Abstract
Beyond the regime of distinguishable particles, many-body quantum interferences influence quantum transport in an intricate manner. However, symmetries of the single-particle transformation matrix alleviate this complexity and even allow the analytic formulation of suppression laws, which predict final states to occur with a vanishing probability due to total destructive interference. Here we investigate the symmetries of hypercube graphs and their generalisations with arbitrary identical subgraphs on all vertices. We find that initial many-particle states, which are invariant under self-inverse symmetries of the hypercube, lead to a large number of suppressed final states. The condition for suppression is determined solely by the initial symmetry, while the fraction of suppressed states is given by the number of independent symmetries of the initial state. Our findings reveal new insights into particle statistics for ensembles of indistinguishable bosons and fermions and may represent a first step towards many-particle quantum protocols in higher-dimensional structures.
Highlights
Quantum transports of single particles on discrete graphs, referred to as continuoustime quantum walks, are governed by the interference of all possible pathways as provided by the graph structure
We have shown that symmetries in many-particle quantum transport on hypercube graphs (HC) graphs allow the formulation of analytic suppression laws, which predict final states occurring with a vanishing probability due to many-particle interference
Each symmetry of the initial state groups all modes into two subsets of equal size and the occupation of these subsets determines the suppression
Summary
Quantum transports of single particles on discrete graphs, referred to as continuoustime quantum walks, are governed by the interference of all possible pathways as provided by the graph structure. Only few such symmetries have been investigated: The discrete Fourier transform [20, 21], Sylvester matrices [22] and the Jx lattice [23, 24] In all these cases, symmetries lead to analytic suppression laws, predicting whether or not a final particle configuration can occur. We consider the quantum transport of N identical particles in hypercube graphs (HC) of arbitrary dimension These highly symmetric graphs attracted much attention in the context of single-particle quantum walks [25,26,27,28,29,30,31]. All derivations of the discussed suppression laws are given in the appendix
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
