Violation of Quantum Mechanical Uncertainty Relations in the Presence of Closed Timelike Curves

Abstract. Recently Brun, Harrington and Wilde [1], using a model first introduced by Deutsch [2], have shown that in the presence of closed timelike curves that can be traversed by two-level quantum systems (i.e. qubits), a party can perfectly distinguish any set of quantum states, thus violating the quantum uncertainty relations. Intriguing as this result is, it was restricted to qubits and was derived from a non-relativistically invariant model. One might also be suspicious that such a radical departure from the standard rules of quantum mechanics might lead to pathological effects such as superluminal signaling. We have introduced an alternative formulation of Deutsch’s model which is more general and provides new physical insights [3]. Using this model we reproduce the results of Brun et al and show explicitly that superluminal signaling is not allowed. Using the techniques introduced in Ref. [4] we will present results of a further generalization of the model to describe in a relativistically invariant way the evolution of a qubit (or indeed any harmonic oscillator) state carried by an electromagnetic field mode traversing a closed timelike curve in 1+1 dimensions. This research offers new insights into the role of time in quantum mechanics and the relationship between general relativity an