Cloning quantum entanglement in arbitrary dimensions (original) (raw)
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Cloning the entanglement of a pair of d-dimensional quantum systems
Physics of Particles and Nuclei Letters, 2007
We derive a quantum cloning machine that maximizes the entanglement of formation of the two copies of any maximally entangled input state, while preserving the separability of all unentangled input states. In addition, it is proven to optimally duplicate the entanglement of formation of all isotropic input states. For large d, the cloning machine behaves classically and outperforms a local entanglement cloner, studied for comparison.
Cloning the entanglement of a pair of quantum bits
Physical Review A, 2004
It is shown that any quantum operation that perfectly clones the entanglement of all maximallyentangled qubit pairs cannot preserve separability. This "entanglement no-cloning" principle naturally suggests that some approximate cloning of entanglement is nevertheless allowed by quantum mechanics. We investigate a separability-preserving optimal cloning machine that duplicates all maximally-entangled states of two qubits, resulting in 0.285 bits of entanglement per clone, while a local cloning machine only yields 0.060 bits of entanglement per clone. PACS numbers: 03.67.-a, 03.65.-w
Local cloning of entangled states
Physical Review A, 2010
We investigate the conditions under which a set S of pure bipartite quantum states on a D × D 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 non-vanishing 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 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.
Local cloning of entangled qubits
Physical Review A, 2007
We discuss the exact cloning of orthogonal but entangled qubits under local operations and classical communication. The amount of entanglement necessary in blank copy is obtained for various cases. Surprisingly this amount is more than 1 ebit for certain set of two nonmaximal but equally entangled states of two qubits system. To clone any three two qubits Bell states at least log2 3 ebit is necessary.
Broadcasting of entanglement and universal quantum cloners
Physical Review A, 1999
We study broadcasting of entanglement where we use universal quantum cloners (in general less optimal) to perform local cloning operations. We show that there is a lower bound on the fidelity of the universal quantum cloners that can be used for broadcasting. We prove that an entanglement is optimally broadcast only when optimal quantum cloners are used for local copying. We also show that broadcasting of entanglement into more than two entangled pairs is forbidden using only local operations.
Local copying of orthogonal entangled quantum states
New Journal of Physics, 2004
In classical information theory one can, in principle, produce a perfect copy of any input state. In quantum information theory, the no cloning theorem prohibits exact copying of nonorthogonal states. Moreover, if we wish to copy multiparticle entangled states and can perform only local operations and classical communication (LOCC), then further restrictions apply. We investigate the problem of copying orthogonal, entangled quantum states with an entangled blank state under the restriction to LOCC. Throughout, the subsystems have finite dimension D. We show that if all of the states to be copied are non-maximally entangled, then novel LOCC copying procedures based on entanglement catalysis are possible. We then study in detail the LOCC copying problem where both the blank state and at least one of the states to be copied are maximally entangled. For this to be possible, we find that all the states to be copied must be maximally entangled. We obtain a necessary and sufficient condition for LOCC copying under these conditions. For two orthogonal, maximally entangled states, we provide the general solution to this condition. We use it to show that for D = 2, 3, any pair of orthogonal, maximally entangled states can be locally copied using a maximally entangled blank state. However, we also show that for any D which is not prime, one can construct pairs of such states for which this is impossible.
Broadcasting of entanglement via local copying
Physical Review A, 1997
We show that inseparability of quantum states can be partially broadcasted (copied, cloned) with the help of local operations, i.e. distant parties sharing an entangled pair of spin 1/2 states can generate two pairs of partially nonlocally entangled states using only local operations. This procedure can be viewed as an inversion of quantum purification procedures.
Journal of Physics A: Mathematical and Theoretical, 2010
In this paper, we show how maximal entanglement between boundary qubits in the open spin chain of an XX model is realized. This creation of maximal entanglement could be used for phase covariant quantum cloning in a spin chain. The maximal entanglement is achieved with specially engineered couplings. We compare our realization with alternative methods and find that the method of pre-engineered couplings is straightforward and the decrease of cloning fidelity due to time errors is smaller.
Usefulness of classical communication for local cloning of entangled states
Physical Review A, 2006
We solve the problem of the optimal cloning of pure entangled two-qubit states with a fixed degree of entanglement using local operations and classical communication. We show, that amazingly, classical communication between the parties can improve the fidelity of local cloning if and only if the initial entanglement is higher than a certain critical value. It is completely useless for weakly entangled states. We also show that bound entangled states with positive partial transpose are not useful as a resource to improve the best local cloning fidelity.