Separable and entangled states

An '''entangled state''' is defined as a state that is '''not separable'''. A separable state can be written as a probability distribution over uncorrelated states, product states, :\rho = \sum_i p_i \rho_i^A \otimes \rho_i^B . == Pure states == For pure states the above definition can be represented as follows. Consider two quantum systems A and B, with respective Hilbert spaces \mathcal{H}_A and \mathcal{H}_B. The Hilbert space of the composite system is the tensor product \mathcal{H}_A\otimes\mathcal{H}_B. If the state |\Psi\rangle_{AB}of the composite system can be represented in the form :|\Psi\rangle_{AB}=|\psi\rangle_A \otimes |\phi\rangle_B, where |\psi\rangle_A\in\mathcal{H}_A and |\phi\rangle_B\in\mathcal{H}_B are the states of the systems A and B respectively, then this state is called a ''separable state''. If a state is not separable, it is known as an ''entangled state''. == Ralated papers == * R. F. Werner, ''[http://www.imaph.tu-bs.de/ftp/werner/p26.pdf Quantum states with Einstein-Rosen-Podolsky correlations admitting a hidden-variable model]'', Phys. Rev. A 40, pp. 4277-4281, 1989. * D. Bruss, ''Characterizing Entanglement'', Math. Phys. 43, pp. 4237, 2002. {{arxiv|number=quant-ph/0110078}} {{stub}} Category:Entanglement Category:Handbook of Quantum Information

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Monday, October 26, 2015 - 17:56