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=== Bipartite quantum states ===
Bell also pointed out that up until then, discussions of [[quantum entanglement]] focused on cases where the results of measurements upon two particles were either perfectly correlated or perfectly anti-correlated. These special cases can also be explained using local hidden variables.<ref name=Bell1964/>
For [[separable state]]s of two particles, there is a simple hidden-variable model for any measurements on the two parties. Surprisingly, there are also [[quantum entanglement|entangled states]] for which all [[Measurement in quantum mechanics|von Neumann measurements]] can be described by a hidden-variable model.<ref>{{cite journal |author1=R. F. Werner | title=Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model |journal=[[Physical Review A]]| year=1989 |volume=40 | issue=8 | doi=10.1103/PhysRevA.40.4277 | pages=4277–4281 |bibcode=1989PhRvA..40.4277W | pmid=9902666 }}</ref> Such states are entangled, but do not violate any Bell inequality. The so-called [[Werner state]]s are a single-parameter family of states that are invariant under any transformation of the type <math>U \otimes U,</math> where <math>U</math> is a unitary matrix. For two qubits, they are noisy singlets given as
<math display="block">\varrho = p \vert \psi^- \rangle \langle \psi^-\vert + (1 - p) \frac{\mathbb{I}}{4},</math>
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