Two-Qubit Operators in No-Splitting Theorems

Mario Mastriani

Christian Brouder

The matrix element of a general many-body operator between two Slater determinants is calculated explicitly. For this, a split-and-pair method is introduced that provides a convenient expression of Wick's theorem and simplifies many-body calculations. The same method is used to determine the generating function of the matrix elements of many-body operators. The split-and-pair method allows also for the diagonalization of the density correlation operators $:n({x}_{1})\ensuremath{\cdots}n({x}_{k}):$, where $n(x)={\ensuremath{\psi}}^{\ifmmode\dagger\else\textdagger\fi{}}(x)\ensuremath{\psi}(x)$ is the density operator. The relation between the split-and-pair method and quantum group theory is clarified.

Shuanping Du, Zhaofang Bai

Метод Санига

Recently Waegell and Aravind [J.Phys.A: Math.Theor.45 (2012), 405301, 13 pages] have given a number of distinct sets of three-qubit observables, each furnishing a proof of the Kochen-Specker theorem.Here it is demonstrated that two of these sets/configurations, namely the 18 2 -12 3 and 2 4 14 2 -4 3 6 4 ones, can uniquely be extended into geometric hyperplanes of the split Cayley hexagon of order two, namely into those of types V 22 (37; 0, 12, 15, 10) and V 4 (49; 0, 0, 21, 28) in the classification of Frohardt and Johnson [Comm.Algebra 22 (1994), 773-797].Moreover, employing an automorphism of order seven of the hexagon, six more replicas of either of the two configurations are obtained.

Guixia Pan

A quantum information splitting scheme of two-qubit state is proposed by using two asymmetric W states as quantum channel.It's showed that if the two-qubit state is known to the sender(Alice),then she can split quantum information and distribute it to the receivers(Bob and Charlie) by performing a two-qubit projective measurement.Bob and Charlie first perform a collective unitary operation on their qubits,and then Charlie can recover the initial quantum state by implementing two single-qubit unitary operations.So the scheme reduces greatly the measurement complexity.The success probability and classical communication cost are calculated within the scheme.