Statistical distance and the geometry of quantum states

Braunstein, Samuel L.; Caves, Carlton M.

doi:10.1103/physrevlett.72.3439

Cited by 2,623 publications

(3,368 citation statements)

References 9 publications

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“…Quantum Fisher information places the fundamental limit to the accuracy of estimating an unknown parameter, playing a paramount role in quantum metrology [4]. It is generalized from the classical Fisher information F ϕ in statistical inference.…”

Section: Quantum Fisher Informationmentioning

confidence: 99%

“…It quantifies the information that one can extract about a parameter from the observed probability distribution. Moving into the quantum regime, the extension of Fisher information is known as the quantum Fisher information (QFI), which predicts the theoretical achievable limit on the measurement precision in quantum metrology [2,3,4,5]. Besides the application in quantum metrology, QFI also plays an important role in the field of quantum information theory.…”

Section: Introductionmentioning

confidence: 99%

“…According to quantum Cramér-Rao theorem [2,3,4,5], the accuracy of estimation is asymptotically bounded by the inverse of QFI. Thus, the quantity χ 2 in equation (1) happens to be the average parameter estimation precision (APEP) of single particles.…”

Section: Introductionmentioning

confidence: 99%

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Quantum Fisher information and spin squeezing in one-axis twisting model

Zhong¹,

Liu²,

Ma³

et al. 2014

Chinese Phys. B

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Abstract. We consider the quantum Fisher information and spin squeezing in oneaxis twisting model with a coherent spin state |θ 0 , φ 0 . We analytically discuss the dependence of the two parameters: spin squeezing parameter ξ 2 K and the average parameter estimation precision χ 2 on the polar angle θ 0 and the azimuth angle φ 0 . Moreover, we discuss the effects of the collisional dephasing on the dynamics of the two parameters. In this case, the analytical solution of ξ 2 K is also obtained.

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Section: Quantum Fisher Informationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Quantum Fisher information and spin squeezing in one-axis twisting model

Zhong¹,

Liu²,

Ma³

et al. 2014

Chinese Phys. B

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“…This fact provides an additional motivation to investigate other possible metrics and distances in the space of mixed quantum states. Nowadays it is widely accepted that the Bures metric [5,6], is distinguished by its rather special properties: it is a Riemannian, monotone metric, which is Fisher-adjusted [1]: in the subspace of diagonal matrices it induces the statistical distance [7]. Moreover, it is also Fubini-Study-adjusted, since it agrees with this metric at the space of pure states [8].…”

Section: Introductionmentioning

confidence: 99%

Bures volume of the set of mixed quantum states

Sommers

Życzkowski

2003

J. Phys. A: Math. Gen.

161

294

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We compute the volume of the N 2 − 1 dimensional set MN of density matrices of size N with respect to the Bures measure and show that it is equal to that of a N 2 − 1 dimensional hyperhemisphere of radius 1/2. For N = 2 we obtain the volume of the Uhlmann hemisphere, 1 2 S 3 ⊂ R 4 . We find also the area of the boundary of the set MN and obtain analogous results for the smaller set of all real density matrices. An explicit formula for the Bures-Hall normalization constants is derived for an arbitrary N .

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“…For pure states, the Bures distance is just the natural distance in the complex projective Hilbert space, such that its infinitesimal form is the Fubini-Study metric [16,17,18]. Notably, the distance between mixed states (density matrices) is given by minimizing the distance between their respective purifications in a larger Hilbert space [19].…”

Section: Information Geometrymentioning

confidence: 99%

Renormalization group and quantum information

Gaite¹

2006

J. Phys. A: Math. Gen.

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The renormalization group is a tool that allows one to obtain a reduced description of systems with many degrees of freedom while preserving the relevant features. In the case of quantum systems, in particular, one-dimensional systems defined on a chain, an optimal formulation is given by White's "density matrix renormalization group". This formulation can be shown to rely on concepts of the developing theory of quantum information. Furthermore, White's algorithm can be connected with a peculiar type of quantization, namely, angular quantization. This type of quantization arose in connection with quantum gravity problems, in particular, the Unruh effect in the problem of black-hole entropy and Hawking radiation. This connection highlights the importance of quantum system boundaries, regarding the concentration of quantum states on them, and helps us to understand the optimal nature of White's algorithm.

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Statistical distance and the geometry of quantum states

Cited by 2,623 publications

References 9 publications

Quantum Fisher information and spin squeezing in one-axis twisting model

Quantum Fisher information and spin squeezing in one-axis twisting model

Bures volume of the set of mixed quantum states

Renormalization group and quantum information

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