quantum Fisher information (QFI), which gives the upper bound on the achievable precision of any measurement of the system and environment, becomes quadratic in observation time (cf. "Heisenberg scaling"). In fact, the QFI is identical to the variance of the dynamical observable that characterizes the phases that coexist at the transition, and enhanced scaling is a consequence of the divergence of the variance of this observable at the transition point. This identification makes it possible to establish the finite time scaling of the QFI. Near the transition the QFI is quadratic in time for times shorter than the correlation time of the dynamics. In the regime of enhanced scaling the optimal measurement whose precision is given by the QFI involves measuring both system and output. As a particular realization of these ideas, we describe a theoretical scheme for quantum enhanced estimation of an optical phase shift using the photons being emitted from a quantum system near the coexistence of dynamical phases with distinct photon emission rates.

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Section: Measurement Schemesmentioning

confidence: 99%

Dynamical phase transitions as a resource for quantum enhanced metrology

et al. 2016

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“…We first consider a parity measurement scheme, which performs well without loss [28,31,49]. After creating the ECS we apply a linear phase shift φ to mode 1, giving:…”

Section: Simple Scheme Without Lossmentioning

confidence: 99%

“…A class of states that show the potential for a great improvement over these alternatives are the entangled coherent * phy5pak@leeds.ac.uk states (ECSs) [25][26][27][28][29][30]. Indeed Joo et al [31] used the quantum Fisher information (QFI) to show that ECSs can beat unentangled states and NOON states for most loss rates-including the higher loss rates inaccessible by other schemes.…”

Section: Introductionmentioning

confidence: 99%

Attaining subclassical metrology in lossy systems with entangled coherent states

2014

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Quantum mechanics allows entanglement enhanced measurements to be performed, but loss remains an obstacle in constructing realistic quantum metrology schemes. However, recent work has revealed that entangled coherent states (ECSs) have the potential to perform robust subclassical measurements [J. Joo et al., Phys. Rev. Lett. 107, 083601 (2011)]. Up to now no read-out scheme has been devised that exploits this robust nature of ECSs, but we present here an experimentally accessible method of achieving precision close to the theoretical bound, even with loss. We show substantial improvements over unentangled classical states and highly entangled NOON states for a wide range of loss values, elevating quantum metrology to a realizable technology in the near future.

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“…All single mode state inputs to the MZI result in path-symmetric states after passing through the first 50:50 beam splitter. The N00N state and the states that result inside the MZI from inputs such as the twin-Fock state [3], the Yuen state [19], the two mode squeezed-vacuum state [16], the coherent state mixed with squeezed-vacuum state [11,17,20], the pair-coherent state [21], which are capable of HL phase sensitivity, are all path-symmetric states. Based on what we prove, it suffices to measure the parity of photon number in one of the output modes alone, in place of number counting in both the modes, in order to achieve the QCRB of all such path-symmetric states, some of which can in turn reach the HL.…”

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confidence: 99%

Phase estimation at the quantum Cramér-Rao bound via parity detection

et al. 2013

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In this letter, we show that for all the so-called path-symmetric states, the measurement of parity of photon number at the output of an optical interferometer achieves maximal phase sensitivity at the quantum Cramer-Rao bound. Such optimal phase sensitivity with parity is attained at a suitable bias phase, which can be determined a priori. Our scheme is applicable for local phase estimation.PACS numbers: 42.50. St, 42.50.Dv, 42.50.Ex, 42.50.Lc Interferometry is a vital component of various precision measurement, sensing, and imaging techniques. It works based on mapping the quantity of interest on to the unknown phase of a system and estimating the latter; for example, the relative phase between the two modes or "arms" of an optical interferometer. Optical interferometry, often described in the Mach-Zehnder configuration, in general differs in the strategies of state preparation and detection. The conventional choice is to use a coherent light source and intensity difference detection. Assuming the unitary phase acquisition operator to be:(wheren a ,n b are the number operators associated with the modes,) the phase sensitivity of the conventional Mach-Zehnder interferometer (MZI) is bounded by the shot noise limit (SNL) δφ = 1/ √n (forn photons in the coherent state on average); whereas, protocols of quantum interferometry promise enhanced phase sensitivities by prescribing the use of states with nonclassical photon correlations and detection strategies that probe the particle nature of the output light, for example, via number counting [1]. As for such nonclassical states, the proposal to squeeze the vacuum state entering the unused port of the conventional MZI, by Caves in 1981, resulted in the first instance of a quantum-enhanced MZI capable of operating below the SNL [2]. Others, such as the twin-Fock state [3], the maximally path-entangled N00N state (|N, 0 + |0, N )/ √ 2, which reach the Heisenberg limit (HL) δφ = 1/N , were later proposed [4].Much of the latest experimental efforts in quantum interferometry have been focussed on attaining the HL [5]. The theory of quantum phase estimation aids in identifying potential schemes for such phase sensitivities [6]. It is based on the information-theoretical concept of the Cramer-Rao bound [7]. For the form of unitary phase acquisition considered in Eq. (1), the quantum CramerRao bound (QCRB)-an attribute of the quantum state input to the MZI alone (independent of detection)-at its best, can reach Heisenberg scaling in the absence of photon losses. On the other hand, the classical CramerRao bound (CCRB)-an attribute of the combination of a quantum state and detection strategy-can optimally reach the QCRB of the state. Uys and Meystre derived optimal quantum states, whose CCRB with number counting-based detection attains the HL in the absence of photon losses [8]. Lee et al. included photon losses to the problem and worked out the optimal inputs [9]. Meanwhile, Dorner et al. found optimal inputs in the presence of photon losses for the generic optimal detecti...

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Heisenberg-limited interferometry with pair coherent states and parity measurements

Cited by 73 publications

References 33 publications

Dynamical phase transitions as a resource for quantum enhanced metrology

Dynamical phase transitions as a resource for quantum enhanced metrology

Attaining subclassical metrology in lossy systems with entangled coherent states

Phase estimation at the quantum Cramér-Rao bound via parity detection

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