Abstract
Nonlocal games yield an unusual perspective on entangled quantum states. The defining property of such games is that a set of players in joint possession of an entangled state can win the game with higher probability than is allowed by classical physics. Here we construct a nonlocal game that can be won with certainty by 2N players if they have access to the ground state of the toric code on as many qubits. By contrast, the game cannot be won by classical players more than half the time in the large N limit. Our game differs from previous examples because it arranges the players on a lattice and allows them to carry out quantum operations in teams, whose composition is dynamically specified. This is natural when seeking to characterize the degree of quantumness of nontrivial many-body states, which potentially include states in much more varied phases of matter than the toric code. We present generalizations of the toric code game to states with ZM topological order.
| Original language | English (US) |
|---|---|
| Article number | 035409 |
| Journal | Physical Review B |
| Volume | 107 |
| Issue number | 3 |
| DOIs | |
| State | Published - Jan 15 2023 |
Bibliographical note
Funding Information:We thank I. Arad, D. S. Borgnia, A. B. Grilo, R. M. Nandkishore, and especially U. V. Vazirani for helpful discussions. V. B. B. is supported by a fellowship at the Princeton Center for Theoretical Science. F. J. B. is supported by NSF Grant No. DMR-1928166, and is grateful to the Carnegie Corporation of New York and the Institute for Advanced Study, where part of this work was carried out. This work was supported by a Leverhulme Trust International Professorship Grant No. LIP-202-014 (S. L. S). For the purpose of Open Access, the author has applied a CC BY public copyright licence to any Author Accepted Manuscript version arising from this submission.
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© 2023 American Physical Society.