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The entropy of entanglement (or entanglement entropy) is a measure of the degree of quantum entanglement between two subsystems constituting a two-part composite quantum system. Given a pure bipartite quantum state of the composite system, it is possible to obtain a reduced density matrix describing knowledge of the state of a subsystem.
For bipartite pure states, the von Neumann entropy of reduced states is the unique measure of entanglement in the sense that it is the only function on the family of states that satisfies certain axioms required of an entanglement measure. [49] [50] It is thus known as the entanglement entropy. [51]
Quantum entanglement is the phenomenon of a group of particles being generated, interacting, or sharing spatial proximity in a manner such that the quantum state of each particle of the group cannot be described independently of the state of the others, including when the particles are separated by a large distance.
Entanglement of formation quantifies how much entanglement (measured in ebits) is necessary, on average, to prepare the state. The measure clearly coincides with entanglement entropy for pure states. It is zero for all separable states and non-zero for all entangled states. By construction, is convex.
The topological entanglement entropy [1] [2] [3] or topological entropy, usually denoted by , is a number characterizing many-body states that possess topological order.. A non-zero topological entanglement entropy reflects the presence of long range quantum entanglements in a many-body quantum state.
This entanglement measure is a generalization of the entanglement of assistance and was constructed in the context of spin chains. Namely, one chooses two spins and performs LOCC operations that aim at obtaining the largest possible bipartite entanglement between them (measured according to a chosen entanglement measure for two bipartite states ...
Many entanglement measures have a simple formulas for entangled ... , [3] where is the binary entropy function. Entanglement of formation: = (+ ()),where ...
The relative entropy of entanglement of ρ is defined by = (‖) where the minimum is taken over the family of separable states. A physical interpretation of the quantity is the optimal distinguishability of the state ρ from separable states.