Metrological resolution and minimum uncertainty states in linear and nonlinear signal detection schemes

Maldonado-Mundo, Daniel; Luis, Alfredo

doi:10.1103/physreva.80.063811

Cited by 17 publications

(20 citation statements)

References 45 publications

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“…Several Authors [80][81][82][83][84][85][86][87][88][89][90][91][92][93][94][95][96] have recently considered the possibility of using nonlinear effects to go beyond the N −1 Heisenberg-like scalings in phase estimation problems. These new regimes have been called "superHeisenberg" scalings in Ref.…”

Section: Beyond the Heisenberg Bound: Nonlinear Estimation Strategiesmentioning

confidence: 99%

“…[97]. Ultimately the idea of these proposals is to consider settings where the unitary transformation that "writes" the unknown parameter x into the probing signals, is characterized by many-body Hamiltonian generators which are no longer extensive functions of the number of probes employed in the estimation [83][84][85][86][87][88][89][90][91][92] or, for the optical implementations which yielded the inequality (6), in the photon number operator of the input signals [80][81][82][83][93][94][95][96]. Consequently, in these setups, the mapping (e −ixH ) ⊗n which acts on the input states ρ (n) 0 , gets replaced by a transformations of the form e −ixH (n) which couples the probes non trivially.…”

Section: Beyond the Heisenberg Bound: Nonlinear Estimation Strategiesmentioning

confidence: 99%

See 1 more Smart Citation

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: Beyond the Heisenberg Bound: Nonlinear Estimation Strategiesmentioning

confidence: 99%

Section: Beyond the Heisenberg Bound: Nonlinear Estimation Strategiesmentioning

confidence: 99%

Advances in quantum metrology

2011

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“…Concerning nonlinear schemes, the most simple example in the single-mode case is G =n k . Variance scaling as G ∝ n k can be reached by quadrature squeezed states, while quadrature coherent states lead to G ∝ n k−1/2 [7,10,16].…”

Section: Unbounded Number Of Particlesmentioning

confidence: 99%

“…Typical effective generators for light propagation in nonresonant nonlinear media are given by powers and products of photon-number operators of the form G =n k in a single-mode approach [4,5,7,8,16,24], G = J 2 z in a two-mode scheme [4], G = ⊗ k jn j in a multimode configuration [7], or even G = jn k j [23].…”

Section: Nonlinear Opticsmentioning

confidence: 99%

Quantum-limited metrology with nonlinear detection schemes

Luis

2010

J. Photon. Energy

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Quantum mechanics limit the resolution of detection schemes. Typical arrangements are based on linear processes, so that the corresponding quantum limits are usually understood as unsurpassable and ultimate. Recently it has been shown that nonlinear schemes allow signal detection and measurement with larger resolution than linear processes. In particular, this affects the quantum limits. We review the proposals introduced so far in this novel area of quantum metrology. C 2010 Society of Photo-Optical Instrumentation Engineers.

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“…(2.10). However, this is not quite so optimum strategy since some other probes may lead to smaller φ via a larger G even though they are not minimum [25].…”

Section: Simple Estimationmentioning

confidence: 99%