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Physics Letters A

Estimation of the disorder degree of the classical static noise using three entangled qubits as quantum probes

Lionel Tenemeza Kenfack, Martin Tchoffo, Lukong Cornelius Fai

Published Jan 4, 2019• 4 citations
Publisher
DOI
10.1016/j.physleta.2018.12.043

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Optimized entanglement for quantum parameter estimation from noisy qubits

François Chapeau‐Blondeau

For parameter estimation from an [Formula: see text]-component composite quantum system, it is known that a separable preparation leads to a mean-squared estimation error scaling as [Formula: see text] while an entangled preparation can in some conditions afford a smaller error with [Formula: see text] 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 [Formula: see text]. To complement this asymptotic characterization, here we characterize how the estimation efficiency evolves as a function of the size [Formula: see text] 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 [Formula: see text] the efficiency of the optimal separable preparation to that of an entangled preparation with arbitrary degree of entanglement. We exhibit the [Formula: see text] superefficiency with no noise, and prove its asymptotic disappearance at large [Formula: see text] for any nonvanishing noise configuration. For maximizing the estimation efficiency, we characterize the existence of an optimum [Formula: see text] 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 [Formula: see text] qubits into independent blocks formed of [Formula: see text] entangled qubits restores at large [Formula: see text] a nonvanishing efficiency that can improve over that of [Formula: see text] independent qubits optimally prepared. Also, one inactive qubit included in the entangled probe sometimes stands as the most efficient setting for estimation. The results further attest with new characterizations the subtlety of entanglement for quantum information in the presence of noise, showing that when entanglement is beneficial, maximum efficiency is not necessarily obtained by maximum entanglement but instead by a controlled degree and finite optimal amount of it.

arXiv:1904.01904•International Journal of Quantum Information•Oct 1, 2018•7 citations
In the present paper, the joint effects of two kinds of classical environmental noises, without direct interaction among each other, on the dynamics of quantum correlations (QCs) of a three-qubit system coupled in independent environments is investigated. More precisely, we join the random telegraph noise (RTN) and the static noise (SN) and focus on the dynamics of entanglement and quantum discord (QD) when the qubits are initially prepared in the GHZ- and W-type states. The overall noise affecting the qubits is obtained by combining the RTN and SN in two different setups. The results show that the disorder of the environmental noise as well as its memory qualities and the purity of the initial state considered play a crucial role in the time evolution of the system in such a way that the dynamics of QCs can be controlled by varying them. In fact, we show that, depending on the initial state and noise regime considered, the rate of collapse of QCs may either decrease or increase with the increase of the degree of disorder of the SN, the switching rate of the RTN and the purity of the initial state.
We use a system of three non-interacting qubits as a quantum probe to classify three classical non-Gaussian noises (namely the static, colored (pink and brown) and random telegraph noise), according to their detrimental effects on the evolution of entanglement of the latter. The probe system is initially prepared in the GHZ state and coupled to the noises in independent environments. Seven configurations for the qubit-noise coupling (QNC) are considered. To estimate the destructive influence of each kind of noise, we employ the tripartite negativity to compare the evolution of entanglement in these QNC configurations to each other with the same noise parameters. The results show that the evolution of entanglement is drastically impacted by the QNC configuration considered as well as the properties of the environmental noises and that the SN is more detrimental to the survival of entanglement than the RTN and CN, regardless of the Markov or non-Markov character of the RTN and the color of the CN. We also observed that pink noise is more fatal to the system than the RTN and that the situation is totally reversed in the case of brown noise. Finally, we show that these noises, in descending order of destructive influence, can be classified as follows: SN>pink noise>RTN>brown noise.
For parameter estimation from an [Formula: see text]-component composite quantum system, it is known that a separable preparation leads to a mean-squared estimation error scaling as [Formula: see text] while an entangled preparation can in some conditions afford a smaller error with [Formula: see text] 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 [Formula: see text]. To complement this asymptotic characterization, here we characterize how the estimation efficiency evolves as a function of the size [Formula: see text] 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 [Formula: see text] the efficiency of the optimal separable preparation to that of an entangled preparation with arbitrary degree of entanglement. We exhibit the [Formula: see text] superefficiency with no noise, and prove its asymptotic disappearance at large [Formula: see text] for any nonvanishing noise configuration. For maximizing the estimation efficiency, we characterize the existence of an optimum [Formula: see text] 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 [Formula: see text] qubits into independent blocks formed of [Formula: see text] entangled qubits restores at large [Formula: see text] a nonvanishing efficiency that can improve over that of [Formula: see text] independent qubits optimally prepared. Also, one inactive qubit included in the entangled probe sometimes stands as the most efficient setting for estimation. The results further attest with new characterizations the subtlety of entanglement for quantum information in the presence of noise, showing that when entanglement is beneficial, maximum efficiency is not necessarily obtained by maximum entanglement but instead by a controlled degree and finite optimal amount of it.