Local cloning of entangled states
- Department of Physics, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213 (United States)
We investigate the conditions under which a set S of pure bipartite quantum states on a DxD system can be locally cloned deterministically by separable operations, when at least one of the states is full Schmidt rank. We allow for the possibility of cloning using a resource state that is less than maximally entangled. Our results include that: (i) all states in S must be full Schmidt rank and equally entangled under the G-concurrence measure, and (ii) the set S can be extended to a larger clonable set generated by a finite group G of order |G|=N, the number of states in the larger set. It is then shown that any local cloning apparatus is capable of cloning a number of states that divides D exactly. We provide a complete solution for two central problems in local cloning, giving necessary and sufficient conditions for (i) when a set of maximally entangled states can be locally cloned, valid for all D; and (ii) local cloning of entangled qubit states with nonvanishing entanglement. In both of these cases, we show that a maximally entangled resource is necessary and sufficient, and the states must be related to each other by local unitary 'shift' operations. These shifts are determined by the group structure, so need not be simple cyclic permutations. Assuming this shifted form and partially entangled states, then in D=3 we show that a maximally entangled resource is again necessary and sufficient, while for higher-dimensional systems, we find that the resource state must be strictly more entangled than the states in S. All of our necessary conditions for separable operations are also necessary conditions for local operations and classical communication (LOCC), since the latter is a proper subset of the former. In fact, all our results hold for LOCC, as our sufficient conditions are demonstrated for LOCC, directly.
- OSTI ID:
- 21448460
- Journal Information:
- Physical Review. A, Vol. 82, Issue 2; Other Information: DOI: 10.1103/PhysRevA.82.022313; (c) 2010 The American Physical Society; ISSN 1050-2947
- Country of Publication:
- United States
- Language:
- English
Similar Records
Local distinguishability with preservation of entanglement
Multicopy and stochastic transformation of multipartite pure states