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- W2050792442 abstract "This paper, a continuation of a previous one (Iwai 2007 J. Phys. A: Math. Theor. 40 1361), studies the geometry of multi-qubit entanglement with respect to bipartite partitions. An n-qubit system (C2)⊗n is isomorphic with , the linear space of 2l × 2m complex matrices, where l + m = n. According to the isomorphism, the local transformation group U(2l) × U(2m) acts on the space of normalized states in . Let M and G denote the space of normalized states and the local transformation group acting on M, respectively. According to the orbit types, M is stratified into strata, among which a principal stratum and the sets of separable states and maximally entangled states will be identified. For , a function F(C) = det(I − CC*) proves to serve as a measure of entanglement, where I denotes the 2l × 2l identity matrix. The F(C) attains the minimal and the maximal values, respectively, on the sets of separable states and maximally entangled states, and further takes no extremal values on the principal stratum. The F(C) projects to a function on the factor space GM. A naturally defined metric on M also projects to that on GM, which serves to measure the distance between the separable states, F−1(0), and the states, F−1(k), of prescribed value k of measure. To be precise, one has to restrict M to the principal stratum, when projecting the metric. Three- and four-qubit systems will be studied intensively, and then multi-qubit systems discussed." @default.
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- W2050792442 date "2007-09-18" @default.
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- W2050792442 title "The geometry of multi-qubit entanglement" @default.
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- W2050792442 doi "https://doi.org/10.1088/1751-8113/40/40/011" @default.
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