Playing nonlocal games with phases of quantum matter

Abstract

The parity game is an example of a nonlocal game: by sharing a Greenberger-Horne-Zeilinger (GHZ) state before playing this game, the players can win with a higher probability than is allowed by classical physics. The GHZ state of $N$ qubits is also the ground state of the ferromagnetic quantum Ising model on $N$ qubits in the limit of vanishingly weak quantum fluctuations. Motivated by this observation, we examine the probability that $N$ players who share the ground state of a generic quantum Ising model, which exhibits non-vanishing quantum fluctuations, still win the parity game using the protocol optimized for the GHZ state. Our main result is a modified parity game for which this protocol asymptotically exhibits quantum advantage in precisely the ferromagnetic phase of the quantum Ising model. We further prove that the ground state of the exactly soluble $d=1+1$ transverse-field Ising model can provide a quantum advantage for the parity game over an even wider region, which includes the entire ferromagnetic phase, the critical point and part of the paramagnetic phase. By contrast, we find examples of topological phases and symmetry-protected topological (SPT) phases of matter, namely the deconfined phase of the toric code Hamiltonian and the ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$ SPT phase in one dimension, that do not exhibit an analogous quantum advantage away from their fixed points.

v2: 18+6 pages, 4 figures, close to published version

References in corpus (12)

• Non-Abelian Anyons and Topological Quantum Computation
• Classification of topological insulators and superconductors in three spatial dimensions
• Device-independent security of quantum cryptography against collective attacks
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Negativity and contextuality are equivalent notions of nonclassicality
• The contextual fraction as a measure of contextuality
• Universal quantum computation with little entanglement
• Diagnosing Deconfinement and Topological Order
• Chiral central charge from a single bulk wave function
• A universal tripartite entanglement signature of ungappable edge states
• Modeling Pauli measurements on graph states with nearest-neighbor classical communication
• Self testing quantum apparatus

Cited by in corpus (2)

• Playing nonlocal games across a topological phase transition on a quantum computer
• Entanglement and private information in many-body thermal states