2002/06/10 by Peter W. Shor, Shor, Peter W.
Physics and Astronomy · #FOS: Physical sciences #Quantum Physics (quant-ph) #quant-ph
paper · pdf · doi:10.48550/arxiv.quant-ph/0206058
44 pages, 17 figures, minor errors corrected and new Conjecture 1 added (thus renumbering all conjectures); replaced in May, 2003 to correct more minor errors
arxiv created 2003/05/22 · arxiv updated 2009/12/01
We investigate the capacity of three symmetric quantum states in three real dimensions to carry classical information. Several such capacities have already been defined, depending on what operations are allowed in the sending and receiving protocols. These include the C1,1 capacity, which is the capacity achievable if separate measurements must be used for each of the received states, and the C1,infinity capacity, which is the capacity achievable if joint measurements are allowed on the tensor product of all the received states. We discover a new classical information capacity of quantum channels, the adaptive capacity C1,A, which lies strictly between the C1,1 and the C1,infinity capacities. The adaptive capacity requires each of the signals to be measured by a separate apparatus, but allows the quantum states of these signals to be measured in stages, with the first stage partially reducing their quantum states, and where measurements in subsequent stages which further reduce the quantum states may depend on the results of a classical computation taking as input the outcomes of the first round of measurements.