Violations of a Leggett-Garg inequality without signaling for a photonic qutrit probed with ambiguous measurements

Rapid Communication

Violations of a Leggett-Garg inequality without signaling for a photonic qutrit probed with ambiguous measurements

Kunkun Wang, Clive Emary, Mengyan Xu, Xiang Zhan, Zhihao Bian, Lei Xiao, and Peng Xue

Phys. Rev. A 97, 020101(R) – Published 5 February 2018

Abstract

We realize a quantum three-level system with photons distributed among three different spatial and polarization modes. Ambiguous measurements of the state of the qutrit are realized by blocking one out for the three modes at any one time. Using these measurements we construct a test of a Leggett-Garg inequality as well as tests of no-signaling-in-time for the measurements. We observe violations of the Leggett-Garg inequality that cannot be accounted for in terms of signaling. Moreover, we tailor the qutrit dynamics such that both ambiguous and unambiguous measurements are simultaneously nonsignaling, which is an essential step for the justification of the use of ambiguous measurements in Leggett-Garg tests.

Received 21 November 2017

DOI:https://doi.org/10.1103/PhysRevA.97.020101

Physics Subject Headings (PhySH)

Quantum benchmarking Quantum information processing

Quantum Information, Science & Technology

Authors & Affiliations

Kunkun Wang¹, Clive Emary², Mengyan Xu¹, Xiang Zhan¹, Zhihao Bian¹, Lei Xiao¹, and Peng Xue^1,3,4,*

¹Department of Physics, Southeast University, Nanjing 211189, China
²Joint Quantum Centre (JQC) Durham-Newcastle, School of Mathematics, Statistics and Physics, Newcastle University, Newcastle-upon-Tyne, NE1 7RU, United Kingdom
³Beijing Computational Science Research Center, Beijing 100084, China
⁴State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200062, China

^*gnep.eux@gmail.com

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 97, Iss. 2 — February 2018

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Experimental setup for the test of LGI. The heralded single photons are created via type-I spontaneous parametric down-conversion in a $β$ -barium-borate (BBO) nonlinear crystal and are injected into the optical network (see figure for acronyms). The first polarizing beam splitter (PBS), half-wave plates (HWPs) at $45^{\circ}$ and ${BD}_{1}$ are used to generate the initial qutrit state. The evolution operations $U_{21}$ and $U_{32}$ are realized by HWPs and beam displacers (BDs). The projective measurement at time $t_{3}$ is realized via the last BD which maps the basis states of the qutrit into three spatial modes. Detecting heralded single photons means in practice registering coincidences between the trigger detector $D_{0}$ and each of the detectors for measurement $D_{1}$ , $D_{2}$ , and $D_{3}$ . The unambiguous and ambiguous measurements at time $t_{2}$ are realized by blocking two channels or one channel at a time.
Reuse & Permissions
Figure 2
Experimentally determined values of the LG correlator $K$ and the corresponding right-hand side $1 + Δ$ of the modified LGI, Eq. (4), with evolution parameters $θ_{1} = 0, χ_{1} = χ_{2} - π / 2 = π / 4, ϕ_{1} = ϕ_{2} = 0$ and a range of $θ_{2}$ values. These parameters are chosen to maxmize the value of the unambiguously measured $K$ . However, although we have $K \geq 1$ for all values of $θ_{2}$ , we have $K \leq 1 + Δ$ throughout the tested range. Thus when the observed signaling is taken into account, the modified LGI, Eq. (4), is never violated. For completeness, we also plot the ambiguously measured $K_{A}$ and $1 + Δ_{A}$ for the same parameters. Here, too, we observe $K_{A} \leq 1 \leq 1 + Δ_{A}$ and no violations are recorded. Theoretical predictions are represented by curves and lines, and the experimental results by symbols. Error bars include both the statistical uncertainty and the error due to the inaccuracy of the wave plate alignment.
Reuse & Permissions
Figure 3
Experimentally determined values of the LG correlator and upper bound for a second set of parameters: $θ_{1} = 0.831 π, χ_{1} = χ_{2} = 0.688 π, ϕ_{1} = ϕ_{2} = 0.423 π$ and a range of values of $θ_{2}$ . In this case, the focus is on the ambiguously measured correlator $K_{A}$ and its bound $1 + Δ_{A}$ . Results are also shown for the unambiguously measured $K$ and $1 + Δ$ . For $θ_{2} = 0.831 π$ , we observe a value of $K_{A} = 1.483 \pm 0.031$ while both $1 + Δ_{A}$ and $1 + Δ$ are close to 1, within experimental certainty. At this point, then, we observe LGI violations in the absence of signaling for both measurement types. Other details as in Fig. 2.
Reuse & Permissions
Figure 4
Experimentally determined values of the inferred joint probabilities $P^{'} (n_{3}, n_{2})$ (for $n_{2}, n_{3} = A, B, C$ ) as a function of the parameter $θ_{2}$ (the other parameters fixed as in Fig. 3). Theoretical predictions are represented by curves and lines, and the experimental results by symbols. That $P^{'}$ takes on negative values is indicative of the quantum-mechanical quasiprobabilistic nature of these quantities.
Reuse & Permissions

Physical Review A

covering atomic, molecular, and optical physics and quantum information