What does it mean for a causal structure to be 'unknown'? Can we even talk about 'repetitions' of an experiment without prior knowledge of causal relations? And under what conditions can we say that a set of processes with arbitrary, possibly indefinite, causal structure are independent and identically distributed? Similar questions for classical probabilities, quantum states, and quantum channels are beautifully answered by so-called "de Finetti theorems", which connect a simple and easy-to-justify condition – symmetry under exchange – with a very particular multipartite structure: a mixture of identical states/channels. Here we extend the result to processes with arbitrary causal structure, including indefinite causal order and multi-time, non-Markovian processes applicable to noisy quantum devices. The result also implies a new class of de Finetti theorems for quantum states subject to a large class of linear constraints, which can be of independent interest.

Any given prescription of quantum time travel necessarily endows a Hilbert space to the chronology-violating (CV) system on the closed timelike curve (CTC). However, under the two foremost models, Deutsch's prescription (D-CTCs) and postselected teleportation (P-CTCs), the CV system is treated very differently: D-CTCs assign a definite form to the state on this system, while P-CTCs do not. To further explore this distinction, we present a methodology by which an operational notion of state may be assigned to their respective CV systems. This is accomplished via a conjunction of state tomography and weak measurements, with the latter being essential in leaving any notions of self-consistency intact. With this technique, we are able to verify the predictions of D-CTCs and, perhaps more significantly, operationally assign a state to the system on the P-CTC. We show that, for any given combination of chronology-respecting input and unitary interaction, it is always possible to recover the unique state on the P-CTC, and we provide a few specific examples in the context of select archetypal temporal paradoxes. We also demonstrate how this state may be derived from analysis of the P-CTC prescription itself, and we explore how it compares to its counterpart in the CV state predicted by D-CTCs.

We investigate timelike and null geodesics within the rotating “time machine” spacetime proposed by Ralph, T.C.; et al. Phys. Rev. D 2020, 102, 124013. This is a rotating analogue of Alcubierre’s warp drive spacetime. We obtain geodesics that begin and end in the surrounding flat space region, yet achieve time travel relative to static observers there. This is a global property, as the geodesics remain locally future-pointing, as well as timelike or null.

According to the general theory of relativity, time can flow at different rates depending on the configuration of massive objects, affecting the temporal order of events. Combined with quantum theory, this gravitational effect can result in events with an indefinite temporal order when a massive object is prepared in a suitable quantum state. This was argued to lead to a theory-independent test of the nonclassical order of events through the violation of Bell-type inequalities for temporal order. Here we show that the theory independence of this protocol is problematic: one of the auxiliary assumptions in the above approach turns out to be essential, while it is explicitly theory dependent. To illustrate this problem, we construct a complete scenario where accelerating particles interacting with optical cavities result in a violation of temporal Bell inequalities. Due to the equivalence principle, the same problem arises when one considers the gravitational case, and thus theory-dependent additional assumptions are needed behind Bell inequalities for temporal order to interpret a violation of the final inequalities as a signature of indefinite temporal order.