(4,1)-Quantum random access coding does not exist—one qubit is not enough to recover one of four bits
(4,1)-Quantum random access coding does not exist—one qubit is not enough to recover one of four bits
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DOI：
10.1088/1367-2630/8/8/129
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发表时间：
2006-04
影响因子：
3.3
通讯作者：
Masahito Hayashi;K. Iwama;H. Nishimura;Raymond H. Putra;S. Yamashita
中科院分区：
文献类型：
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作者：
Masahito Hayashi;K. Iwama;H. Nishimura;Raymond H. Putra;S. Yamashita
Ambainis等人（1999 ACM Symp.计算理论p 376），是以下通信系统：具有n位信息的发送者将他/她的信息编码成一个量子位，该量子位被发送到接收者。接收机可以通过基于正算子值度量的特定解码过程以至少p的概率正确地恢复原始n个比特中的任何一个比特。Ambainis等人证明了（2，1，0.85）-QRA编码的存在性，并证明了经典编码的不可能性。Chuang立即将其推广到（3，1，0.79）-QRA编码，并且从那时起是否存在（4，1，p）-QRA编码使得p > 1/2一直是开放的。本文对这一问题作了否定的回答。此外，我们还将它对单量子比特编码的否定回答推广到多量子比特编码的情况
An (n,1,p)-quantum random access (QRA) coding, introduced by Ambainis et al (1999 ACM Symp. Theory of Computing p 376), 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. Moreover, we generalize its negative answer for one-qubit encoding to the case of multiple-qubit encoding