Trading causal order for locality

TL;DR

This paper demonstrates that quantum nonlocality without entanglement can be perfectly discriminated using local operations and classical communication when indefinite causal order is available, revealing a causal perspective on quantum nonlocality.

Contribution

It introduces a causal framework showing how indefinite causal order enables discrimination of QNLWE ensembles, which is impossible under fixed causal order.

Findings

Indefinite causal order allows perfect discrimination of certain QNLWE ensembles.

Multipartite generalizations of the AF/BW process exhibit QNLWE.

QNLWE ensembles have potential applications in cryptography and quantum operations.

Abstract

Quantum theory admits ensembles of quantum nonlocality without entanglement (QNLWE). These ensembles consist of seemingly classical states (they are perfectly distinguishable and non-entangled) that cannot be perfectly discriminated with local operations and classical communication (LOCC). Here, we analyze QNLWE from a causal perspective, and show how to perfectly discriminate some of these ensembles using local operations and classical communication without definite causal order. Specifically, three parties with access to an instance of indefinite causal order-the AF/BW process-can perfectly discriminate the states in a QNLWE ensemble--the SHIFT ensemble--with local operations. Hence, this type of quantum nonlocality disappears at the expense of definite causal order while retaining classical communication. Our results thereby leverage the fact that LOCC is a conjunction of three constraints: local operations, classical communication, and definite causal order. Moreover, we show how multipartite generalizations of the AF/BW process are transformed into multiqubit ensembles that exhibit QNLWE. Such ensembles are of independent interest for cryptographic protocols and for the study of separable quantum operations unachievable with LOCC.