ISSN 0253-2778

CN 34-1054/N

Open AccessOpen Access JUSTC Physics 04 August 2022

Twenty years of quantum contextuality at USTC

Cite this:
https://doi.org/10.52396/JUSTC-2022-0073
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  • Author Bio:

    Zheng-Hao Liu received his Ph.D. degree from the University of Science and Technology of China in 2022. He was a laureate of the Wang Daheng Optical Award in 2021, the Outstanding Doctoral Dissertation of USTC in 2022, and the national Ph.D. fellowship of China in 2021. His research interest is optical tests of quantum foundations and quantum computing. Further information about him is available at https://manekimeow.github.io/

    Jin-Shi Xu is a Professor at the University of Science and Technology of China (USTC). He received his Ph.D. degree from USTC in 2009. His research field is quantum optics and quantum information. He is now focusing on optical quantum simulation and constructing spin-photon interfaces

    Chuan-Feng Li is a Professor at the University of Science and Technology of China (USTC). He received his Ph.D. degree from USTC in 1999. His research field is quantum optics and quantum information. He is now focusing on constructing quantum network and exploring quantum physics with quantum technology

  • Corresponding author: E-mail: jsxu@ustc.edu.cn; E-mail: cfli@ustc.edu.cn
  • Received Date: 30 April 2022
  • Accepted Date: 11 July 2022
  • Available Online: 04 August 2022
  • Quantum contextuality is one of the most perplexing and peculiar features of quantum mechanics. Concisely, it refers to the observation that the result of a single measurement in quantum mechanics depends on the set of joint measurements actually performed. The study of contextuality has a long history at the University of Science and Technology of China (USTC). Here we review the theoretical and experimental advances in this direction achieved at USTC over the last twenty years. We start by introducing the renowned simplest proof of state-independent contextuality. We then present several experimental tests of quantum versus noncontextual theories with photons. Finally, we discuss the investigation of the role of contextuality in general quantum information science and its application in quantum computation.
    Contextuality causes the result of a quantum measurement to depend on the whole setof co-measured observables. Figure courtesy of Siyuan Ma.
    Quantum contextuality is one of the most perplexing and peculiar features of quantum mechanics. Concisely, it refers to the observation that the result of a single measurement in quantum mechanics depends on the set of joint measurements actually performed. The study of contextuality has a long history at the University of Science and Technology of China (USTC). Here we review the theoretical and experimental advances in this direction achieved at USTC over the last twenty years. We start by introducing the renowned simplest proof of state-independent contextuality. We then present several experimental tests of quantum versus noncontextual theories with photons. Finally, we discuss the investigation of the role of contextuality in general quantum information science and its application in quantum computation.
    • The research advances regarding quantum contextuality at USTC in the new century are discussed.
    • The review presents both theoretical and experimental progresses, with an insight into quantum contextuality’s application in quantum information and quantum computing.
    • The fruitful study of quantum contextuality at USTC signifies its spearheading role in the exploration of quantum science.

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    Figure  1.  The Yu-Oh 13-ray appearing in the state-independent proof of contextuality by Yu and Oh[21]. Left: the geometric representation of the rays in a unit cube. The rays are defined as $y^{-}_{1} =(0,1,-1),\; y_{2} ^{-} =(-1,0,1),\; y_{3} ^{-} =(1,-1,0),\; y_{1} ^{+} =(0,1,1),\; y_{2} ^{+} =(1,0,1),\; y_{3} ^{+} =(1,1,0),\; h_{0} =(1,1,1),\; h_{1} =(-1,1,1),\; h_{2} =(1,-1,1),\; $$ h_{3} =(1,1,-1),\; z_{1} =(1,0,0),\; z_{2} =(0,1,0),\; z_{3} =(0,0,1).$ Right: the orthogonality relationship among the set of rays. Each vertex represents a ray; when two vertices are linked by an edge, the corresponding rays are orthogonal. Figure taken from Ref. [21].

    Figure  2.  Contextuality from a Platonic graph. (a) A regular icosahedron is a Platonic solid with 12 vertices and 20 edges. (b) The icosahedron graph (vertices 1–12) is the skeleton of the icosahedron. With the auxiliary vertices 13–16 every vertex belongs to a 4-clique, and the graph’s complement graph has a Lovász orthogonal representation[151] in dimension 4. (c) The violation of the noncontextuality inequality dual to the icosahedron graph decreases with the linear entropy of a quantum state characterizing the mixedness of the state. Figure taken from Ref. [40].

    Figure  3.  First experimental test of contextuality at USTC. Main: experimental setup. A heralded single photon’s path and polarization degrees of freedom encode two qubits. The half-wave plates and polarizing beam splitters inside the two Mach-Zehnder interferometers conducted the first joint path-polarization measurement and that after the interferometers executed the second joint measurement. HWP half-wave plate and PBS polarizing beam splitter. Inset: Experimental result showing event probabilities in accord with the predictions of the noncontextual hidden-variable and quantum theories. Figure adapted from Ref. [23].

    Figure  4.  A “standard” experimental setup for testing noncontextuality inequalities containing up to two-point correlations with a photonic qutrit system. To extract the two-point correlation without prematurely destroying the photon, the measurement result of the first observable is registered in the path degree of freedom. The inset shows the experimental violation of the noncontextuality inequality (17) for seven pure states and the maximally mixed state. Figure adapted from Ref. [47].

    Figure  5.  Simplification of contextuality experiments. Top: implementing successive measurements poses the main technical challenge on photonic contextuality experiments. Middle: by adopting the graph-theoretical approach to contextuality, the required number of sequential measurements can be reduced to one. Bottom: by assuming the Lüders’ rule, the sequential measurement can be substituted by a destructive measurement and a repreparation procedure, thus completely lifting the requirement of sequential measurements from contextuality experiments at the price of some conceptual disadvantages. Figure taken from Ref. [36].

    Figure  6.  A photonic prepare-and-measure setup for testing graph-theoretic noncontextuality inequalities. (a)-(c) With the repreparation procedure, the two-point correlations can be calculated via Eq. (13) and Eq. (19). (d) Experimental results of the contextuality test. (e) Verification of the no-signaling condition. Figure taken from Ref. [38].

    Figure  7.  A high-dimensional photonic prepare-and-measure setup, where the quantum information was encoded on the orbital angular momentum degree of freedom.

    Figure  8.  Observation of an all-versus-nothing contextuality. (a) Experimental setup. By pumping a nonlinear crystal twice, the two photons received by the two observers became path-polarization hyperentangled. Different apparatuses were devised to measure different path observables. (b) Predictions by noncontextual hidden-variable theory (left) and quantum theory (right) on the probabilities of events in Eq. (23). (c) Experimental results and the quantum prediction are in accord. Figure taken from Ref. [75]

    Figure  9.  Experimental setup for observing a compatibility-loophole-free contextuality. Part A implemented state preparation, where maximally entangled qutrits were generated on the photonic path degrees of freedom. Part B implemented qutrit measurements, where the path states of the photons were analyzed. Figure taken from Ref. [87].

    Figure  10.  Behaviors of topological contextuality under braiding and local noise. (a) A Bloch sphere illustrating the effect of $ \mathbb{Z}_3 $-parafermion braiding on the encoded qutrit. A geometric phase of $ 2\pi/3 $ is obtained between one and the other two computational bases. (b) The real parts of the theoretical (edge) and experimental (filling) braiding process matrices. (c) Permutation of the magic contextuality witnesses. (d) The violations of magic noncontextuality inequality (32) were almost invariant for the sample states. (e) The real parts of the theoretical (edge) and experimental (filling) local noise process matrices. (f) The dynamics of magic contextuality under hopping noise for a topologically-protected qutrit (blue) and under flip noise for a trivial (not protected) qutrit (orange). Figure adapted from Ref. [107].

    Figure  11.  Setup for observation of nonlocality activated by local contextuality. (a) Schematic illustration of the experiment. Alice and Bob share two pairs of Bell states. Alice implements a contextuality test on her qubits and checks the correlations of her observables with Bob’s. (b) Devices for measuring the nine observables in the contextuality test. (c) Experimental result demonstrating the activation of nonlocality from local contextuality. Figure adapted from Ref. [126].

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