  An (n,1,p)-Quantum Random Access (QRA) coding, introduced by Ambainis, Nayak,
Ta-shma and Vazirani in ACM Symp. on Theory of Computing 1999, is the following
communication system: The sender which has n-bit information encodes his/her
information into one qubit, which is sent to the receiver. The receiver can
recover any one bit of the original n bits correctly with probability at least
p, through a certain decoding process based on positive operator-valued
measures. Actually, Ambainis et al. shows the existence of a (2,1,0.85)-QRA
coding and also proves the impossibility of its classical counterpart. Chuang
immediately extends it to a (3,1,0.79)-QRA coding and whether or not a
(4,1,p)-QRA coding such that p > 1/2 exists has been open since then. This
paper gives a negative answer to this open question.
