DECOMPOSITION OF STATES

RUI-JUAN GU, FU-LIN ZHANG, SHAO-MING FEI +1 more

Based on maximally entangled states in the full- and sub-spaces of two-qutrits, we present an alternative decomposition of two-qutrit pure states in a form [Formula: see text]. Similar to the Schmidt decomposition, all two-qutrit pure states can be transformed into the alternative decomposition under local unitary transformations, and the parameter p1 is shown to be an entanglement invariant.

Armin Uhlmann

Masanori Ohya, Dėnes Petz

David Kult, Erik Sjöqvist

We examine evolutions where each component of a given decomposition of a mixed quantal state evolves independently in a unitary fashion. The geometric phase and parallel transport conditions for this type of decomposition dependent evolution are delineated. We compare this geometric phase with those previously defined for unitarily evolving mixed states, and mixed state evolutions governed by completely positive maps.

Gerald V. Dunne

The second-quantized form of the Laughlin states for the fractional quantum Hall effect is discussed by decomposing the Laughlin wavefunctions into the N-particle Slater basis. A general formula is given for the expansion coefficients in terms of the characters of the symmetric group, and the expansion coefficients are shown to possess numerous interesting symmetries. For expectation values of the density operator it is possible to identify individual dominant Slater states of the correct uniform bulk density and filling fraction in the physically relevant N→∞ limit.