Playing nonlocal games with phases of quantum matter
- URL: http://arxiv.org/abs/2206.11252v2
- Date: Fri, 13 Jan 2023 21:10:10 GMT
- Title: Playing nonlocal games with phases of quantum matter
- Authors: Vir B. Bulchandani, Fiona J. Burnell and S. L. Sondhi
- Abstract summary: We show 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.
We further prove that the ground state of the exactly $d=1+1$ transverse-field Ising model can provide a quantum advantage for the parity game over an even wider region.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- 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.
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