Even though a method to perfectly sign quantum messages has not been known, the arbitrated quantum signature scheme has been considered as one of good candidates. However, its forgery problem has been an obstacle to the scheme being a successful meth
od. In this paper, we consider one situation, which is slightly different from the forgery problem, that we check whether at least one quantum message with signature can be forged in a given scheme, although all the messages cannot be forged. If there exist only a finite number of forgeable quantum messages in the scheme then the scheme can be secure against the forgery attack by not sending the forgeable quantum messages, and so our situation does not directly imply that we check whether the scheme is secure against the attack. But, if users run a given scheme without any consideration of forgeable quantum messages then a sender might transmit such forgeable messages to a receiver, and an attacker can forge the messages if the attacker knows them in such a case. Thus it is important and necessary to look into forgeable quantum messages. We here show that there always exists such a forgeable quantum message-signature pair for every known scheme with quantum encryption and rotation, and numerically show that any forgeable quantum message-signature pairs do not exist in an arbitrated quantum signature scheme.
Until now, there have been developed many arbitrated quantum signature schemes implemented with a help of a trusted third party. In order to guarantee the unconditional security, most of them take advantage of the optimal quantum one-time encryption
method based on Pauli operators. However, we in this paper point out that the previous schemes only provides a security against total break and actually show that there exists a simple existential forgery attack to validly modify the transmitted pair of message and signature. In addition, we also provide a simple method to recover the security against the proposed attack.
Quantum bit commitment has been known to be impossible by the independent proofs of Mayers, and Lo and Chau, under the assumption that the whole quantum states right before the unveiling phase are static to users. We here provide an unconditionally s
ecure non-static quantum bit commitment protocol with a trusted third party, which is not directly involved in any communications between users and can be limited not to get any information of commitment without being detected by users. We also prove that our quantum bit commitment protocol is not secure without the help of the trusted third party. The proof is basically different from the Mayers-Lo-Chaus no-go theorem, because we do not assume the staticity of the finally shared quantum states between users.
In this work, we investigate what kinds of quantum states are feasible to perform perfectly secure secret sharing, and present its necessary and sufficient conditions. We also show that the states are bipartite distillable for all bipartite splits, a
nd hence the states could be distillable into the Greenberger-Horne-Zeilinger state. We finally exhibit a class of secret-sharing states, which have an arbitrarily small amount of bipartite distillable entanglement for a certain split.
There is an interesting property about multipartite entanglement, called the monogamy of entanglement. The property can be shown by the monogamy inequality, called the Coffman-Kundu-Wootters inequality [Phys. Rev. A {bf 61}, 052306 (2000); Phys. Rev.
Lett. {bf 96}, 220503 (2006)], and more explicitly by the monogamy equality in terms of the concurrence and the concurrence of assistance, $mathcal{C}_{A(BC)}^2=mathcal{C}_{AB}^2+(mathcal{C}_{AC}^a)^2$, in the three-qubit system. In this paper, we consider the monogamy equality in $2otimes 2 otimes d$ quantum systems. We show that $mathcal{C}_{A(BC)}=mathcal{C}_{AB}$ if and only if $mathcal{C}_{AC}^a=0$, and also show that if $mathcal{C}_{A(BC)}=mathcal{C}_{AC}^a$ then $mathcal{C}_{AB}=0$, while there exists a state in a $2otimes 2 otimes d$ system such that $mathcal{C}_{AB}=0$ but $mathcal{C}_{A(BC)}>mathcal{C}_{AC}^a$.
We develop a three-party quantum secret sharing protocol based on arbitrary dimensional quantum states. In contrast to the previous quantum secret sharing protocols, the sender can always control the state, just using local operations, for adjusting
the correlation of measurement directions of three parties and thus there is no waste of resource due to the discord between the directions. Moreover, our protocol contains the hidden value which enables the sender to leak no information of secret key to the dishonest receiver until the last steps of the procedure.
