Tsirelson bounds for quantum correlations with indefinite causal order.

Area of Science:

• Quantum Information Science
• Foundations of Quantum Mechanics

Background:

• Bell inequalities constrain correlations in definite causal orders.
• Maximum quantum violation of causal inequalities (Tsirelson-like bounds) is an open problem.

Purpose of the Study:

• To develop a general method for bounding violations of arbitrary causal inequalities.
• To establish limits for correlations in local experiments and quantum processes with indefinite causal order.

Main Methods:

• Derivation of a general method for bounding causal inequality violations.
• Determination of Tsirelson-like bounds for a class of causal inequalities.

Main Results:

• The maximum quantum violation of causal inequalities is generally less than the algebraic maximum.
• Tsirelson-like bounds were determined for paradigmatic causal inequalities.

Conclusions:

• The study provides a method to bound quantum correlations in indefinite causal order scenarios.
• Results motivate the search for physical principles defining the boundary of quantum correlations with indefinite causal order.