Experimental Demonstration of Coherent State Estimation with Minimal Disturbance

Andersen, Ulrik L.; Sabuncu, Metin; Filip, Radim; Leuchs, Gerd

doi:10.1103/physrevlett.96.020409

Cited by 38 publications

(52 citation statements)

References 21 publications

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“…The fundamental limit to the precision of the estimate in QPE is set by quantum mechanics [1,2]. Thus one of the key issues in QPE is the development of practical methodologies which allow measurements to approach or exceed the standard quantum limit (SQL) for a given measurement coupling [6,7,8,9,10,11,12]. Because of its wide-ranging technological relevance, the prime example of QPE is estimating an optical phase shift [13,14,15,16,17,18,19,20].…”

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confidence: 99%

Adaptive Optical Phase Estimation Using Time-Symmetric Quantum Smoothing

et al. 2010

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Quantum parameter estimation has many applications, from gravitational wave detection to quantum key distribution. We present the first experimental demonstration of the time-symmetric technique of quantum smoothing. We consider both adaptive and non-adaptive quantum smoothing, and show that both are better than their well-known time-asymmetric counterparts (quantum filtering). For the problem of estimating a stochastically varying phase shift on a coherent beam, our theory predicts that adaptive quantum smoothing (the best scheme) gives an estimate with a mean-square error up to 2 √ 2 times smaller than that from non-adaptive quantum filtering (the standard quantum limit). The experimentally measured improvement is 2.24 ± 0.14.PACS numbers: 42.50. Dv, 42.50.Xa, 03.65.Ta, 06.90.+v Quantum parameter estimation (QPE) is the problem of estimating an unknown classical parameter (or process) which plays a role in the preparation (or dynamics) of a quantum system [1,2], and is central to many fields including gravitational wave interferometry [5], quantum computing [3], and quantum key distribution [4]. The fundamental limit to the precision of the estimate in QPE is set by quantum mechanics [1,2]. Thus one of the key issues in QPE is the development of practical methodologies which allow measurements to approach or exceed the standard quantum limit (SQL) for a given measurement coupling [6,7,8,9,10,11,12]. Because of its wide-ranging technological relevance, the prime example of QPE is estimating an optical phase shift [13,14,15,16,17,18,19,20].Apart from some theoretical papers [19,20], work in this area of QPE has concentrated upon the problem of estimating a fixed, but unknown phase shift, which can be thought of as preparing the quantum state with an average phase equal to this parameter. It was shown theoretically [15] that for this problem adaptive homodyne measurements coupled with an optimal estimation filter can yield an estimate with mean-square error smaller than the standard quantum limit (as set by perfect heterodyne detection). This was demonstrated experimentally in Ref.[16] using very weak coherent states (for which the factor of improvement is at most 2). More recent theory and experiment have shown that interferometric measurements with photon counting can also be improved using adaptive techniques [17,18].A far richer, and in many cases more experimentally relevant, problem of quantum phase estimation arises when the phase evolves dynamically under the influence of an unknown classical stochastic process [19,20]. The general problem of estimating a classical process dynamically coupled to a quantum system under continuous measurement has recently been considered by Tsang [21], who introduced three main categories of quantum estimation: prediction or filtering, smoothing, and retrodiction. Of those, prediction or filtering is a causal estimation technique that can be used in real-time applications [24]. Smoothing and retrodiction are acausal and so cannot be used in real time, but they can be use...

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Adaptive Optical Phase Estimation Using Time-Symmetric Quantum Smoothing

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“…In this section, we will focus on Schrödinger particles since simultaneous measurements of quadrature amplitudes in quantum optics have already been implemented. 24 We will compare our implementation to the latter in the next section.…”

Section: Continuous Measurementsmentioning

confidence: 99%

Minimally disturbing Heisenberg–Weyl symmetric measurements using hard-core collisions of Schrödinger particles

Janzing

Decker

2006

Journal of Mathematical Physics

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In a previous paper we have presented a general scheme for the implementation of symmetric generalized measurements (POVMs) on a quantum computer. This scheme is based on representation theory of groups and methods to decompose matrices that intertwine two representations. We extend this scheme in such a way that the measurement is minimally disturbing, i.e., it changes the state vector |Ψ of the system to √ Π|Ψ where Π is the positive operator corresponding to the measured result.Using this method, we construct quantum circuits for measurements with Heisenberg-Weyl symmetry. A continuous generalization leads to a scheme for optimal simultaneous measurements of position and momentum of a Schrödinger particle moving in one dimension such that the outcomes satisfy ∆x∆p ≥ .The particle to be measured collides with two probe particles, one for the position and the other for the momentum measurement. The position and momentum resolution can be tuned by the entangled joint state of the probe particles which is also generated by a collision with hard-core potential. The parameters of the POVM can then be controlled by the initial widths of the wave functions of the probe particles. We point out some formal similarities and differences to simultaneous measurements of quadrature amplitudes in quantum optics.

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“…(5) of Ref. [17], for harmonic oscillator coherent states one can obtain the following expression for the optimal information-disturbance tradeoff…”

Section: Optimal Information-disturbance Tradeoffmentioning

confidence: 99%

“…The tradeoff between information retrieved from a quantum measurement and the disturbance caused on the state of a quantum system is a fundamental concept of quantum mechanics and has received a lot of attention in the literature [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20]. Such an issue is studied for both foundations and its enormous relevance in practice, in the realm of quantum key distribution and quantum cryptography [21,22].…”

Section: Introductionmentioning

confidence: 99%

“…The optimal tradeoff has been derived in the following cases: in estimating a single copy of an unknown pure state [7], many copies of identically prepared pure qubits [9] and qudits [14], a single copy of a pure state generated by independent phase-shifts [13], an unknown maximally entangled state [18], an unknown coherent state [17] and Gaussian state [19]. Experimental realization of minimal-disturbing measurements has been also reported [15,17]. Recently, the optimal tradeoff has been also derived for quantum state discrimination [20].…”

Section: Introductionmentioning

confidence: 99%

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