Abstract
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.
Highlights
When describing physical phenomena it is commonly assumed that there exists an underlying causal order
We end by giving a second way in which one can express the connection between process matrices and two-time states via a mapping between operators that act on the Hilbert spaces in the process matrix formalism, and vectors in the Hilbert spaces of the two-time state formalism
In our paper we addressed the question of the relation between the process matrix formalism and quantum theory: does the process matrix formalism imply new phenomena, not present in quantum theory or not? We showed that correlations predicted by the process matrix formalism are identical to those obtainable in a subset of pre- and post-selected quantum states
Summary
Original content from this work may be used under the terms of the Creative Abstract. The possible existence of quantum processes with indefinite causal order has been extensively. Any further distribution of discussed, in particular using the formalism of process matrices. We give a new perspective on this this work must maintain attribution to the question, by establishing a direct connection to the theory of multi-time quantum states. We author(s) and the title of 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. 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
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