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Optimized entanglement for quantum parameter estimation from noisy qubits
- Source :
- International Journal of Quantum Information, Vol. 16, No. 07 (2018) 1850056 (25 pages)
- Publication Year :
- 2019
-
Abstract
- For parameter estimation from an $N$-component composite quantum system, it is known that a separable preparation leads to a mean-squared estimation error scaling as $1/N$ while an entangled preparation can in some conditions afford a smaller error with $1/N^2$ scaling. This quantum superefficiency is however very fragile to noise or decoherence, and typically disappears with any small amount of random noise asymptotically at large $N$. To complement this asymptotic characterization, we characterize how the estimation efficiency evolves as a function of the size $N$ of the entangled system and its degree of entanglement. We address a generic situation of qubit phase estimation, also meaningful for frequency estimation. Decoherence is represented by the broad class of noises commuting with the phase rotation, which includes depolarizing, phase-flip, and thermal quantum noises. In these general conditions, explicit expressions are derived for the quantum Fisher information quantifying the ultimate achievable efficiency for estimation. We confront at any size $N$ the efficiency of the optimal separable preparation to that of an entangled preparation with arbitrary degree of entanglement. We exhibit the $1/N^2$ superefficiency with no noise, and prove its asymptotic disappearance at large $N$ for any non-vanishing noise configuration. For maximizing the estimation efficiency, we characterize the existence of an optimum $N_{\rm opt}$ of the size of the entangled system along with an optimal degree of entanglement. For nonunital noises, maximum efficiency is usually obtained at partial entanglement. Grouping the $N$ qubits into independent blocks formed of $N_{\rm opt}$ entangled qubits restores at large $N$ a nonvanishing efficiency that can improve over that of $N$ independent qubits optimally prepared. One inactive qubit in the entangled probe sometimes is most efficient for estimation.<br />Comment: 23 pages, 8 figures, 40 references
- Subjects :
- Quantum Physics
Subjects
Details
- Database :
- arXiv
- Journal :
- International Journal of Quantum Information, Vol. 16, No. 07 (2018) 1850056 (25 pages)
- Publication Type :
- Report
- Accession number :
- edsarx.1904.01904
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1142/S0219749918500569