Trading Causal Order for Locality

Area of Science:

• Quantum Information Science
• Foundations of Quantum Mechanics
• Quantum Causality

Background:

• Quantum theory allows for quantum nonlocality without entanglement (QNLWE) ensembles.
• These ensembles comprise distinguishable, non-entangled states, yet are not perfectly separable using local operations and classical communication (LOCC).

Purpose of the Study:

• To analyze QNLWE from a causal perspective.
• To demonstrate the discrimination of QNLWE ensembles using indefinite causal order and local operations.

Main Methods:

• Analysis of QNLWE ensembles through a causal framework.
• Utilizing the Araújo-Feix-Baumeler-Wolf process, an instance of indefinite causal order.
• Application of local operations and classical communication (LOCC) without definite causal order.

Main Results:

• Perfect discrimination of the SHIFT QNLWE ensemble is achieved using indefinite causal order.
• Quantum nonlocality in these ensembles vanishes when a definite causal order is imposed.
• Multipartite generalizations of the Araújo-Feix-Baumeler-Wolf process generate multiqubit QNLWE ensembles.

Conclusions:

• Indefinite causal order is crucial for maintaining certain types of quantum nonlocality without entanglement.
• LOCC is fundamentally constrained by local operations, classical communication, and definite causal order.
• Generated multiqubit ensembles have implications for quantum cryptography and the study of separable quantum operations.