Fidelity of single qubit maps

Bowdrey, M. D.; Oi, Daniel K. L.; Short, Anthony; Banaszek, Konrad; Jones, Jonathan A.

doi:10.1016/s0375-9601(02)00069-5

Cited by 151 publications

(123 citation statements)

References 12 publications

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“…The trade-off between quantum coherence, a fundamental characteristic of quantumness in the system and mixing is studied. Useful parameters characterizing channel performance are the gate fidelity [50] as well as the average gate fidelity [51]. They represent how well a (noisy) gate performs the operation it is supposed to implement.…”

Section: Jhep02(2017)082mentioning

confidence: 99%

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Characterization of Unruh channel in the context of open quantum systems

Banerjee

Alok

Omkar

et al. 2017

J. High Energ. Phys.

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Abstract:In this work, we study an important facet of field theories in curved spacetime, viz. the Unruh effect, by making use of ideas of statistical mechanics and quantum foundations. Aspects of decoherence and dissipation, natural artifacts of open quantum systems, along with foundational issues such as the trade-off between coherence and mixing as well as various aspects of quantum correlations are investigated in detail for the Unruh effect. We show how the Unruh effect can be quantified mathematically by the Choi matrix approach. We study how environmentally induced decoherence modifies the effect of the Unruh channel. The differing effects of a dissipative or non-dissipative environment are noted. Further, useful parameters characterizing channel performance such as gate and channel fidelity are applied here to the Unruh channel, both with and without external influences. Squeezing, which is known to play an important role in the context of particle creation, is shown to be a useful resource in a number of scenarios.

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Section: Jhep02(2017)082mentioning

confidence: 99%

“…A useful way to understand this is to analyze the average gate and channel fidelities [46] of the Unruh channel under the ambient environmental conditions. The average gate fidelity [45,50,51] has a closed expression…”

Section: Average Gate and Channel Fidelitymentioning

confidence: 99%

Characterization of Unruh channel in the context of open quantum systems

Banerjee

Alok

Omkar

et al. 2017

J. High Energ. Phys.

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“…We then use the Horodecki's result to obtain an explicit formula for the average fidelity F (E, U ). The paper concludes with a discussion of how the formula for F (E, U ) may be useful for experimentally quantifying the quality of quantum gates and quantum channels.The present work is a development of the paper of Bowdrey et al [3], who obtained a simple formula for F (E, U ) when E and U act on qubits. This paper generalizes to the case where E and U act on qudits.…”

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confidence: 95%

A simple formula for the average gate fidelity of a quantum dynamical operation

2002

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This note presents a simple formula for the average fidelity between a unitary quantum gate and a general quantum operation on a qudit, generalizing the formula for qubits found by Bowdrey et al [Phys. Lett. A 294, 258 (2002)]. This formula may be useful for experimental determination of average gate fidelity. We also give a simplified proof of a formula due to Horodecki et al [Phys. Rev. A 60, 1888(1999], connecting average gate fidelity to entanglement fidelity.PACS numbers: 03.67.-a,03.65.-w,89.70.+c Characterizing the quality of quantum channels and quantum gates is a central task of quantum computation and quantum information [1]. The purpose of this note is to present a simple formula for the average fidelity of a quantum channel or quantum gate.The average fidelity of a quantum channel described by a trace-preserving quantum operation E [1] is defined bywhere the integral is over the uniform (Haar) measure dψ on state space, normalized so dψ = 1. We assume E acts on a qudit, that is, a d-dimensional quantum system, with d finite. We use the notational convention that ψ indicates either |ψ or |ψ ψ|, with the meaning determined by context. F (E) quantifies how well E preserves quantum information, with values close to one indicating information is preserved well, while values close to zero indicate poor preservation. F (E) may be extended to a measure of how well E approximates a quantum gate, U ,Note that F (E, U ) = 1 if and only if E implements U perfectly, while lower values indicate that E is a noisy implementation of U . Note that, and • denotes composition. The paper is structured as follows. First, we state and provide a simple proof of a result of M., P. and R. Horodecki connecting F (E) to the entanglement fidelity introduced in [2]. We then use the Horodecki's result to obtain an explicit formula for the average fidelity F (E, U ). The paper concludes with a discussion of how the formula for F (E, U ) may be useful for experimentally quantifying the quality of quantum gates and quantum channels.The present work is a development of the paper of Bowdrey et al [3], who obtained a simple formula for F (E, U ) when E and U act on qubits. This paper generalizes to the case where E and U act on qudits. Related results were also obtained by Fortunato et al [4,5] who found a simple and experimentally useful formula for the entanglement fidelity; [5] had also rediscovered the connection between average fidelity and entanglement fidelity proved in [6], for the special case of a qubit, thus enabling them to recover the results of [3].To define entanglement fidelity, imagine E acts on one half of a maximally entangled state. That is, if E acts on a qudit labelled Q, then imagine another qudit, R, with RQ initially in the maximally entangled state φ. The entanglement fidelity is defined to be the overlap between φ before and after the application of E [14], F e (E) ≡ φ|(I ⊗ E)(φ)|φ , where I denotes the identity operation on system R. The entanglement fidelity is thus a measure of how well entanglement wit...

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“…In a previous work [43] T , thus by adopting the Taylor series expansion of the time evolution operator U (t) = exp(Λt), one can compute the last column ofŨ (t) asŨ :,d 2 = (0, 0, . .…”

Section: Solution Of the Master Equationmentioning

confidence: 99%

State transfer in dissipative and dephasing environments

2010

Eur. Phys. J. D

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Abstract. By diagonalization of a generalized superoperator for solving the master equation, we investigated effects of dissipative and dephasing environments on quantum state transfer, as well as entanglement distribution and creation in spin networks. Our results revealed that under the condition of the same decoherence rate γ, the detrimental effects of the dissipative environment are more severe than that of the dephasing environment. Beside this, the critical time tc at which the transfer fidelity and the concurrence attain their maxima arrives at the asymptotic value t0 = π/2λ quickly as the spin chain length N increases. The transfer fidelity of an excitation at time t0 is independent of N when the system subjects to dissipative environment, while it decreases as N increases when the system subjects to dephasing environment. The average fidelity displays three different patterns corresponding to N = 4r + 1, N = 4r − 1 and N = 2r. For each pattern, the average fidelity at time t0 is independent of r when the system subjects to dissipative environment, and decreases as r increases when the system subjects to dephasing environment. The maximum concurrence also decreases as N increases, and when N → ∞, it arrives at an asymptotic value determined by the decoherence rate γ and the structure of the spin network.

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Fidelity of single qubit maps

Abstract: We give a simple way of characterising the average fidelity between a unitary and a general operation on a single qubit which only involves calculating the fidelities for a few pure input states

Cited by 151 publications

References 12 publications

Characterization of Unruh channel in the context of open quantum systems

Characterization of Unruh channel in the context of open quantum systems

A simple formula for the average gate fidelity of a quantum dynamical operation

State transfer in dissipative and dephasing environments

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