While quantum computers are expected to yield considerable advantages over classical devices, the precise features of quantum theory enabling these advantages remain unclear. Contextuality—the denial of a notion of classical physical reality—has emerged as a promising hypothesis. Magic states are quantum resources critical for practically achieving universal quantum computation. They exhibit th...

The Pauli groups are ubiquitous in quantum information theory because of their usefulness in describing quantum states and operations and their readily understood symmetry properties. In addition, the most well-understood quantum error correcting codes—stabilizer codes—are built using Pauli operators. The eigenstates of these operators—stabilizer states—display a structure (e.g., mutual orthogo...

We discuss quantum non-locality and contextuality using the notion of transition sets [1, 2]. This approach provides a way to obtain a direct logical contradiction with locality/non-contextuality in the EPRB gedanken experiment as well as a clear graphical illustration of what violations of Bell inequalities quantify. In particular, we show graphically how these violations are related to measur...

Contextuality is a central property in comparative analysis of classical, quantum, and supercorrelated systems. We examine and compare two well-motivated approaches to contextuality. One approach (“contextuality-by-default”) is based on the idea that one and the same physical property measured under different conditions (contexts) is represented by different random variables. The other approach...

In classical physics, properties of objects exist independently of the context, i.e., whether and how measurements are performed. Quantum physics showed this assumption to be wrong, and that Nature is indeed "contextual". Contextuality has been observed in the simplest physical systems, such as single particles, and plays fundamental roles in quantum computation advantage. Here, we demonstrate ...

A central question in quantum computation is to identify the resources that are responsible for quantum speed-up. Quantum contextuality has been recently shown to be a resource for quantum computation with magic states for odd-prime dimensional qudits and two-dimensional systems with real wave functions. The phenomenon of state-independent contextuality poses a priori an obstruction to characte...

In this essay, I develop order-theoretic notions of determinism and contextuality on domains and topoi. In the process, I develop a method for quantifying contextuality and show that the order-theoretic sense of contextuality is analogous to the sense embodied in the topos-theoretic statement of the Kochen–Specker theorem. Additionally, I argue that this leads to a relation between the entropy ...

We present unambiguous experimental evidence for (quantum-like) probabilistic contextuality in psychology. All previous attempts to find contextuality in a psychological experiment were unsuccessful because of the gross violations of marginal selectivity in behavioral data, making the traditional mathematical tests developed in quantum mechanics inapplicable. In our crowdsourcing experiment res...

L. F. Wei,1,2 Koji Maruyama,2 X.-B. Wang,2,3 J. Q. You,2,4 and Franco Nori2,5 1Quantum Optoelectronics Laboratory, Southwest Jiaotong University, Chengdu 610031, China 2Advanced Science Institute, The Institute of Physical and Chemical Research (RIKEN), Wako-shi, Saitama 351-0198, Japan 3Department of Physics, Tsinghua University, Beijing 100084, China 4Department of Physics and State Key Labor...