H. T. Williams

Deterministic dense coding and entanglement entropy

We present an analytical study of the standard two-party deterministic dense-coding protocol, under which communication of perfectly distinguishable messages takes place via a qudit from a pair of nonmaximally entangled qudits in a pure state |{psi}>. Our results include the following: (i) We prove that it is possible for a state |{psi}> with lower entanglement entropy to support the sending of a greater number of perfectly distinguishable messages than one with higher entanglement entropy, confirming a result suggested via numerical analysis in Mozes et al. [Phys. Rev. A 71, 012311 (2005)]. (ii) By explicit construction of families of local unitary operators, we verify, for dimensions d=3 and d=4, a conjecture of Mozes et al. about the minimum entanglement entropy that supports the sending of d+j messages, 2{ allows the sending of K messages and has {radical}({lambda}{sub 0}) as its largest Schmidt coefficient, we show that the inequality {lambda}{sub 0}{<=}d/K, established by Wu et al. [Phys. Rev. A 73, 042311 (2006)], must actually take the form {lambda}{sub 0}

Symmetry properties of matrix elements of canonical SU(3) tensor operators

The symmetries of the SU(3) 3‐j symbols, which are defined as symmetrized matrix elements of the canonical SU(3) tensor operators are investigated. The symmetries considered are those which in SU(2) correspond to the interchange of columns of the 3‐j symbol, as well as the symmetry under conjugation. It is found that for each tensor operator in a multiplicity set the matrix elements (for a fixed operator pattern) carry a one‐dimensional representation of the symmetric group S3.

SU3 isoscalar factors

A summary of the properties of the Wigner–Clebsch–Gordan coefficients and iso‐ scalar factors for the group SU3 in the SU2⊗U1 decomposition is presented. The outer degeneracy problem is discussed in detail with a proof of a conjecture (Braunschweig’s) which has been the basis of previous work on the SU3 coupling coefficients. Recursion relations obeyed by the SU3 isoscalar factors are produced, along with an algorithm which allows numerical determination of the factors from the recursion relations. The algorithm produces isoscalar factors which share all the symmetry properties under permutation of states and conjugation which are familiar from the SU2 case. The full set of symmetry properties for the SU3 Wigner–Clebsch–Gordan coefficients and isoscalar factors are displayed.

Augmented message-matrix approach to deterministic dense-coding theory

A useful method for deriving analytical results applicable to the standard two-party deterministic dense-coding protocol is introduced and illustrated. In this protocol, communication of

Automated angular momentum recoupling algebra

K

Gauge invariance and threshold photon scattering on a composite target

perfectly distinguishable messages is attainable via

Unital quantum operations on the Bloch ball and Bloch region

K

Sharp probability estimates for Shor's order-finding algorithm

selected local unitary operations performed on one qudit from a pair of entangled qudits of equal dimension

Symbolic solutions: angular momentum on a PC

d

Abstract of papers to appear in future issuesAutomated angular momentum recoupling algebra

in a pure state