Quantum interference of position and momentum: a particle propagation paradox

Abstract

Optimal simultaneous control of position and momentum can be achieved by maximizing the probabilities of finding their experimentally observed values within two well-defined intervals. The assumption that particles move along straight lines in free space can then be tested by deriving a lower limit for the probability of finding the particle in a corresponding spatial interval at any intermediate time t. Here, it is shown that this lower limit can be violated by quantum superpositions of states confined within the respective position and momentum intervals. These violations of the particle propagation inequality show that quantum mechanics changes the laws of motion at a fundamental level, providing a new perspective on causality relations and time evolution in quantum mechanics.

6 pages, including one figure, added discussions of experimental possibilities and the selection of localized states

References in corpus (5)

• Experimental joint weak measurement on a photon pair as a probe of Hardy's Paradox
• Direct observation of Hardy's paradox by joint weak measurement with an entangled photon pair
• Exotic Looped Trajectories of Photons in Three-Slit Interference
• Measurement and control of spatial qubits generated by passing photons through double-slits
• Quantum Trajectories based on the Weak Value

Cited by in corpus (4)

• Can the double-slit experiment distinguish between quantum interpretations?
• Dependence of measurement outcomes on the dynamics of quantum coherent interactions between the system and the meter
• Single-particle entanglement gives rise to truly nonlocal effects like single-particle steering
• Controlling and measuring a superposition of position and momentum