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Quantum entanglement
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=== Entanglement measures === Entanglement measures quantify the amount of entanglement in a (often viewed as a bipartite) quantum state. As aforementioned, [[entropy of entanglement|entanglement entropy]] is the standard measure of entanglement for pure states (but no longer a measure of entanglement for mixed states). For mixed states, there are some entanglement measures in the literature<ref name="Plenio" /> and no single one is standard. * Entanglement cost * [[entanglement distillation|Distillable entanglement]] * [[Entanglement of formation]] * [[Concurrence (quantum computing)|Concurrence]] * [[quantum relative entropy|Relative entropy of entanglement]] * [[Squashed entanglement]] * [[Negativity (quantum mechanics)#Logarithmic negativity|Logarithmic negativity]] Most (but not all) of these entanglement measures reduce for pure states to entanglement entropy, and are difficult ([[NP-hard]]) to compute for mixed states as the dimension of the entangled system grows.<ref>{{cite journal|last1=Huang|first1=Yichen|title=Computing quantum discord is NP-complete|journal=New Journal of Physics|date=21 March 2014|volume=16|issue=3|pages=033027|doi=10.1088/1367-2630/16/3/033027|bibcode=2014NJPh...16c3027H|arxiv = 1305.5941 |s2cid=118556793}}</ref>
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