Quantum estimation of a damping constant

Venzl, Hannah; Freyberger, Matthias

doi:10.1103/physreva.75.042322

Cited by 21 publications

(22 citation statements)

References 27 publications

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“…We will focus on the theoretical attainable precision and not discuss the details of the implementation of the optimal observables. This will, nevertheless, provide a means to gauge the efficiency of more applied studies such as tomographic [29], single-mode Gaussian [30] and non-Gaussian [31], or entanglement-assisted schemes [32].…”

Section: The Ultimate Quantum Limitsmentioning

confidence: 99%

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

Monràs

Illuminati

2011

Phys. Rev. A

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We present a comprehensive analysis of the performance of different classes of Gaussian states in the estimation of Gaussian phase-insensitive dissipative channels. In particular, we investigate the optimal estimation of the damping constant and reservoir temperature. We show that, for two-mode squeezed vacuum probe states, the quantum-limited accuracy of both parameters can be achieved simultaneously. Moreover, we show that for both parameters two-mode squeezed vacuum states are more efficient than coherent, thermal, or single-mode squeezed states. This suggests that at high-energy regimes, two-mode squeezed vacuum states are optimal within the Gaussian setup. This optimality result indicates a stronger form of compatibility for the estimation of the two parameters. Indeed, not only the minimum variance can be achieved at fixed probe states, but also the optimal state is common to both parameters. Additionally, we explore numerically the performance of non-Gaussian states for particular parameter values to find that maximally entangled states within d-dimensional cutoff subspaces (d⩽6) perform better than any randomly sampled states with similar energy. However, we also find that states with very similar performance and energy exist with much less entanglement than the maximally entangled ones

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Section: The Ultimate Quantum Limitsmentioning

confidence: 99%

“…This problem has been partially addressed in the literature [30][31][32] with different degrees of generality. In previous studies, emphasis is placed in zero-temperature channels (N = 0).…”

Section: Estimating Loss γmentioning

confidence: 99%

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

Monràs

Illuminati

2011

Phys. Rev. A

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“…(21) to the case of thermal sources [see Eq. (27)] has been independently found by Nair and Tsang [42]; these authors also study tailored measurements that are almost optimal for estimating the separation between two thermal sources.…”

Section: Theorem 2 Consider Two Point-like Sources With Unknown Separmentioning

confidence: 99%

“…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.…”

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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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“…The estimation of the damping constant of a bosonic channel has been recently addressed by Refs. [21][22][23][24].…”

Section: Introductionmentioning

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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Quantum estimation of a damping constant

Cited by 21 publications

References 27 publications

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

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

Ultimate Precision Bound of Quantum and Subwavelength Imaging

Optimal detection of losses by thermal probes

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