Entanglement increase from local interactions with not-completely-positive maps

Abstract

Simple examples are constructed that show the entanglement of two qubits being both increased and decreased by interactions on just one of them. One of the two qubits interacts with a third qubit, a control, that is never entangled or correlated with either of the two entangled qubits and is never entangled, but becomes correlated, with the system of those two qubits. The two entangled qubits do not interact, but their state can change from maximally entangled to separable or from separable to maximally entangled. Similar changes for the two qubits are made with a swap operation between one of the qubits and a control; then there are compensating changes of entanglement that involve the control. When the entanglement increases, the map that describes the change of the state of the two entangled qubits is not completely positive. Combination of two independent interactions that individually give exponential decay of the entanglement can cause the entanglement to not decay exponentially but, instead, go to zero at a finite time.

6 Pages, new title, substantially revised

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Cited by in corpus (5)

• Finite-time destruction of entanglement and non-locality by environmental influences
• Entangled Network and Quantum Communication
• Entanglement increase from local interaction in the absence of initial quantum correlation in the environment and between the system and the environment
• Positivity of the assignment map implies complete positivity of the reduced dynamics
• Adapted projection operator technique for the treatment of initial correlations