Quantum correlations which imply causation.

Area of Science:

• Quantum Physics
• Quantum Information Theory
• Quantum Measurement

Background:

• In standard quantum mechanics, time is a parameter, not an observable, with states defined at single time instants.
• Quantum states typically extend across space but are confined to a single point in time.

Purpose of the Study:

• To explore the implications of defining quantum density matrices for multiple spatial and temporal measurements.
• To introduce a novel concept, the pseudo-density matrix (PDM), that treats space and time on an equal footing.
• To develop a measure of causality for quantum systems involving non-simultaneous measurements.

Main Methods:

• Conceptual introduction of the pseudo-density matrix (PDM) for simultaneous space-time considerations.
• Development and mathematical proof of a causality measure, demonstrating properties like monotonicity under local operations.
• Experimental validation using two-qubit Nuclear Magnetic Resonance (NMR) to observe PDM behavior.

Main Results:

• The pseudo-density matrix (PDM) is shown to be non-positive for non-simultaneous measurements, highlighting a breakdown of standard assumptions.
• A new measure of causality is defined, effectively discriminating between spatial and temporal correlations in quantum systems.
• NMR experiments demonstrate that temporal PDMs converge to valid density matrices with increasing decoherence between measurements.

Conclusions:

• The pseudo-density matrix (PDM) provides a framework for analyzing quantum states across space-time, revealing limitations of traditional approaches.
• The developed causality measure is essential for understanding the interplay of space and time in quantum correlations.
• Experimental results confirm the theoretical predictions, showing how decoherence bridges the gap between pseudo-density matrices and valid quantum states.