arXiv subjects
Publications and source records attributed to Marcin Karczewski.
In the quantum world correlations can take form of entanglement which is known to be monogamous. In this work we show that another type of correlations, indistinguishability, is also restricted by some form of monogamy. Namely, if particles A and B simulate bosons, then A and C cannot perfectly imitate fermions. Our main result consists in demonstrating to what extent it is possible.
We investigate an operational description of identical noninteracting particles in multiports. In particular we look for physically motivated restrictions that explain their bunching probabilities. We focus on a symmetric 3-port in which a triple of superquantum particles admitted by our generalized probabilistic framework would bunch with probability 3/4. The bosonic bound of 2/3 can then be restored by imposing the additional requirement of product evolution of certain input states. These states are characterized by the fact that, much like composite systems, their entropy equals the sum of entropies of its one-particle substates. This principle is however not enough to exclude the possibility of superquantum particles in higher-order multiports.
The entanglement between two bosons or fermions can be accessed if there exists an auxiliary degree of freedom which can be used to label and effectively distinguish the two particles. For some types of entanglement between two indistinguishable particles one can observe duality, i.e., if the entanglement is present in the Hilbert space H and an auxiliary Hilbert space H' is used to label the particles, then if we used H as a label the entanglement would be present in H'. For distinguishable particles this effect does not occur because of superselection rules which prevent superpositions of different types of particles. However, it is known that superselection rules can be bypassed if one uses special auxiliary states that are known as reference frames. Here we study properties of reference frames which allow for an observation of a duality in entanglement between two distinguishable particles. Finally, we discuss the consequences of this result from the resource-theoretic point of view.