Augmented message-matrix approach to deterministic dense-coding theory

作者：Gerjuoy E^*; Williams H T; Bourdon P S

来源：Physical Review A, 2009, 79(4): 042315.

DOI：10.1103/PhysRevA.79.042315

• encoding
• mathematical operators
• protocols
• quantum communication
• quantum entanglement

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 K perfectly distinguishable messages is attainable via K selected local unitary operations performed on one qudit from a pair of entangled qudits of equal dimension d in a pure state parallel to psi > with largest Schmidt coefficient root lambda(0)>. The method takes advantage of the fact that the K message states, together with d(2)-K augmenting orthonormal state vectors, yield a unitary matrix, thereby implying properties of the K message states which otherwise are not readily recognized. Employing this augmented message matrix, we produce simple proofs of previously established results including (i) lambda(0)<= d/K, (ii) lambda(0)< d/K when K=d+1, and (iii) the impossibility of finding a parallel to psi > that can enable transmission of K=d(2)-1 messages but not d(2). Additional results obtained using the method include proofs that the lambda(0)<= d/K bound is reduced to at least (i) lambda(0)<=(1/2)[1+root(d-2)/(d+2)root] when K=d+1 and (ii) lambda(0)<=(K-m)/(2K-m-d) whenever (d+1)<= K <= 2d and the selected local unitaries include the first m non-negative integral powers of the shift operator X.

• 出版日期2009-4