Optimal parameter estimation of Pauli channels

Ruppert, László; Virosztek, Dániel; Hangos, Katalin M.

doi:10.1088/1751-8113/45/26/265305

Cited by 19 publications

(20 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…1-4 by the probability p, can be known to some extent, to appreciate whether its increase is pro¯table and have control on its tuning when implemented. For this purpose, estimation techniques can be employed [47][48][49], which to some extent rest on the same principles as those reported in Sec. 2.…”

Section: Discussionmentioning

confidence: 99%

Stochastic Resonance with Unital Quantum Noise

2019

View full text Add to dashboard Cite

The fundamental quantum information processing task of estimating the phase of a qubit is considered. Following quantum measurement, the estimation efficiency is evaluated by the classical Fisher information which determines the best performance limiting any estimator and achievable by the maximum likelihood estimator. The estimation process is analyzed in the presence of decoherence represented by essential quantum noises that can affect the qubit and belonging to the broad class of unital quantum noises. Such a class especially contains the bit-flip, the phase-flip, the depolarizing noises, or the whole family of Pauli noises. As the level of noise is increased, we report the possibility of non-standard behaviors where the estimation efficiency does not necessarily deteriorate uniformly, but can experience non-monotonic variations. Regimes are found where higher noise levels prove more favorable to estimation. Such behaviors are related to stochastic resonance effects in signal estimation, shown here feasible for the first time with unital quantum noises. The results provide enhanced appreciation of quantum noise or decoherence, manifesting that it is not always detrimental for quantum information processing.

show abstract

Section: Discussionmentioning

confidence: 99%

Stochastic Resonance with Unital Quantum Noise

2019

View full text Add to dashboard Cite

show abstract

“…, d − 1}. Their applications range between the quantum process tomography [13], optimal parameter estimation [14], and geometrical quantum mechanics [15]. In the theory of open quantum systems and non-Markovian dynamics, the channels and their evolution were analyzed in both the time-local evolution [9,16] and the memory kernel approach [17].…”

Section: Generalized Pauli Channelsmentioning

confidence: 99%

Regularized maximal fidelity of the generalized Pauli channels

Siudzińska

2019

Phys. Rev. A

View full text Add to dashboard Cite

We consider the asymptotic regularization of the maximal fidelity for the generalized Pauli channels, which is a problem similar to the classical channel capacity. In particular, we find the formulas for the extremal channel fidelities and the maximal output ∞-norm. For wide classes of channels, we show that these quantities are multiplicative. Finally, we find the regularized maximal fidelity for the channels satisfying the time-local master eqeuations.

show abstract

“…Suppose that the operation is applied once to each of m qubits, each of which is in the identical initial state, given by Eq. (23) and which appear leftmost in the mathematical representation of the entire system state. The final state of the collection of qubits isρ f = ρ f s ⊗ · · · ⊗ρ f s ⊗ρ 0 ⊗ · · · ⊗ρ 0 (m factors ofρ f s ) where the final state for the individual qubits to which the operation is applied isρ f s = (1 − λ)ρ 0 + λσ zρ0σz .…”

Section: Independent Channel Use Protocolmentioning

confidence: 99%

“…Parameter estimation for Pauli channels has been considered in the context of finding an optimal scheme using all possible input states of the quantum systems involved [7,[19][20][21][22][23]. The results, reviewed in Sec.…”

Section: Introductionmentioning

confidence: 99%

Mixed-state Pauli-channel parameter estimation

Collins

2013

Phys. Rev. A

View full text Add to dashboard Cite

The accuracy of any physical scheme used to estimate the parameter describing the strength of a single qubit Pauli channel can be quantified using standard techniques from quantum estimation theory. It is known that the optimal estimation scheme, with m channel invocations, uses initial states for the systems which are pure and unentangled and provides an uncertainty of O(1/ √ m). This protocol is analogous to a classical repetition and averaging scheme. We consider estimation schemes where the initial states available are not pure and compare a protocol involving quantum correlated states to independent state protocols analogous to classical repetition schemes. We show, that unlike the pure state case, the quantum correlated state protocol can yield greater estimation accuracy than any independent state protocol. We show that these gains persist even when the system states are separable and, in some cases, when quantum discord is absent after channel invocation. We describe the relevance of these protocols to nuclear magnetic resonance measurements.

show abstract

Optimal parameter estimation of Pauli channels

Cited by 19 publications

References 21 publications

Stochastic Resonance with Unital Quantum Noise

Stochastic Resonance with Unital Quantum Noise

Regularized maximal fidelity of the generalized Pauli channels

Mixed-state Pauli-channel parameter estimation

Contact Info

Product

Resources

About