Measurement of damping and temperature: Precision bounds in Gaussian dissipative channels

Monràs, Alex; Illuminati, Fabrizio

doi:10.1103/physreva.83.012315

Cited by 81 publications

(79 citation statements)

References 48 publications

(94 reference statements)

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“…In general, neither the RLD bound nor the SLD bound is attainable [6]. Here the fundamental noncommutativity of quantum theory forbids simultaneously obtaining the optimal estimations of all parameters, and optimizing the measurement for one parameter will usually disturb the measurement precision on the others.…”

Section: Introductionmentioning

confidence: 99%

“…Then, we consider the problem of estimating the parameters of a Gaussian channel [6] describing the evolution of a bosonic mode a 1 , coupled with strength γ to a thermal bath mode υ 1 with mean excitation number N . The completely positive dynamics of the mode a 1 in the interaction frame under the Markovian approximation is represented by the unitary transformation…”

Section: Estimation Of Damping and Temperaturementioning

confidence: 99%

“…Most of the work on quantum parameter estimation are devoted to the SLD bound [6][7][8][9] (notable contributions are Refs. [10,11]).…”

Section: Introductionmentioning

confidence: 99%

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Bounds on quantum multiple-parameter estimation with Gaussian state

Gao

Lee

2014

Eur. Phys. J. D

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We investigate the quantum Cramer-Rao bounds on the joint multiple-parameter estimation with the Gaussian state as a probe. We derive the explicit right logarithmic derivative and symmetric logarithmic derivative operators in such a situation. We compute the corresponding quantum Fisher information matrices, and find that they can be fully expressed in terms of the mean displacement and covariance matrix of the Gaussian state. Finally, we give some examples to show the utility of our analytical results.

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Section: Introductionmentioning

confidence: 99%

Section: Estimation Of Damping and Temperaturementioning

confidence: 99%

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Bounds on quantum multiple-parameter estimation with Gaussian state

Gao

Lee

2014

Eur. Phys. J. D

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“…1). Thus, we reduce the estimate of the separation to the estimate of the transmissivity of a beam splitter [24][25][26][27][28][29][30]. In this way, not only we are able to compute the quantum Fisher information for any pair of sources but we also determine the optimal sources that saturate the ultimate precision bound.…”

mentioning

confidence: 99%

Ultimate Precision Bound of Quantum and Subwavelength Imaging

2016

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We determine the ultimate potential of quantum imaging for boosting the resolution of a far-field, diffractionlimited, linear imaging device within the paraxial approximation. First we show that the problem of estimating the separation between two point-like sources is equivalent to the estimation of the loss parameters of two lossy bosonic channels, i.e., the transmissivities of two beam splitters. Using this representation, we establish the ultimate precision bound for resolving two point-like sources in an arbitrary quantum state, with a simple formula for the specific case of two thermal sources. We find that the precision bound scales with the number of collected photons according to the standard quantum limit. Then we determine the sources whose separation can be estimated optimally, finding that quantum-correlated sources (entangled or discordant) can be super-resolved at the sub-Rayleigh scale. Our results set the upper bounds on any present or future imaging technology, from astronomical observation to microscopy, which is based on quantum detection as well as source engineering. Introduction. Quantum imaging aims at harnessing quantum features of light to obtain optical images of high resolution beyond the boundary of classical optics. Its range of potential applications is very broad, from telescopy to microscopy and medical diagnosis, and has motivated a substantial research activity [1][2][3][4][5][6][7][8][9][10]. Typically, quantum imaging is scrutinized to outperform classical imaging in two ways. First, to resolve details below the Rayleigh length (sub-Rayleigh imaging). Second, to improve the way the precision scales with the number of photons, by exploiting non-classical states of light. It is well known that a collective state of N quantum particles has an effective wavelength that is N times smaller than individual particles [11][12][13][14][15][16][17][18]. If N independent photons are measured one expects that the blurring of the image scales as 1/ √ N (known as standard quantum limit or shot-noise limit), while for N entangled photons one can sometimes achieve a 1/N scaling (known as the Heisenberg limit).

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“…(14). From the small-est of these symplectic eigenvalues, we can compute the logarithmic negativity, which is equal to E = max{0, − log 2d − } .…”

Section: Analysis Of the Correlationsmentioning

confidence: 99%

Optimal detection of losses by thermal probes

2011

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We consider the discrimination of lossy bosonic channels and focus to the case when one of the values for the loss parameter is zero, i.e., we address the detection of a possible loss against the alternative hypothesis of an ideal lossless channel. This discrimination is performed by inputting one-mode or two-mode squeezed thermal states with fixed total energy. By optimizing over this class of states, we find that the optimal inputs are pure, thus corresponding to single-and two-mode squeezed vacuum states. In particular, we show that for any value of the damping rate smaller than a critical value there is a threshold on the energy that makes the two-mode squeezed vacuum state more convenient than the corresponding single-mode state, whereas for damping larger than this critical value two-mode squeezed vacua are always better. We then consider the discrimination in realistic conditions, where it is unlikely to have pure squeezing. Thus by fixing both input energy and squeezing, we show that two-mode squeezed thermal states are always better than their singlemode counterpart when all the thermal photons are directed into the dissipative channel. Besides, this result also holds approximately for unbalanced distribution of the thermal photons. Finally, we also investigate the role of correlations in the improvement of detection. For fixed input squeezing (single-mode or two-mode), we find that the reduction of the quantum Chernoff bound is a monotone function of the two-mode entanglement as well as the quantum mutual information and the quantum discord. We thus verify that employing squeezing in the form of correlations (quantum or classical) is always a resource for loss detection whenever squeezed thermal states are taken as input.

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Measurement of damping and temperature: Precision bounds in Gaussian dissipative channels

Cited by 81 publications

References 48 publications

Bounds on quantum multiple-parameter estimation with Gaussian state

Bounds on quantum multiple-parameter estimation with Gaussian state

Ultimate Precision Bound of Quantum and Subwavelength Imaging

Optimal detection of losses by thermal probes

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