A purification postulate for quantum mechanics with indefinite causal order

Mateus Araújo1,2,3, Adrien Feix1,2, Miguel Navascués2, and Časlav Brukner1,2

1Faculty of Physics, University of Vienna, Boltzmanngasse 5 1090 Vienna, Austria
2Institute for Quantum Optics and Quantum Information (IQOQI), Boltzmanngasse 3 1090 Vienna, Austria
3Institute for Theoretical Physics, University of Cologne, Germany

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To study which are the most general causal structures which are compatible with local quantum mechanics, Oreshkov $et$ $al.$ [1] introduced the notion of a process: a resource shared between some parties that allows for quantum communication between them without a predetermined causal order. These processes can be used to perform several tasks that are impossible in standard quantum mechanics: they allow for the violation of causal inequalities, and provide an advantage for computational and communication complexity. Nonetheless, no process that can be used to violate a causal inequality is known to be physically implementable. There is therefore considerable interest in determining which processes are physical and which are just mathematical artefacts of the framework. Here we make key progress in this direction by proposing a purification postulate: processes are physical only if they are purifiable. We derive necessary conditions for a process to be purifiable, and show that several known processes do not satisfy them.

Among the most fundamental concepts in physics are those of causality and reversibility. The first encapsulates the idea that events in the present are caused by events in the past and, in their turn, act as causes for events in the future. The second is the idea that physical processes are reversible, that is, that information is never created or destroyed.

Recently, a theoretical class of processes was found that do not respect causality, but nevertheless can not create logical paradoxes such as those where you travel back in time and kill your own grandfather. Whether such “non-causal” processes are physical and can be found in nature is an open question. In our paper we showed that there exists “non-causal” processes that do not generate paradoxes, but nevertheless violate the condition of reversibility. If reversibility is indeed respected in nature, then these processes must be unphysical.

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