Treating Time Travel Quantum Mechanically

Abstract

The fact that closed timelike curves (CTCs) are permitted by general relativity raises the question as to how quantum systems behave when time travel to the past occurs. Research into answering this question by utilising the quantum circuit formalism has given rise to two theories: Deutschian-CTCs (D-CTCs) and "postselected" CTCs (P-CTCs). In this paper the quantum circuit approach is thoroughly reviewed, and the strengths and shortcomings of D-CTCs and P-CTCs are presented in view of their non-linearity and time travel paradoxes. In particular, the "equivalent circuit model"---which aims to make equivalent predictions to D-CTCs, while avoiding some of the difficulties of the original theory---is shown to contain errors. The discussion of D-CTCs and P-CTCs is used to motivate an analysis of the features one might require of a theory of quantum time travel, following which two overlapping classes of new theories are identified. One such theory, the theory of "transition probability" CTCs (T-CTCs), is fully developed. The theory of T-CTCs is shown not to have certain undesirable features---such as time travel paradoxes, the ability to distinguish non-orthogonal states with certainty, and the ability to clone or delete arbitrary pure states---that are present with D-CTCs and P-CTCs. The problems with non-linear extensions to quantum mechanics are discussed in relation to the interpretation of these theories, and the physical motivations of all three theories are discussed and compared.

20 pages, 4 figures. Edited in response to peer review

References in corpus (5)

• Closed timelike curves via post-selection: theory and experimental demonstration
• The quantum mechanics of time travel through post-selected teleportation
• The structure of preserved information in quantum processes
• Can closed timelike curves or nonlinear quantum mechanics improve quantum state discrimination or help solve hard problems?
• Closed Timelike Curves Make Quantum and Classical Computing Equivalent

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• Replicating the benefits of closed timelike curves without breaking causality
• Nonclassical advantage in metrology established via quantum simulations of hypothetical closed timelike curves
• Agnostic Phase Estimation
• Simulations of closed timelike curves
• Equivalence of Grandfather and Information Antinomy Under Intervention
• Closed timelike curves and the second law of thermodynamics
• Deutschian closed timelike curves can create entanglement
• Time-travelling billiard-ball clocks: a quantum model
• Quantum State Discrimination Circuits Inspired by Deutschian Closed Timelike Curves
• The D-CTC condition is generically fulfilled in classical (non-quantum) statistical systems
• Revisiting Integer Factorization using Closed Timelike Curves
• Reality, Causality, and Quantum Theory
• Billiard-ball paradox for a quantum wave packet
• Distinguishing quantum states using time travelling qubits in a presence of thermal environments
• Quantum state tomography on closed timelike curves using weak measurements