Entanglement protection via periodic environment resetting in continuous-time quantum-dynamical processes

Thomas Bullock, Francesco Cosco, Marwan Haddara, Sina Hamedani Raja, Oskari Kerppo, Leevi Leppäjärvi, Olli Siltanen, N. Walter Talarico, Antonella De Pasquale, Vittorio Giovannetti, and Sabrina Maniscalco

Phys. Rev. A 98, 042301 – Published 2 October 2018

Abstract

The temporal evolution of entanglement between a noisy system and an ancillary system is analyzed in the context of continuous-time open quantum system dynamics. Focusing on a couple of analytically solvable models for qubit systems, we study how Markovian and non-Markovian characteristics influence the problem, discussing in particular their associated entanglement-breaking regimes. These performances are compared with those one could achieve when the environment of the system is forced to return to its input configuration via periodic instantaneous resetting procedures.

Received 7 August 2018

DOI:https://doi.org/10.1103/PhysRevA.98.042301

Physics Subject Headings (PhySH)

Entanglement manipulation

Quantum Information, Science & Technology

Authors & Affiliations

Thomas Bullock, Francesco Cosco, Marwan Haddara, Sina Hamedani Raja, Oskari Kerppo, Leevi Leppäjärvi, Olli Siltanen, and N. Walter Talarico

QTF Centre of Excellence, Turku Centre for Quantum Physics, Department of Physics and Astronomy, University of Turku, FI-20014 Turun yliopisto, Finland

Antonella De Pasquale

Department of Physics and Astronomy, University of Florence, Via G. Sansone 1, 50019, Sesto Fiorentino (FI), Italy; INFN Sezione di Firenze, via G. Sansone 1, I-50019 Sesto Fiorentino (FI), Italy; and NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR, I-56127 Pisa, Italy

Vittorio Giovannetti

NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR, I-56127 Pisa, Italy

Sabrina Maniscalco

QTF Centre of Excellence, Turku Centre for Quantum Physics, Department of Physics and Astronomy, University of Turku, FI-20014 Turun yliopisto, Finland and QTF Centre of Excellence, Department of Applied Physics, Aalto University, FI-00076 Aalto, Finland

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Vol. 98, Iss. 4 — October 2018

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Images

Figure 1
Time evolution of the CJ concurrence (16) of the amplitude-damping channel (11) characterized by probability $P (t)$ of Eq. (19), in the non-Markovian regime with $α = 5 ω_{0}$ and $ℓ = 0.1 ω_{0}$ (blue solid line). The black dotted line on top corresponds to the exponential envelope of the curve, i.e., the function $e^{- ℓ t / 2}$ which incidentally corresponds to the CJ concurrence of the time-homogenous Markovian process of Eq. (14) with constant rate $λ = ℓ$ .
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Figure 2
(a) Time-dependent decay rate $γ_{k} (t)$ of Eq. (36) of the Pauli channel model, with $s_{k} = 2$ and $γ_{k} = 0.25$ . (b) Time evolution of the associated CJ concurrence $C (t)$ of Eq. (34) with time-dependent decay rate.
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Figure 3
CJ concurrence $C (t)$ for the Pauli channel model with uniform rates (37) as a function of time in the non-Markovian regime $2 α_{k} / λ_{k} > 1$ (blue line) and the decaying envelope (black dotted line above).
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Figure 4
Plot of the CJ concurrence (16) of the amplitude-damping evolution for $α = 5 ω_{0}$ and $ℓ = 0.1 ω_{0}$ , as a function of time without interruptions to the dynamics (solid blue line) and the envelope of its peaks (dotted black line). The dynamics of CJ concurrence (44) for the perturbed map are depicted for $τ^{'} < τ_{c}$ (red dot-dashed line), $τ^{''} > τ_{c}$ (dashed brown line), and for $τ = τ_{c}$ (wider-dashed green line). The inset shows the initial behavior of these functions.
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Figure 5
Temporal evolution of the unperturbed (blue solid curve) and perturbed CJ concurrences of a depolarizing channel, for two different values of $τ$ : $τ^{'} < τ_{c}$ (red dot-dashed) and $τ^{''} > τ_{c}$ (brown dashed). The dotted black curve shows the decaying envelope of the unperturbed dynamical map. The inset contains a zoom-in of the short-time behavior. All curves have been produced assuming the rates of the Pauli channel as in Eq. (37) with $α_{k} = 5 ω_{0}$ and $λ_{k} = 10^{- 3}$ for all $k$ .
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Figure 6
The effect of different instantaneous unitaries applied between the channels in the construction of the perturbed channels of Eq. (40). In each plot we show the CJ concurrence $C (t)$ of the unperturbed amplitude-damping processes $Φ_{0 \to t}$ without interruptions (solid blue line) and its decaying envelope (black dotted line), for $α = 5 ω_{0}$ and $λ = 0.1 ω_{0}$ as in Fig. 4. The temporal behavior of CJ concurrence of the associated perturbed maps (38) for different exemplary unitaries is shown by the red dot-dashed line: (a) the unitary is the identity operator, $θ = 0$ ; (b) $θ = 3.11$ and $ϕ = 0.5$ ; (c) $θ = 3.11$ and $ϕ = 1.2$ . The identity leads to optimal entanglement preservation (the same result has been verified numerically for other choices of the system parameters). Furthermore, as shown in panel (c), some choices of unitary $U$ can lead to the complete and irreversible destruction of entanglement in the state.
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