Source-linked AI summary
Quantum correlations which imply causation
Joseph Fitzsimons, Jonathan Jones, Vlatko Vedral
TL;DR
The paper asks how quantum states and correlations can be represented across multiple spatial and temporal measurement events, rather than at one time. It introduces pseudo-density matrices and a trace-norm causality measure, proves monotonicity under local operations, and uses NMR experiments to study decoherence-driven transitions toward valid density matrices.
Problem
Standard quantum density matrices describe a state at one time, motivating a framework that treats spatial and temporal measurement correlations together.
Method
The paper defines pseudo-density matrices from multi-event Pauli correlations and introduces the trace-norm measure ftr(R) = ||R||tr −1 to quantify temporal character.
Results
Pseudo-density matrices can have negative eigenvalues for timelike correlations, while the causality measure is a monotone under local operations and NMR experiments show decoherence-dependent causal transitions.
Takeaways & Limitations
Nonpositive pseudo-density matrices certify a temporal element in the correlations, although positive matrices do not establish spacelike separation.
Abstract
from arXiv · showhide
In ordinary, non-relativistic, quantum physics, time enters only as a parameter and not as an observable: a state of a physical system is specified at a given time and then evolved according to the prescribed dynamics. While the state can, and usually does, extend across all space, it is only defined at one instant of time, in conflict with special relativity where space and time are treated on an equal footing. Here we ask what would happen if we defined the notion of the quantum density matrix for multiple spatial and temporal measurements. We introduce the concept of a pseudo-density matrix which treats space and time indiscriminately. This matrix in general fails to be positive for timelike separated measurements, motivating us to define a measure of causality that discriminates between spacelike and timelike correlations. Important properties of this measure, such as monotonicity under local operations, are proved. Two qubit NMR experiments are presented that illustrate how a temporal pseudo-density matrix approaches a genuinely allowed density matrix as the amount of decoherence is increased between two consecutive measurements.