Open timelike curves violate Heisenberg's uncertainty principle

Abstract

Toy models for quantum evolution in the presence of closed timelike curves (CTCs) have gained attention in the recent literature due to the strange effects they predict. The circuits that give rise to these effects appear quite abstract and contrived, as they require non-trivial interactions between the future and past which lead to infinitely recursive equations. We consider the special case in which there is no interaction inside the CTC, referred to as an open timelike curve (OTC), for which the only local effect is to increase the time elapsed by a clock carried by the system. Remarkably, circuits with access to OTCs are shown to violate Heisenberg's uncertainty principle, allowing perfect state discrimination and perfect cloning of coherent states. The model is extended to wave-packets and smoothly recovers standard quantum mechanics in an appropriate physical limit. The analogy with general relativistic time-dilation suggests that OTCs provide a novel alternative to existing proposals for the behaviour of quantum systems under gravity.

References in corpus (6)

• Probing Planck-scale physics with quantum optics
• Closed timelike curves via post-selection: theory and experimental demonstration
• Can closed timelike curves or nonlinear quantum mechanics improve quantum state discrimination or help solve hard problems?
• Quantum Connectivity of Space-Time and Gravitationally Induced Decorrelation of Entanglement
• Relativistic quantum information and time machines
• Quantum fields on closed time-like curves

Cited by in corpus (21)

• Quantum computation with indefinite causal structures
• Experimental Simulation of Closed Timelike Curves
• Quantum state cloning using Deutschian closed timelike curves
• Estimating distinguishability measures on quantum computers
• Entanglement decoherence in a gravitational well according to the event formalism
• Theoretical description and experimental simulation of quantum entanglement near open time-like curves via pseudo-density operators
• Discrete mechanics, time machines and hybrid systems
• Reversible dynamics with closed time-like curves and freedom of choice
• Replicating the benefits of closed timelike curves without breaking causality
• Advanced-Retarded Differential Equations in Quantum Photonic Systems
• Nonclassical advantage in metrology established via quantum simulations of hypothetical closed timelike curves
• Local softening of information geometric indicators of chaos in statistical modeling in the presence of quantum-like considerations
• Simulations of closed timelike curves
• Asymptotic Properties for Markovian Dynamics in Quantum Theory and General Probabilistic Theories
• Deutschian closed timelike curves can create entanglement
• Quantum physics, fields and closed timelike curves: The D-CTC condition in quantum field theory
• Bell Correlations and the Common Future
• Causality Violation and Nonlinear Quantum Mechanics
• Information geometric complexity of entropic motion on curved statistical manifolds
• Mixedness and Entanglement in the presence of Localized Closed Timelike Curves
• Quantum Signaling to the Past Using P-CTCS