title: Quantum correlations which imply causation.
abstract: 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. 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 (PDM) which treats space and time indiscriminately. This matrix in general fails to be positive for measurement events which do not occur simultaneously, motivating us to define a measure of causality that discriminates between spatial and temporal 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.
authors.affiliation: Singapore University of Technology and Design, 20 Dover Drive, Singapore 138682.|Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543.
authors.forename: Joseph F
authors.initials: JF
authors.lastname: Fitzsimons
authors.affiliation: Clarendon Laboratory, Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, U.K.
authors.forename: Jonathan A
authors.initials: JA
authors.lastname: Jones
authors.affiliation: Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543.|Clarendon Laboratory, Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, U.K.|Department of Physics, National University of Singapore, 2 Science Drive 3, Singapore 117542.
authors.forename: Vlatko
authors.initials: V
authors.lastname: Vedral