Experimental device-independent tests of classical and quantum entropy

Feng Zhu, Wei Zhang, Sijing Chen, Lixing You, Zhen Wang, and Yidong Huang

Phys. Rev. A 94, 062340 – Published 30 December 2016

Abstract

In quantum information processing, it is important to witness the entropy of the message in the device-independent way which was proposed recently [R. Chaves, J. B. Brask, and N. Brunner, Phys. Rev. Lett. 115, 110501 (2015)]. In this paper, we theoretically obtain the minimal quantum entropy for three widely used linear dimension witnesses, which is considered “a difficult question.” Then we experimentally test the classical and quantum entropy in a device-independent manner. The experimental results agree well with the theoretical analysis, demonstrating that entropy is needed in quantum systems that is lower than the entropy needed in classical systems with the given value of the dimension witness.

Received 10 May 2016

DOI:https://doi.org/10.1103/PhysRevA.94.062340

Physics Subject Headings (PhySH)

Entanglement measures Quantum communication Quantum cryptography

General PhysicsQuantum Information, Science & Technology

Authors & Affiliations

Feng Zhu¹, Wei Zhang^1,*, Sijing Chen², Lixing You², Zhen Wang², and Yidong Huang¹

¹Tsinghua National Laboratory for Information Science and Technology, Department of Electronic Engineering, Tsinghua University, Beijing 100084, China
²State Key Laboratory of Functional Materials for Informatics, Shanghai Institute of Microsystem and Information Technology (SIMIT), Chinese Academy of Sciences, Shanghai 200050, China

^*zwei@tsinghua.edu.cn

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Vol. 94, Iss. 6 — December 2016

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Images

Figure 1
Prepare-and-measure scenario.
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Figure 2
The minimal classical (red) and quantum (blue) entropies with the given values of different dimension witnesses. Panels (a), (b), and (c) are the results for the dimension witnesses $I_{3}, I_{4}$ , and $R_{4}$ . Panels (d), (e), and (f) are the differences between the minimal classical and quantum entropies for each dimension witness. The unit of the longitudinal coordinates in all figures is bit.
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Figure 3
The experimental setup. The left part is the state preparator. The linearly polarized pulsed pump light is generated by a passive mode-locked fiber laser with a repetitive rate of 40 MHz. Its linewidth is narrowed to 132 GHz by an optical filter (DWDM-1) with a central wavelength of 1552.52 nm. Then it is amplified by an erbium-doped fiber amplifier (EDFA). The noise produced by the EDFA is suppressed by another optical filter (DWDM-2). The correlated photon pairs are generated in a piece of dispersion-shifted fiber (DSF) with a length of 250 m. It is placed in a cryostat with the superconducting nanowire single-photon detectors (SNSPDs) used in this experiment and is cooled to 2.2 K to suppress the noise photons generated by the spontaneous Raman scattering. The signal and idler photons are selected and routed to two paths by the third optical filter (DWDM-3). Both of them have a linewidth of 63 GHz. Two polarization controllers (PC-1 and PC-2) and two polarization beam splitters (PBS-1 and PBS-2) are used to collimate the polarization of the signal and idler photons to the vertical direction. Then, the photons are coupled to free-space by two collimators (Col-1 and Col-2). The quarter-wave plate (QWP- $q_{s}^{(p)}$ ) and half-wave plates (HWP- $h_{s}^{(p)}$ and HWP- $h_{i}^{(p)}$ ) are used to encode the information on the state of the photon pairs. The right part is the measurement device. The input photons pass through two half-wave plates (HWP- $h_{s}^{(m)}$ and HWP- $h_{i}^{(m)}$ ) and two quarter-wave plates (QWP- $q_{s}^{(m)}$ and QWP- $q_{i}^{(m)}$ ), and then they are directed to four ports (a, b, c, and d) by two polarization beam splitters (PBS-3 and PBS-4). These components are used to realize the projection measurement of the biphoton states. Four collimators (Col-3 to Col-6) are used to couple the photons back to the fiber from different ports. The signal and idler photons from two specific ports are selected to be detected by two SNSPDs (fabricated by SIMIT, China). Their efficiencies and dark counts are about $40 %$ and 80 Hz, respectively. Before the single-photon detection, two additional optical filters (DWDM-4 and DWDM-5) are used to filter out the noise and two polarization controllers (PC-3 and PC-4) are used to collimate the polarizations of the photons since the efficiencies of the SNSPDs are polarization dependent. The detection events of the SNSPDs are recorded by a time-correlated single-photon counting module (TCSPC, PicoQuant, PicoHarp 400).
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Figure 4
The experimental results of the state $ρ$ and the message $M$ for $I_{3}, I_{4}$ , and $R_{4}$ . (a) Real part of ρ for $I_{3}$ , (b) Imaginary part of ρ for $I_{3}$ , (c) Distribution of $M$ for $I_{3}$ , (d) Results for $I_{3}$ , (e) Real part of $ρ$ for $I_{4}$ , (f) Imaginary part of $ρ$ for $I_{4}$ , (g) Distribution of $M$ for $I_{4}$ , (h) Results for $I_{4}$ , (i) Real part of $ρ$ for $R_{4}$ , (j) Imaginary part of $ρ$ for $R_{4}$ , (k) Distribution of $M$ for $R_{4}$ , and (l) Results for $R_{4}$ .
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