Talk:Super-dense coding

Hi there,

is there some definition for maximally entangled? There seems to be a plethora of research work w.r.t. entanglement measures (Bures metrics, Quantum relative entropy, Hilbert-Schmidt norm, ...).

Thanks in advance.


Hi,

as far as I know a state of a bipartite system of dimension d\times d is called maximally entangled if it can be written as

\frac{1}{\sqrt{d}}\sum_{k=1}^d |k\rangle_A \otimes |k\rangle_B

where |k\rangle_A is an orthonormal basis of system A and |k\rangle_B is an orthonormal basis of system B. Examples for a system of two qubits are the Bell states.

Alternatively, a maximally entangled state can be defined as a pure bipartite state |\psi\rangle_{AB} with a fully mixed partial trace, i.e.

\textrm{Tr}_A|\psi\rangle_{AB}=1_B/d.

This means that the entanglement (as measured by the reduced von Neumann entropy) is really maximal.

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