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Temporal postselection and time as state

Blind Review

Published Apr 2, 2023• 0 citations
Publisher

Abstract

It is typically thought that indefinite causal order and some variants of holographic gravity are incompatible with the conventional quantum circuit model. These theoretic developments are saved from incompatibility when temporal (which can be causal order or 'time') postselection is introduced. To be natural, these require introducing time as a state in the quantum circuit framework, if no modification of the framework is to be made. Temporal postselection is not really different from spatial entanglement - once we have some knowledge of time or causal order information, a collapsed quantum state must be compatible with this knowledge. At least for all known cases, right before quantum measurements are made, causal order or time of an observer is fixed, which naturally leads to temporal postselection. If the 'time as a state' view is correct, then the postselection variants of quantum complexity classes become more central notions than the original classes. Despite this, an increasing difficulty level of physical implementations of computation models may be conjectured - heavy utilization of gravitational physics may be required for a temporal postselection-based quantum computation model to be physically realized.

DOI
10.31219/osf.io/dt9rg

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It is typically thought that indefinite causal order and some variants of holographic gravity are incompatible with the conventional quantum circuit model. These theoretic developments are saved from incompatibility when temporal (which can be causal order or 'time') postselection is introduced. To be natural, these require introducing time as a state in the quantum circuit framework, if no modification of the framework is to be made. Temporal postselection is not really different from spatial entanglement - once we have some knowledge of time or causal order information, a collapsed quantum state must be compatible with this knowledge. At least for all known cases, right before quantum measurements are made, causal order or time of an observer is fixed, which naturally leads to temporal postselection. If the 'time as a state' view is correct, then the postselection variants of quantum complexity classes become more central notions than the original classes. Despite this, an increasing difficulty level of physical implementations of computation models may be conjectured - heavy utilization of gravitational physics may be required for a temporal postselection-based quantum computation model to be physically realized.
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.
We propose a theoretical framework in which time is not a fundamental variable but an emergentproperty arising from the transition between indefinite and definite causal order in quantum processes.Building on the process matrix formalism and the established phenomenon of indefinite causal order,we introduce the concept of Pre-Time, a fully quantum domain where no global temporal directionexists and causal relations remain in coherent superposition. Within this framework, we define acausal-emergence measure λ(W ) that quantifies the distance between a given process matrix W andthe convex set of causally separable processes; λ(W ) > 0 identifies genuinely pre-temporal systems,whereas λ(W ) = 0 corresponds to the emergence of a classical temporal order. We show that, underincreasing decoherence or environmental coupling, any physically realizable process must undergo amonotonic reduction of λ(W ), providing a mathematical mechanism for the conformation of temporalorder. Within this framework, apparent retrocausal paradoxes associated with delayed-choice andquantum eraser experiments do not arise, since the “past” is not a pre-existing entity but a structureformed only upon causal consolidation. The model remains fully consistent with quantum mechanics,relativity, and thermodynamic irreversibility, while offering novel predictions about intermediatepre-temporal phases and the emergence of classical causality. Our results suggest that time ariseswhen the universe selects a definite causal order, and that the pre-temporal quantum regime may playa central role in foundational physics and future quantum-gravity research.
The study of causal relations has recently been applied to the quantum realm, leading to the discovery that not all physical processes have a definite causal structure. While indefinite causal processes have previously been experimentally shown, these proofs relied on the quantum description of the experiments. Yet, the same experimental data could also be compatible with definite causal structures within different descriptions. Here, we present the first demonstration of indefinite temporal order outside of quantum formalism. We show that our experimental outcomes are incompatible with a class of generalised probabilistic theories satisfying the assumptions of locality and definite temporal order. To this end, we derive physical constraints (in the form of a Bell-like inequality) on experimental outcomes within such a class of theories. We then experimentally invalidate these theories by violating the inequality using entangled temporal order. This provides experimental evidence that there exist correlations in nature which are incompatible with the assumptions of locality and definite temporal order.
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We study the notion of causal orders for the cases of (classical and quantum) circuits and spacetime events. We show that every circuit can be immersed into a classical spacetime, preserving the compatibility between the two causal structures. Using the process matrix formalism, we analyse the realisations of the quantum switch using 4 and 3 spacetime events in classical spacetimes with fixed causal orders, and the realisation of a gravitational switch with only 2 spacetime events that features superpositions of different gravitational field configurations and their respective causal orders. We show that the current quantum switch experimental implementations do not feature superpositions of causal orders between spacetime events, and that these superpositions can only occur in the context of superposed gravitational fields. We also discuss a recently introduced operational notion of an event, which does allow for superpositions of respective causal orders in flat spacetime quantum switch implementations. We construct two observables that can distinguish between the quantum switch realisations in classical spacetimes, and gravitational switch implementations in superposed spacetimes. Finally, we discuss our results in the light of the modern relational approach to physics.
The standard formulation of quantum theory relies on a fixed space-time metric determining the localisation and causal order of events. In general relativity, the metric is influenced by matter, and is expected to become indefinite when matter behaves quantum mechanically. Here, we develop a framework to operationally define events and their localisation with respect to a quantum clock reference frame, also in the presence of gravitating quantum systems. We find that, when clocks interact gravitationally, the time localisability of events becomes relative, depending on the reference frame. This relativity ia a signature of an indefinite metric, where events can occur in an indefinite causal order. Even if the metric is indefinite, for any event we can find a reference frame where local quantum operations take their standard unitary dilation form. This form is preserved when changing clock reference frames, yielding physics covariant with respect to quantum reference frame transformations.