Cloning quantum entanglement in arbitrary dimensions

Abstract

We have found a quantum cloning machine that optimally duplicates the entanglement of a pair of $d$-dimensional quantum systems. It maximizes the entanglement of formation contained in the two copies of any maximally-entangled input state, while preserving the separability of unentangled input states. Moreover, it cannot increase the entanglement of formation of all isotropic states. For large $d$, the entanglement of formation of each clone tends to one half the entanglement of the input state, which corresponds to a classical behavior. Finally, we investigate a local entanglement cloner, which yields entangled clones with one fourth the input entanglement in the large-$d$ limit.

6 pages, 3 figures

References in corpus (9)

• Mixed State Entanglement and Quantum Error Correction
• Quantum Copying: Beyond the No-Cloning Theorem
• Entanglement Measures under Symmetry
• The Entanglement of Formation for Isotropic States
• Quantum cloning and the capacity of the Pauli channel
• Asymmetric quantum cloning machines in any dimension
• Cloning a real d-dimensional quantum state on the edge of the no-signaling condition
• Extremal equation for optimal completely-positive maps
• Cloning the entanglement of a pair of quantum bits

Cited by in corpus (11)

• Quantum discord and its allies: a review
• Quantum Cloning Machines and the Applications
• Location-Dependent Communications using Quantum Entanglement
• Quantum Cloning of Continuous Variable Entangled States
• Quantum Location Verification in Noisy Channels
• Units of rotational information
• Equi-entangled bases in arbitrary dimensions
• Usefulness of classical communication for local cloning of entangled states
• Universal covariant quantum cloning circuits for qubit entanglement manipulation
• Temperature effects on quantum cloning of states and entanglement
• Test of Common Sense in Quantum Copying Process