A Model for Non-Linear Quantum Evolution based on Time Displaced Entanglement

We discuss time displaced entanglement, produced by taking one member of a Bell pair on a round trip at relativistic speeds, thus inducing a time-shift between the pair. We show that decoherence with respect to Bell measurements on the pair is predicted. We then study a teleportation protocol, using time displaced entanglement as its resource, in which a time-like loop is apparently formed. The result is non-unitary, non-linear evolution of the teleported state.

Quantum theory is compatible with special relativity. In particular, though measurements on entangled systems are correlated in a way that cannot be reproduced by local hidden variables, they cannot be used for superluminal signalling. As Czachor, Gisin and Polchinski pointed out, this is not true for general nonlinear modifications of the Schroedinger equation. Excluding superluminal signalling has thus been taken to rule out most nonlinear versions of quantum theory. The no...

The author calls attention to previous work with related results, which has escaped scrutiny before the publication of the article "Nonlinear quantum evolution with maximal entropy production", Phys.Rev.A63, 022105 (2001).

In this doctoral thesis we provide one of the first theoretical expositions on a quantum effect known as entanglement in time. It can be viewed as an interdependence of quantum systems across time, which is stronger than could ever exist between classical systems. We explore this temporal effect within the study of quantum information and its foundations as well as through relativistic quantum information. An original contribution of this thesis is the design of one of the fi...

In quantum theory it is possible to explain time, and dynamics, in terms of entanglement. This is the timeless approach to time, which assumes that the universe is in a stationary state, where two non-interacting subsystems, the clock and the rest, are entangled. As a consequence, by choosing a suitable observable of the clock, the relative state of the rest of the universe evolves unitarily with respect to the variable labelling the clock observable's eigenstates, which is t...

Recent work has shown that relativistic time dilation results in correlations between a particle's internal and external degrees of freedom, leading to decoherence of the latter. In this note, we briefly summarize the results and address the comments and concerns that have been raised towards these findings. In addition to brief replies to the comments, we provide a pedagogical discussion of some of the underlying principles of the work. This note serves to clarify some of th...

This paper shall define and discuss two types of quantum process - Disentangling and Entangling. The first type will be shown to contradict Unitarity and is therefore ruled out as a possible signalling process within standard linear Quantum Mechanics. The paper will argue that the second type - the entangling process - is both allowed by the principles of Quantum Mechanics, and can transmit superluminal signals. A proposal will be made for addressing the objection to superlum...

It is currently unknown whether the laws of physics permit time travel into the past. While general relativity indicates the theoretical possibility of causality violation, it is now widely accepted that a theory of quantum gravity must play an essential role in such cases. As a striking example, the logical paradoxes usually associated with causality violation can be resolved by quantum effects. We ask whether the explicit construction of a theory that allows causality viola...

We argue that usual quantum statics and the dynamical equivalence of mixed quantum states to {\it probabilistic mixtures}suffice to guarantee a linear evolution law, which necessarily complies with the no-signaling condition. Alternatively, there are nonlinear dynamical extensions that treat mixed states as {\it elementary mixtures} and evolve {\it every}pure state linearly and unitarily. But if all {\it entangled} pure states evolve linearly, then elementary mixtures cannot ...

The hilbert-space structure of quantum mechanics is related to the causal structure of space-time. The usual measurement hypotheses apparently preclude nonlinear or stochastic quantum evolution. By admitting a difference in the calculus of joint probabilities of events in space-time according to whether the separation is space-like or time-like, a relativistic nonlinear or stochastic quantum theory may be possible.