The D-CTC Condition in Quantum Field Theory

Abstract

A condition proposed by David Deutsch to describe analogues of processes in the presence of closed timelike curves (D-CTC condition) in bipartite quantum systems is investigated within the framework of local relativistic quantum field theory. The main result is that in relativistic quantum field theory on spacetimes where closed timelike curves are absent, the D-CTC condition can nevertheless be fulfilled to arbitrary precision, under very general, model-independent conditions. Therefore, the D-CTC condition should not be taken as characteristic for quantum processes in the presence of closed timelike curves in the sense of general relativity. This report is a very condensed extract of the publication [35]. A new result showing that the D-CTC condition can be approximately fulfilled by entangled states is also presented.

The D-CTC Condition is Generically Fulfilled in Classical (Non-quantum) Statistical Systems

“…In [17] we have pointed out that the results in [16] (as well as in [17]) on whether the D-CTC condition can be fulfilled or not depend very much on the assumptions made, and on whether one insists that the D-CTC condition is fulfilled exactly, or just approximately (to arbitrary precision). In fact the question of the adequate mathematical idealization is a common problem when trying to explore unchartered territory in physics by theoretical methods.…”

“…The results obtained in [16,17] are, roughly, as follows (we give here a mainly qualitative description and refer to the cited references for full details). States fulfilling the D-CTC condition cannot be found if the states are also required to fulfill a Reeh-Schlieder like property [18] which implies a strong form of entanglement [21].…”

“…In a recent paper [16] (see also [17] for a summary), we have investigated the D-CTC condition in the setting of operator-algebraic quantum field theory [18]. It is useful to briefly outline some of the basic elements of that approach as it helps to make parallels between the D-CTC condition as formulated above for quantum 1 The article [8] portrays quantum mechanics as a natural mechanism for avoiding paradoxes that would occur in the presence of CTCs in the framework of classical physics; however in [4] it is pointed out that forming statistical mixtures would in a similar way allow it to avoid those paradoxes.…”