Finding a maximally correlated state: Simultaneous Schmidt decomposition of bipartite pure states

@article{citeulike:1324435, abstract = {We consider a bipartite mixed state of the form = alpha,beta = 1l" align="middle">a|, where | are normalized bipartite state vectors, and matrix (a) is positive semidefinite. We provide a necessary and sufficient condition for the state taking the form of maximally correlated states by a local unitary transformation. More precisely, we give a criterion for simultaneous Schmidt decomposability of | for = 1,2,,l. Using this criterion, we can judge completely whether or not the state is equivalent to the maximally correlated state, in which the distillable entanglement is given by a simple formula. For generalized Bell states, this criterion is written as a simple algebraic relation between indices of the states. We also discuss the local distinguishability of the generalized Bell states that are simultaneously Schmidt decomposable.}, author = {Hiroshima, Tohya and Hayashi, Masahito }, citeulike-article-id = {1324435}, comment = {Referenced in Khasin/Kosloff/Steinitz's "Negativity as a distance from a separable state."}, doi = {10.1103/PhysRevA.70.030302}, journal = {Physical Review A (Atomic, Molecular, and Optical Physics)}, keywords = {bipartite, schmidt}, number = {3}, posted-at = {2007-05-24 07:30:47}, priority = {3}, publisher = {APS}, title = {Finding a maximally correlated state: Simultaneous Schmidt decomposition of bipartite pure states}, url = {http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal\&id=PLRAAN000070000003030302000001\&idtype=cvips\&gifs=yes}, volume = {70}, year = {2004} }

TY - JOUR ID - citeulike:1324435 L3 - citeulike-article-id:1324435 TI - Finding a maximally correlated state: Simultaneous Schmidt decomposition of bipartite pure states JF - Physical Review A (Atomic, Molecular, and Optical Physics) VL - 70 IS - 3 PB - APS N2 - We consider a bipartite mixed state of the form = alpha,beta = 1l" align="middle">a|, where | are normalized bipartite state vectors, and matrix (a) is positive semidefinite. We provide a necessary and sufficient condition for the state taking the form of maximally correlated states by a local unitary transformation. More precisely, we give a criterion for simultaneous Schmidt decomposability of | for = 1,2,,l. Using this criterion, we can judge completely whether or not the state is equivalent to the maximally correlated state, in which the distillable entanglement is given by a simple formula. For generalized Bell states, this criterion is written as a simple algebraic relation between indices of the states. We also discuss the local distinguishability of the generalized Bell states that are simultaneously Schmidt decomposable. KW - bipartite KW - schmidt N1 - Referenced in Khasin/Kosloff/Steinitz's "Negativity as a distance from a separable state." AU - Hiroshima, Tohya AU - Hayashi, Masahito PY - 2004/// UR - http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=PLRAAN000070000003030302000001&idtype=cvips&gifs=yes ER -