Dynamic conditioning of two particle discrete-time quantum walks

Abstract

In real photonic quantum systems losses are an unavoidable factor limiting the scalability to many modes and particles, restraining their application in fields as quantum information and communication. For this reason, a considerable amount of engineering effort has been taken in order to improve the quality of particle sources and system components. At the same time, data analysis and collection methods based on post-selection have been used to mitigate the effect of particle losses. This has allowed for investigating experimentally multi-particle evolutions where the observer lacks knowledge about the system's intermediate propagation states. Nonetheless, the fundamental question how losses affect the behaviour of the surviving subset of a multi-particle system has not been investigated so far. For this reason, here we study the impact of particle losses in a quantum walk of two photons reconstructing the output probability distributions for one photon conditioned on the loss of the other in a known mode and temporal step of our evolution network. We present the underlying theoretical model that we have devised in order to model controlled particle losses, we describe an experimental platform based on time-multiplexing, capable of implementing our theory and in the end we show how localized particle losses change the output distributions without altering their asymptotic spreading properties. Finally we devise a quantum civilization problem, a two walker generalisation of single particle recurrence processes.

Two-particle Hadamard walk on dynamically percolated line and circle

“…Single-particle walk was implemented in [25], where dynamical changes of the graph were realized by programmable fast-switching electro-optical modulators. Together with optimized photon pair sources [58] and recent advances in photonic time-multiplexing [59,60] we anticipate the implementation of two-particle walk on a percolated graph with 3 to 5 vertices to be feasible. i i 1, , and their respective eigenvectors can be directly constructed through the tensor product.…”