Upper bounds of a class of imperfect quantum sealing protocols

Abstract

The model of the quantum protocols sealing a classical bit is studied. It is shown that there exist upper bounds on its security. For any protocol where the bit can be read correctly with the probability α, and reading the bit can be detected with the probability β, the upper bounds are β 1/2 and α + β 9/8.

Comment on “Quantum string seal is insecure”

“…Also, the result is in agreement with β 1/2, while no analog to the finding α + β 9/8 of Ref. [5] was found in Ref. [4].…”

“…[4] is less general than that of He's in Ref. [5], and Chau's bound is not tighter. More rigorously, in He's model, measuring the sealed states can result in three outcome sets G 0 , G 1 and {g / ∈ G 0 ∪ G 1 }, where G 0 and G 1 are corresponding to the decoded bit values 0 and 1 respectively, while {g / ∈ G 0 ∪ G 1 } tells the reader that the decoding fails [5].…”

“…[4]). It was claimed that the security bounds of imperfect quantum single bit seal obtained by He [5] are not tight, while Chau proved that all imperfect quantum bit seals are insecure, and obtained a greater lower bound [4]. But in fact, Chau's model of quantum bit seal studied in Ref.…”

“…[5], and Chau's bound is not tighter. More rigorously, in He's model, measuring the sealed states can result in three outcome sets G 0 , G 1 and {g / ∈ G 0 ∪ G 1 }, where G 0 and G 1 are corresponding to the decoded bit values 0 and 1 respectively, while {g / ∈ G 0 ∪ G 1 } tells the reader that the decoding fails [5]. Also, the maximum probability α for the sealed bit b to be read correctly can be kept secret from the reader.…”

“…By proposing an explicit cheating strategy, two security bounds β 1/2 and α + β 9/8 were obtained in Ref. [5]. But in Ref.…”