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.
In this paper, we present sufficient conditions for states to have positive distillable key rate. Exploiting the conditions, we show that the bound entangled states given by Horodecki et al. [Phys. Rev. Lett. 94, 160502 (2005), quant-ph/0506203] have nonzero distillable key rate, and finally exhibit new classes of bound entangled states with positive distillable key rate, but with negative Devetak-Winter lower bound of distillable key rate for the ccq states of their privacy squeezed versions.
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 method. 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.
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-KunduWootters inequality [Phys. Rev. A 61, 052306 (2000); Phys. Rev. Lett. 96, 220503 (2006)], and more explicitly by the monogamy equality in terms of the concurrence and the concurrence of assistance,2 , in the three-qubit system. In this paper, we consider the monogamy equality in 2 ⊗ 2 ⊗ d quantum systems. We show that C A(BC) = CAB if and only if C Entanglement provides us with a lot of useful applications in quantum communications, such as quantum key distribution and teleportation. In order to apply entanglement to more various and useful quantum information processing, there are several important things which we should take into account. One is to quantify the degree of entanglement, and another one is to know about more properties of entanglement. We here consider two measures of entanglement, and investigate some properties of entanglement related to the two entanglement measures in multipartite systems, especially 2 ⊗ 2 ⊗ d quantum systems.Wootters' concurrence [1], C has been considered as one of the simplest measure of entanglement, although there does not in general exist its explicit formula. For any pure state |φ AB , it is defined as C(|φ AB ) = 2(1 − trρ 2 A ), wherewhere the minimum is taken over its all possible decompositions,Recently, another measure of entanglement has been presented, and it is called the concurrence of assistance (CoA) [2], which is defined aswhere the maximum is taken over all possible decompositions of ρ AB . In multiqubit systems, there is an interesting property about multipartite entanglement, which is called the monogamy of entanglement (MoE). Coffman, Kundu, and Wootters (CKW) first proposed the monogamy inequality [3], which states the MoE in the 3-qubit system,and then its generalization was proved by Osborne and Verstraete [4]. Symmetrically, its dual inequality in terms of the CoA for 3-qubit states,and its generalization into n-qubit cases have been also shown in [5,6]. In particular, for 3-qubit states, it can be readily proved that the monogamy equality [7,8],holds. We note that this monogamy equality shows the MoE more explicitly than the CKW inequality. Thus, it could be important to investigate whether the monogamy equality would be possible in any higher dimensional tripartite quantum systems, and could be helpful for us to understand multipartite entanglement.In this paper, we consider the monogamy equality in 2 ⊗ 2 ⊗ d systems. We show that C A(BC) = C AB if and only if C a AC = 0, and also show that if C A(BC) = C a AC then C AB = 0, whereas there exists a state in a 2 ⊗ 2 ⊗ d system such that C AB = 0 but C A(BC) > C a AC . Now, we present the first main theorem. Theorem 1. Let |Ψ ABC be a state in a 2⊗2⊗d system. Then the followings are equivalent.In order to prove Theorem 1, we introduce the following lemma, which is called the Lewenstein-Sanpera decomposition for two-qubit s...
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