Application of Quantum Seal Theory on Quantum Repeaters

Abstract

It is revealed that quantum repeaters and quantum seals have a very close relationship, thus the theory in one field can be applied to the other. We give examples of novel results found by applying the existing theory of quantum seals on quantum repeater problem. I. INTRODUCTIONConsider that different users share a single quantum communication channel in multiuser transmission. Each user decodes the transmitted information from the channel, and passes the carrier to the subsequent user. In this case, they need a quantum repeater [1] in which the information can be decoded reliably, while the quantum state of the carrier should be optimally preserved. When quantum information is being transmitted, the information/disturbance trade-off was intensively studied in literature [4]-[7]. Optimal quantum repeaters were also proposed in Refs. [1], [8]-[10]. Nevertheless, in most cases of quantum communication, a user generally cares little about the exact quantum state of the carrier. Instead, he only wants to know the classical information encoded in this quantum state. For example, in the well-know quantum key distribution (QKD) problem [11]-[13], a classical bit 0 (1) can be encoded as the quantum state |0 or |+ (|1 or |− ), where |0 and |1 are the two orthogonal states of a qubit, and |± = (|0 ± |1 )/ √2. An eavesdropper is only interested in whether the classical content is 0 or 1. There is no need for him to distinguish |0 from |+ , or |1 from |− . Therefore it is more important to study the trade-off between classical information gained versus quantum disturbance in quantum cryptography, and search for optimal quantum repeaters for this purpose.On the other hand, the concept of quantum seals (QS) is a relatively less-known quantum cryptographic problem. Its goal can be summarized as follows. Alice, the owner of the secret data to be sealed, encodes the data with quantum states.