Environment-induced sudden change of coherence in quantum systems

Yu Meng, Shang Yu, Zhih-Ahn Jia, Yi-Tao Wang, Zhi-Jin Ke, Wei Liu, Zhi-Peng Li, Yuan-Ze Yang, Hang Wang, Yu-Chun Wu, Jian-Shun Tang, Chuan-Feng Li, and Guang-Can Guo

Phys. Rev. A 102, 042415 – Published 28 October 2020

Abstract

Manipulating dynamical evolution is an important task in quantum information. The sudden death phenomenon (SDP), which is predicted to be unattainable beyond entanglement [T. Yu and J. H. Eberly, Sudden death of entanglement, Science 323, 598 (2009)], would be an especially surprising feature in quantum coherence. In this paper, we modulate the spatial modes of photons and build a spatially inclined channel using a series of specially made quartz plate pairs. Within this channel, sudden changes in coherence occur in open-quantum systems. We, then, describe the SDP within a general theoretical framework of sudden quantum-coherence changes and by defining the $n th$ -order sudden coherence change. Moreover, by adding non-Markovian noise, we find that coherence can rebirth after a sudden death. We further compare the sudden change features in coherence and quantum entanglement. We find that both coherence and entanglement perform identical dynamical processes upon Bell diagonal states, although their dynamical characteristics change when the initial state is partially entangled. Our results provide insights into the sudden change phenomena of quantum correlations beyond entanglement along with intriguing perspectives on quantum coherence dynamics.

Received 14 May 2019
Revised 2 March 2020
Accepted 21 September 2020

DOI:https://doi.org/10.1103/PhysRevA.102.042415

Physics Subject Headings (PhySH)

Open quantum systems & decoherence Quantum channels Quantum coherence & coherence measures Quantum correlations in quantum information Quantum discord Quantum information processing Resource theories

General PhysicsQuantum Information, Science & Technology

Authors & Affiliations

Yu Meng ^1,2, Shang Yu ^1,2,*, Zhih-Ahn Jia^3,4,1,2,†, Yi-Tao Wang^1,2, Zhi-Jin Ke^1,2, Wei Liu^1,2, Zhi-Peng Li^1,2, Yuan-Ze Yang^1,2, Hang Wang^1,2, Yu-Chun Wu^1,2,‡, Jian-Shun Tang^1,2,§, Chuan-Feng Li ^1,2,∥, and Guang-Can Guo^1,2

¹CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China
²CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
³Microsoft Station Q, University of California, Santa Barbara, California 93106-6105, USA
⁴Department of Mathematics, University of California, Santa Barbara, California 93106-6105, USA

^*yushang@mail.ustc.edu.cn
^†giannjia@foxmail.com
^‡wuyuchun@ustc.edu.cn
^§tjs@ustc.edu.cn
^∥cfli@ustc.edu.cn

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Vol. 102, Iss. 4 — October 2020

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Images

Figure 1
Experimental setup. The whole experimental setup is divided into five parts: (i) generation of entangled photon pairs; (ii) remote preparation of the system state on path B; (iii) modulation of the spatial (environment) mode; (iv) dephasing through a channel composed of inclined quartz plates; (v) measurement of the system state. The initial environmental state is a spatial mode with a Gaussian-shaped facula, which can be tailored by the DMD into a ${| f (x) |}^{2}$ -shaped mode. Along the series of inclined quartz plates, the polarization and spatial degrees of freedom are coupled, and the inclination angle is varied to simulate the evolution time. The photons are, then, detected by a single-photon detector (SPD), and the value of the coherence (or entanglement is obtained by quantum state tomography.
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Figure 2
Simulation the non-Markovian noise on the DMD screen [the experimental results are shown in Fig. 3]. The enlarged image (right) highlights the periodic attributes. The grating constant ( $d = 27$ pixels) and the width of each seam ( $a = 18$ pixels) are clearly discernible. Here, $1 pixel = 13.7 μ m$ .
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Figure 3
Results of coherence sudden death and rebirth. (a) Evolution of coherence quantified by the $l_{1}$ norm and relative entropy (inset is an enlargement of the sudden death behavior). (b) Coherence measured by the $l_{1}$ norm, showing the discontinuous feature in the first-order derivative. (c) and (d) Coherence measured by the relative entropy, showing a continuous first-order derivative but a jump (sudden change) in the second-order derivative. (e) After adding a non-Markovian noise on the spatial mode, we observe a sudden birth (at $α = 0.160 rad$ ) after the sudden death (inset is an enlargement of the sudden birth feature). The errors (and those in subsequent figures) were derived using the Monte Carlo method.
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Figure 4
Derivative of coherence defined by the $l_{1}$ norm and relative entropy. (a) After adding the non-Markovian noise $N (x)$ , the discontinuous feature is detected at $α = 0.160 rad$ in the first-order derivative, showing a first-order sudden rebirth of coherence. (b) and (c) In the coherence defined by the relative entropy, the first-order derivative is continuous but a jump at $α = 0.160 rad$ appears in the second-order derivative, indicating a sudden change in the rebirth of coherence.
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Figure 5
Sudden change in coherence and entanglement. (a) Maximally entangled state situation. The coherence (black circles) and concurrence (red squares) simultaneously disappear at $α = 0.090 rad$ (green line). (b) Partially entangled state situation. The concurrence (red squares) is consumed completely, but the coherence decays up to $α = 0.090 rad$ (this period is shadowed in green). The red dashed line corresponding to the negative $Γ$ [53]. (c) Interval between the sudden changes in entanglement and coherence. The interval is extended when the mixing of the state increases ( $χ_{0}$ reduces).
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