Connecting processes with indefinite causal order and multi-time quantum states

Recently, the possible existence of quantum processes with indefinite causal order has been extensively discussed, in particular using the formalism of process matrices. Here we give a new perspective on this question, by establishing a direct connection to the theory of multi-time quantum states. Specifically, we show that process matrices are equivalent to a particular class of pre- and post-selected quantum states. This offers a new conceptual point of view to the nature of process matrices. Our results also provide an explicit recipe to experimentally implement any process matrix in a probabilistic way, and allow us to generalize some of the previously known properties of process matrices. Finally we raise the issue of the difference between the notions of indefinite temporal order and indefinite causal order, and show that one can have indefinite causal order even with definite temporal order.

[1]  S. Popescu,et al.  Multiple-Time States and Multiple-Time Measurements In Quantum Mechanics , 2007, 0712.0320.

[2]  B. Valiron,et al.  Quantum computations without definite causal structure , 2009, 0912.0195.

[3]  Stefan Wolf,et al.  Perfect signaling among three parties violating predefined causal order , 2013, 2014 IEEE International Symposium on Information Theory.

[4]  R. Stephenson.  A and V , 1962, The British journal of ophthalmology.

[5]  vCaslav Brukner,et al.  Witnessing causal nonseparability , 2015, 1506.03776.

[6]  C. Branciard,et al.  Multipartite causal correlations: Polytopes and inequalities , 2016, 1608.01528.

[7]  Vaidman,et al.  Superpositions of time evolutions of a quantum system and a quantum time-translation machine. , 1990, Physical review letters.

[8]  J. Lebowitz,et al.  TIME SYMMETRY IN THE QUANTUM PROCESS OF MEASUREMENT , 1964 .

[9]  N. Brunner,et al.  Pre- and postselected quantum states: Density matrices, tomography, and Kraus operators , 2013, 1308.2089.

[10]  N. Cerf,et al.  Operational quantum theory without predefined time , 2014, 1406.3829.

[11]  J. Urry.  Complexity , 2006, Interpreting Art.

[12]  J. Maldacena,et al.  The black hole final state , 2003, hep-th/0310281.

[13]  Exactly soluble dynamics of (p,q) string near macroscopic fundamental strings , 2004, hep-th/0411099.

[14]  G. Chiribella.  Perfect discrimination of no-signalling channels via quantum superposition of causal structures , 2011, 1109.5154.

[15]  Brane new world , 2000, hep-th/0003052.

[16]  Mateus Araújo,et al.  Computational advantage from quantum-controlled ordering of gates. , 2014, Physical review letters.

[17]  R. Spekkens,et al.  Quantum common causes and quantum causal models , 2016, 1609.09487.

[18]  Yakir Aharonov,et al.  Quantum Paradoxes: Quantum Theory for the Perplexed , 2005 .

[19]  Č. Brukner,et al.  Quantum correlations with no causal order , 2011, Nature Communications.

[20]  Seth Lloyd,et al.  Quantum mechanics of time travel through post-selected teleportation , 2010, 1007.2615.

[21]  Philip Walther,et al.  Experimental superposition of orders of quantum gates , 2014, Nature Communications.

[22]  Y. Aharonov,et al.  Complete description of a quantum system at a given time , 1991 .

[23]  L. Hardy.  Towards quantum gravity: a framework for probabilistic theories with non-fixed causal structure , 2006, gr-qc/0608043.

[24]  R. Spekkens,et al.  Towards a formulation of quantum theory as a causally neutral theory of Bayesian inference , 2011, 1107.5849.