Transformations in quantum networks via local operations assisted by
finitely many rounds of classical communication
- URL: http://arxiv.org/abs/2105.01090v3
- Date: Sun, 10 Mar 2024 12:00:56 GMT
- Title: Transformations in quantum networks via local operations assisted by
finitely many rounds of classical communication
- Authors: Cornelia Spee, Tristan Kraft
- Abstract summary: Recent advances have led towards first prototypes of quantum networks in which entanglement is distributed by sources producing bipartite entangled states.
This raises the question of which states can be generated in quantum networks based on bipartite sources using local operations and classical communication.
We study state transformations under finite rounds of local operations and classical communication in networks based on maximally entangled two-qubit states.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Recent advances have led towards first prototypes of quantum networks in
which entanglement is distributed by sources producing bipartite entangled
states. This raises the question of which states can be generated in quantum
networks based on bipartite sources using local operations and classical
communication. In this work, we study state transformations under finite rounds
of local operations and classical communication (LOCC) in networks based on
maximally entangled two-qubit states. We first derive the symmetries for
arbitrary network structures, as these determine which transformations are
possible. Then, we show that contrary to tree graphs, for which it has already
been shown that any state within the same entanglement class can be reached,
there exist states which can be reached probabilistically but not
deterministically if the network contains a cycle. Furthermore, we provide a
systematic way to determine states which are not reachable in networks
consisting of a cycle. Moreover, we provide a complete characterization of the
states which can be reached in a cycle network with a protocol where each party
measures only once, and each step of the protocol results in a deterministic
transformation. Finally, we present an example which cannot be reached with
such a simple protocol, and constitutes, up to our knowledge, the first example
of a LOCC transformation among fully entangled states requiring three rounds of
classical communication.
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