Date : 22 May 2024, 13:00

Speaker : prof. Karol Zyczkowski, Jagiellonian University, Cracow; Center for Theoretical Physics, Warsaw

Title : Entropy of Quantum Entanglement

Abstract :

A brief introduction to entanglement of multipartite pure quantum states will be provided. Entanglement of a bi-partite pure quantum state can be characterized by its entanglement entropy, defined as von Neumann entropy of the partial trace. This quantity measures the information lost by tracing out one subsystem.

As the Bell states are known to be maximally entangled among all two-qubit quantum states, a natural question arises: What is the most entangled state for the quantum system consisting of N sub-systems with d levels each? The answer depends on the entanglement measure selected, but already for four-qubit system there is no state, which displays maximal entanglement with respect to all three possible splittings of the systems into two pairs of qubits.

Absolutely maximally entangled (AME) states of 2n subsystems, being maximally entangled with respect to all possible symmetric splitting of the system, find their applications for information processing tasks. For instance, the |GHZ> state of four qutrits allows one to teleport a single qutrit between any two parties, while the 'more entangled' AME state of four qutrits enables us to teleport two qutrits from any selected pair of users to the remaining two parties. After a brief review of the issue of entanglement in multipartite systems some open problems will be presented.

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