Probabilistic and Statistical Aspects of Quantum Theory

Холево, Александр Семенович

doi:10.1007/978-88-7642-378-9

Cited by 1,278 publications

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“…For each value of g x and g p , we have a specific positive-operator-valued measure(POVM) which achieves the bound. Also, as in classical statistics, we have (Holevo, 1982),…”

Section: A Optimal Bounds For Gaussian Cloners Of Coherent Statesmentioning

confidence: 99%

Quantum cloning machines and the applications

et al. 2014

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No-cloning theorem is fundamental for quantum mechanics and for quantum information science that states an unknown quantum state cannot be cloned perfectly. However, we can try to clone a quantum state approximately with the optimal fidelity, or instead, we can try to clone it perfectly with the largest probability. Thus various quantum cloning machines have been designed for different quantum information protocols. Specifically, quantum cloning machines can be designed to analyze the security of quantum key distribution protocols such as BB84 protocol, six-state protocol, B92 protocol and their generalizations. Some well-known quantum cloning machines include universal quantum cloning machine, phase-covariant cloning machine, the asymmetric quantum cloning machine and the probabilistic quantum cloning machine etc. In the past years, much progress has been made in studying quantum cloning machines and their applications and implementations, both theoretically and experimentally. In this review, we will give a complete description of those important developments about quantum cloning and some related topics. On the other hand, this review is self-consistent, and in particular, we try to present some detailed formulations so that further study can be taken based on those results.

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“…For each value of g x and g p , we have a specific positive-operator-valued measure(POVM) which achieves the bound. Also, as in classical statistics, we have (Holevo, 1982),…”

Section: A Optimal Bounds For Gaussian Cloners Of Coherent Statesmentioning

confidence: 99%

Quantum cloning machines and the applications

et al. 2014

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“…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%

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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“…If we want to estimate θ through measuring ρ(θ ), the variance of θ is limited by a fundamental bound, which is given by the quantum Cramer-Rao (QCR) [42,43] inequality…”

Section: Atomic Quantum Fisher Information (Qfi)mentioning

confidence: 99%