Optimal estimation of entanglement in optical qubit systems

Brida, G.; Degiovanni, I. P.; Florio, Angela; Genovese, M.; Giorda, Paolo; Meda, A.; Paris, Matteo G. A.; Shurupov, A. P.

doi:10.1103/physreva.83.052301

Cited by 32 publications

(34 citation statements)

References 48 publications

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“…Hence, any conceivable strategy aimed at evaluating the quantity of interest ultimately reduces to a parameter-estimation problem. Relevant examples of this situation are given by estimation of the quantum phase of a harmonic oscillator [12][13][14][15], the amount of entanglement of a bipartite quantum state [16][17][18], and the coupling constants of different kinds of interactions [19][20][21][22][23][24][25][26][27][28][29]. Here we focus on the estimation of temperature [30] and, motivated by recent experimental achievements [11], we specifically refer to schemes where a micromechanical resonator is coupled to a superconducting qubit, and then a measurement of the excited state population is performed on the qubit itself.…”

Section: Introductionmentioning

confidence: 99%

Qubit thermometry for micromechanical resonators

2011

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We address estimation of temperature for a micromechanical oscillator lying arbitrarily close to its quantum ground state. Motivated by recent experiments, we assume that the oscillator is coupled to a probe qubit via Jaynes-Cummings interaction and that the estimation of its effective temperature is achieved via quantum-limited measurements on the qubit. We first consider the ideal unitary evolution in a noiseless environment and then take into account the noise due to nondissipative decoherence. We exploit local quantum estimation theory to assess and optimize the precision of estimation procedures based on the measurement of qubit population and to compare their performances with the ultimate limit posed by quantum mechanics. In particular, we evaluate the Fisher information (FI) for population measurement, maximize its value over the possible qubit preparations and interaction times, and compare its behavior with that of the quantum Fisher information (QFI). We found that the FI for population measurement is equal to the QFI, i.e., population measurement is optimal, for a suitable initial preparation of the qubit and a predictable interaction time. The same configuration also corresponds to the maximum of the QFI itself. Our results indicate that the achievement of the ultimate bound to precision allowed by quantum mechanics is in the capabilities of the current technology.

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Section: Introductionmentioning

confidence: 99%

Qubit thermometry for micromechanical resonators

2011

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“…Comparing with (6), we can see that (26) constitutes a rotation of angle να, where ϕ-determined by the relative phase of E(t)-defines the rotation axis. Notice from (27) that ν is linearly proportional to the square root of the intensity of the pulse at the transition frequency.…”

Section: Unitary Operationmentioning

confidence: 96%

“…Our method for SCT may also improve the robustness of standard tomography, where calibrated unitary operations undergo small errors and fluctuations over the course of the 3 experiment. For other modifications to standard QST due to inaccessible information or preferable measurements choices, we refer the reader to [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30].…”

Section: Introductionmentioning

confidence: 99%

Self-calibrating quantum state tomography

et al. 2012

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We introduce and experimentally demonstrate a technique for performing quantum state tomography (QST) on multiple-qubit states despite incomplete knowledge about the unitary operations used to change the measurement basis. Given unitary operations with unknown rotation angles, our method can be used to reconstruct the density matrix of the state up to localσ z rotations as well as recover the magnitude of the unknown rotation angle. We demonstrate high-fidelity self-calibrating tomography on polarization-encoded one-and two-photon states. The unknown unitary operations are realized in two ways: using a birefringent polymer sheet-an inexpensive smartphone screen protector-or alternatively a liquid crystal wave plate with a tuneable retardance. We explore how our technique may be adapted for QST of systems such as biological molecules where the magnitude and orientation of the transition dipole moment is not known with high accuracy.

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“…The value of these quantities should be estimated through indirect measurements and thus their determination corresponds to a parameter estimation problem. [23][24][25][26] Local quantum estimation theory provides tools to determine the most precise estimator, solving the corresponding optimization problem. 13 Given a set of quantum states described by the one-parameter family of density operator , the estimation problem is that of¯nding an estimator, that is a map ¼ðÞ from the set of the outcomes to the space of parameters.…”

Section: Local Quantum Estimation Theorymentioning

confidence: 99%

Quantum limits to estimation of photon deformation

Cillis¹,

Paris

2014

Int. J. Quantum Inform.

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We address potential deviations of radiation field from the bosonic behaviour and employ local quantum estimation theory to evaluate the ultimate bounds to precision in the estimation of these deviations using quantum-limited measurements on optical signals. We consider different classes of boson deformation and found that intensity measurement on coherent or thermal states would be suitable for their detection making, at least in principle, tests of boson deformation feasible with current quantum optical technology. On the other hand, we found that the quantum signal-to-noise ratio (QSNR) is vanishing with the deformation itself for all the considered classes of deformations and probe signals, thus making any estimation procedure of photon deformation inherently inefficient. A partial way out is provided by the polynomial dependence of the QSNR on the average number of photon, which suggests that, in principle, it would be possible to detect deformation by intensity measurements on high-energy thermal states.Comment: 9 page

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Optimal estimation of entanglement in optical qubit systems

Cited by 32 publications

References 48 publications

Qubit thermometry for micromechanical resonators

Qubit thermometry for micromechanical resonators

Self-calibrating quantum state tomography

Quantum limits to estimation of photon deformation

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