arXiv subjects

Daowen Qiu

Publications and source records attributed to Daowen Qiu.

At least 55 records · Page 3Linked to original sources

arXiv2017

Security of a single-state semi-quantum key distribution protocol

Semi-quantum key distribution protocols are allowed to set up a secure secret key between two users. Compared with their full quantum counterparts, one of the two users is restricted to perform some "classical" or "semi-quantum" operations, which makes them easily realizable by using less quantum resource. However, the semi-quantum key distribution protocols mainly rely on a two-way quantum channel. The eavesdropper has two opportunities to intercept the quantum states transmitted in the quantum communication stage. It may allow the eavesdropper to get more information and make the security analysis more complicated. In the past ten years, many semi-quantum key distribution protocols have been proposed and proved to be robust. But there are few works concerned about their unconditional security. It is doubted that how secure the semi-quantum ones are and how much noise can they tolerate to establish a secure secret key. In this paper, we prove the unconditional security of a single-state semi-quantum key distribution protocol proposed by $Zou$ et al. in [Phys. Rev. A. 79]. We present a complete proof from information theory aspect by deriving a lower bound of the protocol's key rate in the asymptotic scenario. Using this bound, we figure out an error threshold value such that all error rates are less than this threshold value, the secure secret key can be established between the legitimate users definitely. Otherwise, the users should abort the protocol. we make an illustration of the protocol under the circumstance of the reverse quantum channel is a depolarizing one with parameter $q$. Additionally, we compare the error threshold value with some full quantum protocols and several existing semi-quantum ones whose unconditional security proofs have been provided recently.

quant-ph↗

arXiv2017

Characterizations of symmetrically partial Boolean functions with exact quantum query complexity

We give and prove an optimal exact quantum query algorithm with complexity $k+1$ for computing the promise problem (i.e., symmetric and partial Boolean function) $DJ_n^k$ defined as: $DJ_n^k(x)=1$ for $|x|=n/2$, $DJ_n^k(x)=0$ for $|x|$ in the set $\{0, 1,\ldots, k, n-k, n-k+1,\ldots,n\}$, and it is undefined for the rest cases, where $n$ is even, $|x|$ is the Hamming weight of $x$. The case of $k=0$ is the well-known Deutsch-Jozsa problem. We outline all symmetric (and partial) Boolean functions with degrees 1 and 2, and prove their exact quantum query complexity. Then we prove that any symmetrical (and partial) Boolean function $f$ has exact quantum 1-query complexity if and only if $f$ can be computed by the Deutsch-Jozsa algorithm. We also discover the optimal exact quantum 2-query complexity for distinguishing between inputs of Hamming weight $\{ \lfloor n/2\rfloor, \lceil n/2\rceil \}$ and Hamming weight in the set $\{ 0, n\}$ for all odd $n$. In addition, a method is provided to determine the degree of any symmetrical (and partial) Boolean function.

quant-ph↗

arXiv2017

Analyses and improvement of a broadcasting multiple blind signature scheme based on quantum GHZ entanglement

A broadcasting multiple blind signature scheme based on quantum GHZ entanglement has been presented recently by Tian et al. It is said that the scheme's unconditional security is guaranteed by adopting quantum key preparation, quantum encryption algorithm and quantum entanglement. In this paper, we prove that each signatory can get the signed message just by an intercept-resend attack. Then, we show there still exists some participant attacks and external attacks. Specifically, we verify the message sender Alice can impersonate each signatory to sign the message at will, and so is the signature collector Charlie. Also, we demonstrate that the receiver Bob can forge the signature successfully, and with respect to the external attacks, the eavesdropper Eve can modify the signature at random. Besides, we discover Eve can change the signed message at will, and Eve can impersonate Alice as the message sender without being discovered. In particular, we propose an improved scheme based on the original one and show that it is secure against not only the attacks mentioned above but also some collusion attacks.

quant-ph↗

arXiv2017

A single-state semi-quantum key distribution protocol and its security proof

Semi-quantum key distribution (SQKD) can share secret keys by using less quantum resource than its fully quantum counterparts, and this likely makes SQKD become more practical and realizable. In this paper, we present a new SQKD protocol by introducing the idea of B92 into semi-quantum key distribution and prove its unconditional security. In this protocol, the sender Alice just sends one qubit to the classical Bob and Bob just prepares one state in the preparation process. Indeed the classical user's measurement is not necessary either. This protocol can reduce some quantum communication and make it easier to be implemented. It can be seen as the semi-quantum version of B92 protocol, comparing to the protocol BKM2007 as the semi-quantum version of BB84 in fully quantum cryptography. We verify it has higher key rate and therefore is more efficient. Specifically we prove it is unconditionally secure by computing a lower bound of the key rate in the asymptotic scenario from information theory aspect. Then we can find a threshold value of errors such that for all error rates less than this value, the secure key can be established between the legitimate users definitely. We make an illustration of how to compute the threshold value in case of the reverse channel is a depolarizing one with parameter $p$. Though the threshold value is a little smaller than those of some existed SQKD protocols, it can be comparable to the B92 protocol in fully quantum cryptography.

quant-ph↗

arXiv2017

Optimal Separation in Exact Query Complexities for Simon's Problem

Simon's problem is one of the most important problems demonstrating the power of quantum computers, which achieves a large separation between quantum and classical query complexities. However, Simon's discussion on his problem was limited to bounded-error setting, which means his algorithm can not always get the correct answer. Exact quantum algorithms for Simon's problem have also been proposed, which deterministically solve the problem with O(n) queries. Also the quantum lower bound Ω(n) for Simon's problem is known. Although these algorithms are either complicated or specialized, their results give an O(n) versus Ω(\sqrt{2^{n}}) separation in exact query complexities for Simon's problem (Ω(\sqrt{2^{n}}) is the lower bound for classical probabilistic algorithms), but it has not been proved whether this separation is optimal. In this paper, we propose another exact quantum algorithm for solving Simon's problem with O(n) queries, which is simple, concrete and does not rely on special query oracles. Our algorithm combines Simon's algorithm with the quantum amplitude amplification technique to ensure its determinism. In particular, we show that Simon's problem can be solved by a classical deterministic algorithm with O(\sqrt{2^{n}}) queries (as we are aware, there were no classical deterministic algorithms for solving Simon's problem with O(\sqrt{2^{n}}) queries). Combining some previous results, we obtain the optimal separation in exact query complexities for Simon's problem: Θ({n}) versus Θ({\sqrt{2^{n}}}).

quant-ph↗

arXiv2016

Supervisory Control of Fuzzy Discrete Event Systems for Simulation Equivalence

The supervisory control theory of fuzzy discrete event systems (FDESs) for fuzzy language equivalence has been developed. However, in a way, language equivalence has limited expressiveness. So if the given specification can not be expressed by language equivalence, then the control for language equivalence does not work. In this paper, we further establish the supervisory control theory of FDESs for fuzzy simulation equivalence whose expressiveness is stronger than that of fuzzy language equivalence. First, we formalize the notions of fuzzy simulation and fuzzy simulation equivalence between two FDESs. Then we present a method for deciding whether there is a fuzzy simulation or not. In addition, we also show several basic properties of fuzzy simulation relations. Afterwards, we put forward the notion of fuzzy simulation-based controllability, and particularly show that it serves as a necessary and sufficient condition for the existence of the fuzzy supervisors of FDESs. Moreover, we study the "range" control problem of FDESs. Some examples are given to illustrate the main results obtained.

eess.SY↗

arXiv2016

Bi-Fuzzy Discrete Event Systems and Their Supervisory Control Theory

It is well known that type-1 fuzzy sets (T1 FSs) have limited capabilities to handle some data uncertainties directly, and type-2 fuzzy sets (T2 FSs) can cover the shortcoming of T1 FSs to a certain extent. Fuzzy discrete event systems (FDESs) were proposed based on T1 FSs theory. Hence, FDES may not be a satisfactory model to characterize some high-uncertainty systems. In this paper, we propose a new model, called as bi-fuzzy discrete event systems (BFDESs), by combining classical DESs theory and T2 FSs theory. Then, we consider the supervisory control problem of BFDESs. The bi-fuzzy controllability theorem and nonblocking bi-fuzzy controllability theorem are demonstrated. Also, an algorithm for checking the bi-fuzzy controllability condition is presented. In addition, two controllable approximations to an uncontrollable language are investigated in detail. An illustrative example is provided to show the applicability and the advantages of BFDESs model.

eess.SY↗

arXiv2016

Time-space tradeoffs for two-way finite automata

We explore bounds of {\em time-space tradeoffs} in language recognition on {\em two-way finite automata} for some special languages. We prove: (1) a time-space tradeoff upper bound for recognition of the languages $L_{EQ}(n)$ on {\em two-way probabilistic finite automata} (2PFA): $TS={\bf O}(n\log n)$, whereas a time-space tradeoff lower bound on {\em two-way deterministic finite automata} is ${\bf Ω}(n^2)$, (2) a time-space tradeoff upper bound for recognition of the languages $L_{INT}(n)$ on {\em two-way finite automata with quantum and classical states} (2QCFA): $TS={\bf O}(n^{3/2}\log n)$, whereas a lower bound on 2PFA is $TS={\bf Ω}(n^2)$, (3) a time-space tradeoff upper bound for recognition of the languages $L_{NE}(n)$ on exact 2QCFA: $TS={\bf O}(n^{1.87} \log n)$, whereas a lower bound on 2PFA is $TS={\bf Ω}(n^2)$. It has been proved (Klauck, STOC'00) that the exact one-way quantum finite automata have no advantage comparing to classical finite automata in recognizing languages. However, the result (3) shows that the exact 2QCFA do have an advantage in comparison with their classical counterparts, which has been the first example showing that the exact quantum computing have advantage in time-space tradeoff comparing to classical computing. Usually, two communicating parties, Alice and Bob, are supposed to have an access to arbitrary computational power in {\em communication complexity} model that is used. Instead of that we will consider communication complexity in such a setting that two parties are using only finite automata and we prove in this setting that quantum automata are better than classical automata and also probabilistic automata are better than deterministic automata for some well known tasks.

quant-ph↗

arXiv2016

Secure $N$-dimensional Simultaneous Dense Coding and Applications

Simultaneous dense coding guarantees that Bob and Charlie simultaneously receive their respective information from Alice in their respective processes of dense coding. The idea is to use the so-called locking operation to "lock" the entanglement channels, thus requiring a joint unlocking operation by Bob and Charlie in order to simultaneously obtain the information sent by Alice. We present some new results on simultaneous dense coding: (1) We propose three simultaneous dense coding protocols, which use different $N$-dimensional entanglement (Bell state, W state and GHZ state). (2) Besides the quantum Fourier transform, two new locking operators are introduced (the double controlled-NOT operator and the SWAP operator). (3) In the case that spatially distant Bob and Charlie have to finalise the protocol by implementing the unlocking operation through communication, we improve our protocol's fairness, with respect to Bob and Charlie, by implementing the unlocking operation in series of steps. (4) We improve the security of simultaneous dense coding against the intercept-resend attack. (5) We show that simultaneous dense coding can be used to implement a fair contract signing protocol. (6) We also show that the $N$-dimensional quantum Fourier transform can act as the locking operator in simultaneous teleportation of $N$-level quantum systems.

quant-ph↗

arXiv2015

Improvement of a quantum broadcasting multiple blind signature scheme based on quantum teleportation

Recently, a broadcasting multiple blind signature scheme based on quantum teleportation has been proposed for the first time. It is claimed to have unconditional security and properties of quantum multiple signature and quantum blind signature. In this paper, we analyze the security of the protocol and show that the signatory Ui can learn the signed message m by a single particle measurement and the signed message m can be modified at random by anyone according to the scheme. Furthermore, there are some participant attacks and external attacks existing in the scheme. Finally we present an improved protocol and show that the improved scheme can resist all of the mentioned attacks. Meanwhile, the secret keys can be used again and again, which will make it more efficient and practical.

quant-ph↗

arXiv2015

Promise problems solved by quantum and classical finite automata

The concept of promise problems was introduced and started to be systematically explored by Even, Selman, Yacobi, Goldreich, and other scholars. It has been argued that promise problems should be seen as partial decision problems and as such that they are more fundamental than decision problems and formal languages that used to be considered as the basic ones for complexity theory. The main purpose of this paper is to explore the promise problems accepted by classical, quantum and also semi-quantum finite automata. More specifically, we first introduce two acceptance modes of promise problems, recognizability and solvability, and explore their basic properties. Afterwards, we show several results concerning descriptional complexity on promise problems. In particular, we prove: (1) there is a promise problem that can be recognized exactly by measure-once one-way quantum finite automata (MO-1QFA), but no deterministic finite automata (DFA) can recognize it; (2) there is a promise problem that can be solved with error probability $ε\leq 1/3$ by one-way finite automaton with quantum and classical states (1QCFA), but no one-way probability finite automaton (PFA) can solve it with error probability $ε\leq 1/3$; and especially, (3) there are promise problems $A(p)$ with prime $p$ that can be solved {\em with any error probability} by MO-1QFA with only two quantum basis states, but they can not be solved exactly by any MO-1QFA with two quantum basis states; in contrast, the minimal PFA solving $A(p)$ with any error probability (usually smaller than $1/2$) has $p$ states. Finally, we mention a number of problems related to promise for further study.

cs.FL↗

arXiv2015

Lower bounds on the size of semi-quantum finite automata

In the literature, there exist several interesting hybrid models of finite automata which have both quantum and classical states. We call them semi-quantum automata. In this paper, we compare the descriptional power of these models with that of DFA. Specifically, we present a uniform method that gives a lower bound on the size of the three existing main models of semi-quantum automata, and this bound shows that semi-quantum automata can be at most exponentially more concise than DFA. Compared with a recent work (Bianchi, Mereghetti, Palano, Theoret. Comput. Sci., 551(2014), 102-115), our method shows the following two advantages: (i) our method is much more concise; and (ii) our method is universal, since it is applicable to the three existing main models of semi-quantum automata, instead of only a specific model.

cs.FL↗

arXiv2015

Power of the interactive proof systems with verifiers modeled by semi-quantum two-way finite automata

In this paper we explore the power of AM for the case that verifiers are {\em two-way finite automata with quantum and classical states} (2QCFA)--introduced by Ambainis and Watrous in 2002--and the communications are classical. It is of interest to consider AM with such "semi-quantum" verifiers because they use only limited quantum resources. Our main result is that such Quantum Arthur-Merlin proof systems (QAM(2QCFA)) with polynomial expected running time are more powerful than in the case verifiers are two-way probabilistic finite automata (AM(2PFA)) with polynomial expected running time. Moreover, we prove that there is a language which can be recognized by an exponential expected running time QAM(2QCFA), but can not be recognized by any AM(2PFA), and that the NP-complete language $L_{knapsack}$ can also be recognized by a QAM(2QCFA) working only on quantum pure states using unitary operators.

cs.CC↗

arXiv2015

Generalizations of the distributed Deutsch-Jozsa promise problem

In the {\em distributed Deutsch-Jozsa promise problem}, two parties are to determine whether their respective strings $x,y\in\{0,1\}^n$ are at the {\em Hamming distance} $H(x,y)=0$ or $H(x,y)=\frac{n}{2}$. Buhrman et al. (STOC' 98) proved that the exact {\em quantum communication complexity} of this problem is ${\bf O}(\log {n})$ while the {\em deterministic communication complexity} is ${\bf Ω}(n)$. This was the first impressive (exponential) gap between quantum and classical communication complexity. In this paper, we generalize the above distributed Deutsch-Jozsa promise problem to determine, for any fixed $\frac{n}{2}\leq k\leq n$, whether $H(x,y)=0$ or $H(x,y)= k$, and show that an exponential gap between exact quantum and deterministic communication complexity still holds if $k$ is an even such that $\frac{1}{2}n\leq k<(1-λ) n$, where $0< λ<\frac{1}{2}$ is given. We also deal with a promise version of the well-known {\em disjointness} problem and show also that for this promise problem there exists an exponential gap between quantum (and also probabilistic) communication complexity and deterministic communication complexity of the promise version of such a disjointness problem. Finally, some applications to quantum, probabilistic and deterministic finite automata of the results obtained are demonstrated.

quant-ph↗

arXiv2014

Potential of quantum finite automata with exact acceptance

The potential of the exact quantum information processing is an interesting, important and intriguing issue. For examples, it has been believed that quantum tools can provide significant, that is larger than polynomial, advantages in the case of exact quantum computation only, or mainly, for problems with very special structures. We will show that this is not the case. In this paper the potential of quantum finite automata producing outcomes not only with a (high) probability, but with certainty (so called exactly) is explored in the context of their uses for solving promise problems and with respect to the size of automata. It is shown that for solving particular classes $\{A^n\}_{n=1}^{\infty}$ of promise problems, even those without some very special structure, that succinctness of the exact quantum finite automata under consideration, with respect to the number of (basis) states, can be very small (and constant) though it grows proportional to $n$ in the case deterministic finite automata (DFAs) of the same power are used. This is here demonstrated also for the case that the component languages of the promise problems solvable by DFAs are non-regular. The method used can be applied in finding more exact quantum finite automata or quantum algorithms for other promise problems.

cs.FL↗

arXiv2014

From Quantum Query Complexity to State Complexity

State complexity of quantum finite automata is one of the interesting topics in studying the power of quantum finite automata. It is therefore of importance to develop general methods how to show state succinctness results for quantum finite automata. One such method is presented and demonstrated in this paper. In particular, we show that state succinctness results can be derived out of query complexity results.

cs.CC↗

arXiv2014

On the state complexity of semi-quantum finite automata

Some of the most interesting and important results concerning quantum finite automata are those showing that they can recognize certain languages with (much) less resources than corresponding classical finite automata \cite{Amb98,Amb09,AmYa11,Ber05,Fre09,Mer00,Mer01,Mer02,Yak10,ZhgQiu112,Zhg12}. This paper shows three results of such a type that are stronger in some sense than other ones because (a) they deal with models of quantum automata with very little quantumness (so-called semi-quantum one- and two-way automata with one qubit memory only); (b) differences, even comparing with probabilistic classical automata, are bigger than expected; (c) a trade-off between the number of classical and quantum basis states needed is demonstrated in one case and (d) languages (or the promise problem) used to show main results are very simple and often explored ones in automata theory or in communication complexity, with seemingly little structure that could be utilized.

cs.FL↗

arXiv2013

Communication complexity of promise problems and their applications to finite automata

Equality and disjointness are two of the most studied problems in communication complexity. They have been studied for both classical and also quantum communication and for various models and modes of communication. Buhrman et al. [Buh98] proved that the exact quantum communication complexity for a promise version of the equality problem is ${\bf O}(\log {n})$ while the classical deterministic communication complexity is $n+1$ for two-way communication, which was the first impressively large (exponential) gap between quantum and classical (deterministic and probabilistic) communication complexity. If an error is tolerated, both quantum and probabilistic communication complexities for equality are ${\bf O}(\log {n})$. However, even if an error is tolerated, the gaps between quantum (probabilistic) and deterministic complexity are not larger than quadratic for the disjointness problem. It is therefore interesting to ask whether there are some promise versions of the disjointness problem for which bigger gaps can be shown. We give a positive answer to such a question. Namely, we prove that there exists an exponential gap between quantum (even probabilistic) communication complexity and classical deterministic communication complexity of some specific versions of the disjointness problem. Klauck [Kla00] proved, for any language, that the state complexity of exact quantum/classical finite automata, which is a general model of one-way quantum finite automata, is not less than the state complexity of an equivalent one-way deterministic finite automata (1DFA). In this paper we show, using a communication complexity result, that situation may be different for some promise problems. Namely, we show for certain promise problem that the gap between the state complexity of exact one-way quantum finite automata and 1DFA can be exponential.

cs.CC↗