Manipulating the direction of Einstein-Podolsky-Rosen steering

Zhongzhong Qin, Xiaowei Deng, Caixing Tian, Meihong Wang, Xiaolong Su, Changde Xie, and Kunchi Peng

Phys. Rev. A 95, 052114 – Published 15 May 2017

Abstract

Einstein-Podolsky-Rosen (EPR) steering exhibits an inherent asymmetric feature that differs from both entanglement and Bell nonlocality, which leads to one-way EPR steering. Although this one-way EPR steering phenomenon has been experimentally observed, the schemes to manipulate the direction of EPR steering have not been investigated thoroughly. In this paper, we propose and experimentally demonstrate three schemes to manipulate the direction of EPR steering, either by varying the noise on one party of a two-mode squeezed state (TMSS) or transmitting the TMSS in a noisy channel. The dependence of the direction of EPR steering on the noise and transmission efficiency in the quantum channel is analyzed. The experimental results show that the direction of EPR steering of the TMSS can be changed in the presented schemes. Our work is helpful in understanding the fundamental asymmetry of quantum nonlocality and has potential applications in future asymmetric quantum information processing.

Received 28 November 2016

DOI:https://doi.org/10.1103/PhysRevA.95.052114

Physics Subject Headings (PhySH)

Entanglement manipulation Nonlocality Quantum information processing with continuous variables

Quantum Information, Science & TechnologyGeneral Physics

Authors & Affiliations

Zhongzhong Qin, Xiaowei Deng, Caixing Tian, Meihong Wang, Xiaolong Su^*, Changde Xie, and Kunchi Peng

State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Opto-Electronics, Shanxi University, Taiyuan 030006, People's Republic of China and Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, People's Republic of China

^*suxl@sxu.edu.cn

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Vol. 95, Iss. 5 — May 2017

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Figure 1
Schematic of nontrivial manipulation schemes. (a) Manipulation scheme I. One mode of the TMSS is transmitted over a lossy channel to Bob's station and the loss is modeled by a beam splitter with transmission efficiency $η$ . Vacuum state $\hat{ν}$ is coupled into the signal channel through another input port of the beam splitter. In this case, Alice adds a Gaussian noise with variance $δ_{A}$ to her state by using a beam splitter with transmission efficiency approaching unity. Alice and Bob make measurements on the amplitude and phase quadratures ${\hat{X}}_{A}$ , ${\hat{P}}_{A}$ and ${\hat{X}}_{B}$ , ${\hat{P}}_{B}$ of two remote modes by homodyne detectors, respectively. $V$ represents the variance of one mode of the TMSS. (b) Manipulation scheme II. Bob adds a Gaussian noise with variance $δ_{B}$ to his state by using a beam splitter with transmission efficiency approaching unity. (c) Manipulation scheme III. One mode of the TMSS is transmitted in a noisy channel with an excess noise higher than the vacuum noise. The excess noise with variance $δ_{C}$ is coupled to the state through the beam splitter.
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Figure 2
Schematic of the experimental setup. Laser beams at 540 and 1080 nm from a dual-wavelength laser are used as the pump and seed beams of a NOPA, respectively. Homodyne detections are performed at Alice's and Bob's stations, respectively. A half-wave plate and PBS are used to adjust the transmission efficiency of the channel to Bob's station. Noise at Alice's (or Bob's) station is added by mixing the signal with an auxiliary beam on a high transmissivity beam splitter (99:1), where the Gaussian white noises are modulated on the auxiliary beam by EOMs [Inset (a)]. The noisy channel is modeled by combining the signal channel and another auxiliary beam modulated by EOMs at a PBS followed by another half-wave plate and a PBS [Inset (b)]. DM, dichroic mirror; NOPA, nondegenerate optical parametric amplifier; LO, local oscillator; EOM, electro-optic modulator.
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Figure 3
Calculated parameter dependencies of EPR steering direction and experimental results. (a)–(c) Different regions of EPR steering for a TMSS with noise added to Alice's state, Bob's state, and the channel to Bob's station, respectively. The unit of noise is the shot noise level (SNL). Red curves and blue curves represent boundaries for $G^{A \to B} (σ_{A B}) \geq 0$ and $G^{B \to A} (σ_{A B}) \geq 0$ in three different cases, respectively. Region I corresponds to two-way steering $A \leftrightarrow B$ , while regions II and III correspond to one-way EPR steering $A \to B$ and $B \to A$ , respectively. The black dashed line $δ_{B} = (1 - η) (V - 1)$ in panel (b) and $δ_{C} = V - 1$ in panel (c) represent the condition for $det σ_{A} = det σ_{B}$ , i.e., $G^{A \to B} = G^{B \to A}$ . (d)–(f) Quantum steering of a TMSS as a function of transmission efficiency $η$ , with different amounts of noise added to Alice's state, Bob's state, and the channel to Bob's station, respectively. Solid lines and dashed lines show theoretical predictions of $G^{A \to B}$ and $G^{B \to A}$ , respectively. Blue lines in the three cases represent the situation in which there is no noise added ( $δ_{A, B, C} = 0$ ) but only the loss exists. Red lines and purple lines in panel (d) [panel (e)] represent $δ_{A} = 0.112$ $[δ_{B} = 0.112]$ and $δ_{A} = 0.201$ $[δ_{B} = 0.201]$ , respectively. Red lines and purple lines in (f) represent $δ_{C} = 0.251$ and $δ_{C} = 1$ , respectively. The variance of the original TMSS is chosen to be $V = 1.251$ in theoretical predictions, corresponding to $- 3$ dB squeezing. Error bars of experimental data represent $\pm 1$ standard deviation and are obtained based on the statistics of the measured data.
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