A special simplex in the state space for entangled qudits

Abstract

Focus is on two parties with Hilbert spaces of dimension d, i.e. "qudits". In\nthe state space of these two possibly entangled qudits an analogue to the well\nknown tetrahedron with the four qubit Bell states at the vertices is presented.\nThe simplex analogue to this magic tetrahedron includes mixed states. Each of\nthese states appears to each of the two parties as the maximally mixed state.\nSome studies on these states are performed, and special elements of this set\nare identified. A large number of them is included in the chosen simplex which\nfits exactly into conditions needed for teleportation and other applications.\nIts rich symmetry - related to that of a classical phase space - helps to study\nentanglement, to construct witnesses and perform partial transpositions. This\nsimplex has been explored in details for d=3. In this paper the mathematical\nbackground and extensions to arbitrary dimensions are analysed.\n