Experimental evaluation of the nonclassical relation between measurement errors using entangled photon pairs as a probe

Masataka Iinuma, Masayuki Nakano, Holger F. Hofmann, and Yutaro Suzuki

Phys. Rev. A 98, 062109 – Published 7 December 2018

Abstract

We have experimentally evaluated the nonclassical relation between measurement errors in a joint measurement of two noncommuting polarizations by using entangled photon pairs as a probe. The joint measurement was realized by filtering polarization directions that are sensitive to both of the two target polarizations, and the same filtering procedures were applied independently to the two photons of an entangled pair. Since the statistically independent measurement errors of two identical measurements performed on entangled pairs will reduce an overall visibility of the correlation by the square of the local visibilities, the squared visibilities of the local measurements can be obtained directly from the measurement data. We apply this method to determine the visibility of the correlation between the products of the two noncommuting polarizations, a characteristic of the measurement errors that cannot be obtained locally since there is no self-adjoint operator that describes this product of measurement outcomes as a single-photon observable. The experimental results clearly show that the square of the product visibility is negative, indicating the nonclassical nature of the statistical relation between the measurement errors of noncommuting polarizations.

Received 15 July 2018

DOI:https://doi.org/10.1103/PhysRevA.98.062109

Physics Subject Headings (PhySH)

Quantum coherence & coherence measures Quantum foundations Quantum measurements

General Physics

Authors & Affiliations

Masataka Iinuma^*, Masayuki Nakano^†, and Holger F. Hofmann

Graduate School of Advanced Sciences of Matter, Hiroshima University, 1-3-1 Kagamiyama, Higashi-Hiroshima 739-8530, Japan

Yutaro Suzuki^‡

Department of Physics, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan

^*iinuma@hiroshima-u.ac.jp; http://home.hiroshima-u.ac.jp/qfg/qfg/index.html
^†Present address: NTTDATA Customer Service Corporation, Sumitomo Fudosan Toyosu Building 4F, 9-6, Edagawa 1-choume, Koto-ku, Tokyo 135-0051, Japan.
^‡Present address: Magellan Systems Japan, Inc., Amagasaki Research Incubation Center 315, 7-1-3, Doicho, Amagasaki, Hyogo 660-0083, Japan.

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Issue

Vol. 98, Iss. 6 — December 2018

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Images

Figure 1
Joint measurement of $\hat{X}$ and $\hat{Y}$ . The $m$ represents a pair of two outcomes $(x, y)$ and can take following four possibilities, $a = (+ 1, + 1), b = (+ 1, - 1), c = (- 1, + 1)$ , and $d = (- 1, - 1)$ . The joint measurement provides three experimentally obtained averages, ${〈 x 〉}_{exp}, {〈 y 〉}_{exp}$ , and ${〈 x y 〉}_{exp}$ , which are related to the expectation values in the initial state, ${〈 x 〉}_{0}, {〈 y 〉}_{0}$ , and the hypothetical initial expectation value ${〈 x y 〉}_{0}$ , through each visibility, which corresponds to the measurement error.
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Figure 2
Correlation measurement of the entangled pair with two local joint measurements. We can obtain three experimental correlations, ${〈 x_{1} x_{2} 〉}_{exp}, {〈 y_{1} y_{2} 〉}_{exp}$ , and ${〈 (x_{1} y_{1}) (x_{2} y_{2}) 〉}_{exp}$ , from two combination outcomes in the two joint measurements, which correspond to three initial correlations of the entangled input pairs. The overall visibilities of the two joint measurements can be expressed by a product of the two local visibilities, since the visibilities represent measurement errors that occur independently in the two local measurements.
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Figure 3
Experimental setup for entanglement generation and polarization measurements. Pump light is generated by a laser diode (LD) with a wavelength of 405 nm and an output power of 10 mW. The pump light passes through a Glan-Thompson (GT) prism and a half-wave-plate (HWP) before being reflected at a dichroic mirror (DM) and entering the triangle Sagnac-type interferometer through the double-polarization beam splitter (DPBS), where it pumped a periodically poled KTP (PPKTP) crystal from both sides, generating counterpropagating photon pairs. The double half-wave-plate (DHWP) rotates the polarization of both 405-nm pump light and 810-nm downconverted photons, generating the intended polarization entanglement by interference at the DPBS. Polarization filters for the two output ports are constructed by a sequence of quarter-wave-plate (QWP) and half-wave-plate (HWP) rotated to the appropriate angles and followed by a polarization beam splitter (PBS). After passing through a band-pass filter (BPF) with a bandwidth of about 1 nm, the photons were detected by the photon counting modules (Excelitas SPCM-AQS04) D1 and D2 and coincidence events were recorded based on the electronic signals from the detectors.
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Figure 4
Experimental results for the outcomes of (a) $s_{H V 1}$ and $s_{H V 2}$ , of (b) $s_{P M 1}$ and $s_{P M 2}$ , and of (c) the products $s_{H V 1} s_{P M 1}$ and $s_{H V 2} s_{P M 2}$ . The results clearly show that opposite results are most likely in all three cases. This presents a paradoxical situation in the case of the product correlation shown in (c), since the input correlation for the entangled state was positive, suggesting a higher probability for equal outcomes in the input state.
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