Superqubits

Abstract

We provide a supersymmetric generalization of n quantum bits by extending the local operations and classical communication entanglement equivalence group [SU(2)]^n to the supergroup [uOSp(1|2)]^n and the stochastic local operations and classical communication equivalence group [SL(2,C)]^n to the supergroup [OSp(1|2)]^n. We introduce the appropriate supersymmetric generalizations of the conventional entanglement measures for the cases of $n=2$ and $n=3$. In particular, super-Greenberger-Horne-Zeilinger states are characterized by a nonvanishing superhyperdeterminant.Comment: 16 pages, 4 figures, 4 tables, revtex; minor corrections, version appearing in Phys. Rev.

The black-hole/qubit correspondence: an up-to-date review

“…There is a remarkable connection between 4-dimensional supergravity theories and what have come to be known as "groups of type E 7 " [37,38,41,42,138,139,[162][163][164]. These groups may be characterized by the FTS.…”

“…For example, although Freudenthal triple systems (FTS) [34][35][36] have been well-known to the supergravity community [37][38][39], their relevance to special entangled systems [20,21,40] has only recently been realised within the framework of the BHQC. This, in turn, inspired new applications of the Freudenthal triple system to black holes in the form of Freudenthal and Jordan dualities [41,42].…”

Special entangled quantum systems and the Freudenthal construction

“…Such systems can be used as a representation of the charge vector space occurring when studying certain black hole solutions in N = 8, d = 4 supergravity [17,18,19,20,21]. Recently striking multiple relations have been established between the physics of such stringy black hole solutions and quantum information theory [22,23,24,25,26,27,28,29,32,30]. Though this "black hole analogy" still begs for a physical basis, the underlying correspondences have repeatedly proved to be useful for obtaining new insights into one of these fields by exploiting the methods established within the other.…”

“…Though this "black hole analogy" still begs for a physical basis, the underlying correspondences have repeatedly proved to be useful for obtaining new insights into one of these fields by exploiting the methods established within the other. Since Freudenthal triples have already turned out to be important in the string theoretic context the idea is to use this algebraic structure also in quantum information [31,32]. A latest variation on this theme that appeared in the literature is a Freudenthal triple based reconsideration of three qubit entanglement [33].…”

Black holes and qubits

“…Here 0 and 1 are bosonic and $ is fermionic [11]. Such values can be realised in condensed matter physics, such as the excitations of the t-J model of strongly correlated electrons, known as spinons and holons.…”