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Estimation of Phase and Diffusion: Combining Quantum Statistics and Classical Noise
Quantum Physics · Submitted 1 Jul 2013
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Unlike other noise types, it is shown for $N \gg 1$ that phase and diffusion can be measured simultaneously and optimally.
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The abstract, sentence by sentence
Coherent ensembles of $N$ qubits present an advantage in quantum phase estimation over separable mixtures, but coherence decay due to classical phase diffusion reduces overall precision. In some contexts, the strength of diffusion may be the parameter of interest. We examine estimation of both phase and diffusion in large spin systems using a novel mathematical formulation. For the first time, we show a closed form expression for the quantum Fisher information for estimation of a unitary parameter in a noisy environment. The optimal probe state has a non-Gaussian profile and differs also from the canonical phase state; it saturates a new tight precision bound. For noise below a critical threshold, entanglement always leads to enhanced precision, but the shot-noise limit is beaten only by a constant factor, independent of $N$. We provide upper and lower bounds to this factor, valid in low and high noise regimes. Unlike other noise types, it is shown for $N \gg 1$ that phase and diffusion can be measured simultaneously and optimally.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Coherent ensembles of $N$ qubits present an advantage in quantum phase estimation over separable mixtures, but coherence decay due to classical phase diffusion reduces overall precision. | background 1.00 | 0.06 | 0.06 | asserted 1.00 |
| s1 | In some contexts, the strength of diffusion may be the parameter of interest. | background 0.92 | 0.06 | 0.03 | hedged possibility 0.97 |
| s2 | We examine estimation of both phase and diffusion in large spin systems using a novel mathematical formulation. | contribution 0.90 | 0.93 | 0.07 | asserted 0.97 |
| s3 | For the first time, we show a closed form expression for the quantum Fisher information for estimation of a unitary parameter in a noisy environment. | contribution 0.58 | 0.95 | 0.18 | asserted 1.00 |
| s4 | The optimal probe state has a non-Gaussian profile and differs also from the canonical phase state; it saturates a new tight precision bound. | result 0.99 | 0.92 | 0.21 | asserted 1.00 |
| s5 | For noise below a critical threshold, entanglement always leads to enhanced precision, but the shot-noise limit is beaten only by a constant factor, independent of $N$. | result 0.99 | 0.88 | 0.27 | asserted 1.00 |
| s6 | We provide upper and lower bounds to this factor, valid in low and high noise regimes. | result 0.52 | 0.93 | 0.07 | asserted 0.99 |
| s7 | Unlike other noise types, it is shown for $N \gg 1$ that phase and diffusion can be measured simultaneously and optimally. | result 0.99 | 0.91 | 0.29 | asserted 1.00 |
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The paper
Original abstract
Coherent ensembles of $N$ qubits present an advantage in quantum phase estimation over separable mixtures, but coherence decay due to classical phase diffusion reduces overall precision. In some contexts, the strength of diffusion may be the parameter of interest. We examine estimation of both phase and diffusion in large spin systems using a novel mathematical formulation. For the first time, we show a closed form expression for the quantum Fisher information for estimation of a unitary parameter in a noisy environment. The optimal probe state has a non-Gaussian profile and differs also from the canonical phase state; it saturates a new tight precision bound. For noise below a critical threshold, entanglement always leads to enhanced precision, but the shot-noise limit is beaten only by a constant factor, independent of $N$. We provide upper and lower bounds to this factor, valid in low and high noise regimes. Unlike other noise types, it is shown for $N \gg 1$ that phase and diffusion can be measured simultaneously and optimally.
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References
How the literature uses it
27 arXiv papers cite this in 40 sentences
Papers citing it · 24 sentences without a confident label
Uses its method or tool 1 paper
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Recently, a different formulation was proposed, useful in the large $N$ case, where $F(θ)$ may be expanded as an exact asymptotic series [ref] :
Goldilocks Probes for Noisy Interferometry via Quantum Annealing to Criticality · Calculating Quantum Fisher Information · 0.96
Compares with it 2 papers
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This asymptotic disappearance of incompatibility agrees with the results of a direct QFI maximization in parallel strategies, reported in [ref] .
Probe incompatibility in multiparameter noisy quantum metrology · Phase and dephasing · 0.90
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These conclusions are therefore similar to the ones obtained in [ref] where a different model assuming collective instead of uncorrelated dephasing was analyzed and again asymptotic possibility of performing optimal simultanous estimation of phase and the dephasing parameter has been demonstrated.
Compatibility in Multiparameter Quantum Metrology · Estimation of phase and dephasing · 0.96
Cites it as background 11 papers
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Theoretical studies on the joint quantum-limited estimation of phase and phase diffusion using a quantum state comprised of a large number of qubits [ref] have been undertaken, as well as experimental studies on single qubit systems [ref] .
Reaching for the quantum limits in the simultaneous estimation of phase and phase diffusion · Introduction · 0.90
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Previous works in quantum metrology have analysed quantum-limited estimation of related noise parameters including loss [ref] , diffusion in phase shifts [ref] and displacements [ref] , and classical stochastic processes [ref] .
Quantum enhanced estimation of diffusion · Introduction · 1.00
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This has served as a common test for multiparameter estimation [ref] .
Fisher information susceptibility for multiparameter quantum estimation · Simultaneous estimation of phase and dephasing · 0.90
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