Entangled pure state transformations via local operations assisted by finitely many rounds of classical communication

Abstract

We consider generic pure $n$-qubit states and a general class of pure states of arbitrary dimensions and arbitrarily many subsystems. We characterize those states which can be reached from some other state via Local Operations assisted by finitely many rounds of Classical Communication ($LOC{C}_{\mathbb{N}}$). For $n$ qubits with $n>3$ we show that this set of states is of measure zero, which implies that the maximally entangled set is generically of full measure if restricted to the practical scenario of $LOC{C}_{\mathbb{N}}$. Moreover, we identify a class of states for which any $LOC{C}_{\mathbb{N}}$ protocol can be realized via a concatenation of deterministic steps. We show, however, that in general there exist state transformations which require a probabilistic step within the protocol, which highlights the difference between bipartite and multipartite LOCC.

5 pages, 1 figure. See also the companion paper arXiv:1607.05145

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• Strong bounds on required resources for quantum channels by local operations and classical communication
• Detecting genuine multipartite entanglement in multi-qubit devices with restricted measurements
• Dynamic LOCC Circuits for Automated Entanglement Manipulation
• Analogs of absolutely maximally entangled states in nonlocal correlations via the sheaf-theoretic framework and its applications