Optimized probing states for qubit phase estimation with general quantum noise

Chapeau‐Blondeau, François

doi:10.1103/physreva.91.052310

Cited by 28 publications

(64 citation statements)

References 27 publications

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“…When measuring ρ ξ for estimating ξ, the overall best efficiency is controlled by the quantum Fisher information F q (ξ) contained in the density operator ρ ξ about the parameter ξ [10,2]. By referring to the eigendecomposition of ρ ξ in its orthonormal eigenbasis ρ ξ = D j=1 λ j |λ j λ j |, one has access to the expression [29,2,6]…”

Section: The Estimation Taskmentioning

confidence: 99%

“…More complicated quantum noises exist, with an optimal probe maximizing F q (ξ) which is not orthogonal to the rotation axis n in Bloch representation, as exemplified in Ref. [6]. These are noises that do not share the commutation property with the rotations around n as it holds with the noise model of Eqs.…”

Section: The Estimation Taskmentioning

confidence: 99%

“…For applying the noise model of Eqs. (4)- (6) to the N-qubit entangled state of Eq. (9), it is convenient to use the equivalent characterization by the four transformations…”

Section: With N Entangled Qubitsmentioning

confidence: 99%

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Optimized entanglement for quantum parameter estimation from noisy qubits

Chapeau‐Blondeau

2018

Int. J. Quantum Inform.

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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, here 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 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 opt entangled qubits restores at large N a nonvanishing efficiency that can improve over that of N 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.

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Section: The Estimation Taskmentioning

confidence: 99%

Section: The Estimation Taskmentioning

confidence: 99%

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Optimized entanglement for quantum parameter estimation from noisy qubits

Chapeau‐Blondeau

2018

Int. J. Quantum Inform.

Self Cite

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“…Efforts have been made along these directions, for example, in [30] where a systematic study was made of the problem of Fisher information in the presence of a number of well-known noisy channels such as the phase damping, which is essentially a QND channel and generalised amplitude damping (GAD) channel, which is a subset of the SGAD channel. A similar study was also made in [31] where the problem of estimation of probe states with the feature of best resistance to noise was studied. In both of these works, the geometric visualisation offered by the Bloch vector formalism was made use of in estimating the Fisher information.…”

Section: Quantum Fisher Information In the Bloch Vector Formalismmentioning

confidence: 99%

“…The estimation of the initial state parameters has been of interest for quite some time and in recent years this approach has been turned towards state estimation in the context of open quantum systems [30,31].…”

Section: Introductionmentioning

confidence: 99%

Quantum Fisher and skew information for Unruh accelerated Dirac qubit

2016

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We develop a Bloch vector representation of the Unruh channel for a Dirac field mode. This is used to provide a unified, analytical treatment of quantum Fisher and skew information for a qubit subjected to the Unruh channel, both in its pure form as well as in the presence of experimentally relevant external noise channels. The time evolution of Fisher and skew information is studied along with the impact of external environment parameters such as temperature and squeezing. The external noises are modelled by both purely dephasing phase damping and the squeezed generalised amplitude damping channels. An interesting interplay between the external reservoir temperature and squeezing on the Fisher and skew information is observed, in particular, for the action of the squeezed generalised amplitude damping channel. It is seen that for some regimes, squeezing can enhance the quantum information against the deteriorating influence of the ambient environment. Similar features are also observed for the analogous study of skew information, highlighting a similar origin of the Fisher and skew information.

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Quantum image coding with a reference-frame-independent scheme

Chapeau‐Blondeau

Belin

2016

Quantum Inf Process

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For binary images, or bit planes of non-binary images, we investigate the possibility of a quantum coding decodable by a receiver in the absence of reference frames shared with the emitter. Direct image coding with one qubit per pixel and non-aligned frames leads to decoding errors equivalent to a quantum bit-flip noise increasing with the misalignment. We show the feasibility of frame-invariant coding by using for each pixel a qubit pair prepared in one of two controlled entangled states. With just one common axis shared between the emitter and receiver, exact decoding for each pixel can be obtained by means of two two-outcome projective measurements operating separately on each qubit of the pair. With strictly no alignment information between the emitter and receiver, exact decoding can be obtained by means of a two-outcome projective measurement operating jointly on the qubit pair. In addition, the frame-invariant coding is shown much more resistant to quantum bit-flip noise compared to the direct non-invariant coding. For a cost per pixel of two (entangled) qubits instead of one, complete frame-invariant image coding and enhanced noise resistance are thus obtained.

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Optimized probing states for qubit phase estimation with general quantum noise

Cited by 28 publications

References 27 publications

Optimized entanglement for quantum parameter estimation from noisy qubits

Optimized entanglement for quantum parameter estimation from noisy qubits

Quantum Fisher and skew information for Unruh accelerated Dirac qubit

Quantum image coding with a reference-frame-independent scheme

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