arXiv subjects

Daowen Qiu

Publications and source records attributed to Daowen Qiu.

At least 73 records · Page 4Linked to original sources

arXiv2013

Exponentially more concise quantum recognition of non-RMM regular languages

We show that there are quantum devices that accept all regular languages and that are exponentially more concise than deterministic finite automata (DFA). For this purpose, we introduce a new computing model of {\it one-way quantum finite automata} (1QFA), namely, {\it one-way quantum finite automata together with classical states} (1QFAC), which extends naturally both measure-only 1QFA and DFA and whose state complexity is upper-bounded by both. The original contributions of the paper are the following. First, we show that the set of languages accepted by 1QFAC with bounded error consists precisely of all regular languages. Second, we prove that 1QFAC are at most exponentially more concise than DFA. Third, we show that the previous bound is tight for families of regular languages that are not recognized by measure-once (RMO), measure-many (RMM) and multi-letter 1QFA. % More concretely we exhibit regular languages $L^0(m)$ for $m$ prime such that: (i) $L^0(m)$ cannot be recognized by measure-once, measure-many and multi-letter 1QFA; (ii) the minimal DFA that accepts $L^0(m)$ has $O(m)$ states; (iii) there is a 1QFAC with constant classical states and $O(\log(m))$ quantum basis that accepts $L^0(m)$. Fourth, we give a polynomial-time algorithm for determining whether any two 1QFAC are equivalent. Finally, we show that state minimization of 1QFAC is decidable within EXPSPACE. We conclude the paper by posing some open problems.

quant-ph↗

arXiv2013

Decidability of minimization of fuzzy automata

State minimization is a fundamental problem in automata theory. The problem is also of great importance in the study of fuzzy automata. However, most work in the literature considered only state reduction of fuzzy automata, whereas the state minimization problem is almost untouched for fuzzy automata. Thus in this paper we focus on the latter problem. Formally, the decision version of the minimization problem of fuzzy automata is as follows: \begin{itemize} \item Given a fuzzy automaton $\mathcal{A}$ and a natural number $k$, that is, a pair $\langle \mathcal{A}, k\rangle$, is there a $k$-state fuzzy automaton equivalent to $\mathcal{A}$? \end{itemize} We prove for the first time that the above problem is decidable for fuzzy automata over totally ordered lattices. To this end, we first give the concept of systems of fuzzy polynomial equations and then present a procedure to solve these systems. Afterwards, we apply the solvability of a system of fuzzy polynomial equations to the minimization problem mentioned above, obtaining the decidability. Finally, we point out that the above problem is at least as hard as PSAPCE-complete.

cs.FL↗

arXiv2012

Investigating the implementation of restricted sets of multiqubit operations on distant qubits: a communication complexity perspective

We propose a protocol for Alice to implement a multiqubit quantum operation from the restricted sets on distant qubits possessed by Bob, and then we investigate the communication complexity of the task in different communication scenarios. By comparing with the previous work, our protocol works without prior sharing of entanglement, and requires less communication resources than the previous protocol in the qubit-transmission scenario. Furthermore, we generalize our protocol to $d$-dimensional operations.

quant-ph↗

arXiv2012

State succinctness of two-way finite automata with quantum and classical states

{\it Two-way quantum automata with quantum and classical states} (2QCFA) were introduced by Ambainis and Watrous in 2002. In this paper we study state succinctness of 2QCFA. For any $m\in {\mathbb{Z}}^+$ and any $ε<1/2$, we show that: {enumerate} there is a promise problem $A^{eq}(m)$ which can be solved by a 2QCFA with one-sided error $ε$ in a polynomial expected running time with a constant number (that depends neither on $m$ nor on $\varepsilon$) of quantum states and $\mathbf{O}(\log{\frac{1}ε)}$ classical states, whereas the sizes of the corresponding {\it deterministic finite automata} (DFA), {\it two-way nondeterministic finite automata} (2NFA) and polynomial expected running time {\it two-way probabilistic finite automata} (2PFA) are at least $2m+2$, $\sqrt{\log{m}}$, and $\sqrt[3]{(\log m)/b}$, respectively; there exists a language $L^{twin}(m)=\{wcw| w\in\{a,b\}^*\}$ over the alphabet $Σ=\{a,b,c\}$ which can be recognized by a 2QCFA with one-sided error $ε$ in an exponential expected running time with a constant number of quantum states and $\mathbf{O}(\log{\frac{1}ε)}$ classical states, whereas the sizes of the corresponding DFA, 2NFA and polynomial expected running time 2PFA are at least $2^m$, $\sqrt{m}$, and $\sqrt[3]{m/b}$, respectively; {enumerate} where $b$ is a constant.

quant-ph↗

arXiv2011

Some Languages Recognized by Two-Way Finite Automata with Quantum and Classical States

{\it Two-way finite automata with quantum and classical states} (2QCFA) were introduced by Ambainis and Watrous, and it was shown that 2QCFA have superiority over {\it two-way probabilistic finite automata} (2PFA) for recognizing some non-regular languages such as the language $L_{eq}=\{a^{n}b^{n}\mid n\in \mathbf{N}\}$ and the palindrome language $L_{pal}=\{ω\in \{a,b\}^*\midω=ω^R\}$, where $x^R$ is $x$ in the reverse order. It is interesting to find more languages like these that witness the superiority of 2QCFA over 2PFA. In this paper, we consider the language $L_{m}=\{xcy\mid Σ=\{a, b, c\}, x,y\in\{a,b\}^{*},c\inΣ, |x|=|y|\}$ that is similar to the middle language $L_{middle}=\{xay\mid x,y\inΣ^{*},a\inΣ, |x|=|y|\}$. We prove that the language $L_{m}$ can be recognized by 2QCFA with one-sided error in polynomial expected time. Also, we show that $L_{m}$ can be recognized by 2PFA with bounded error, but only in exponential expected time. Thus $L_{m}$ is another witness of the fact that 2QCFA are more powerful than their classical counterparts.

quant-ph↗

arXiv2011

One-way finite automata with quantum and classical states

In this paper, we introduce and explore a new model of {\it quantum finite automata} (QFA). Namely, {\it one-way finite automata with quantum and classical states} (1QCFA), a one way version of {\it two-way finite automata with quantum and classical states} (2QCFA) introduced by Ambainis and Watrous in 2002 \cite{AJ}. First, we prove that {\it one-way probabilistic finite automata} (1PFA) \cite{AP} and {\it one-way quantum finite automata with control language} (1QFACL) \cite{ACB} as well as several other models of QFA, can be simulated by 1QCFA. Afterwards, we explore several closure properties for the family of languages accepted by 1QCFA. Finally, the state complexity of 1QCFA is explored and the main succinctness result is derived. Namely, for any prime $m$ and any $ε_1>0$, there exists a language $L_{m}$ that cannot be recognized by any {\it measure-many one-way quantum finite automata} (MM-1QFA) \cite{Kon97} with bounded error $7/9+ε_1$, and any 1PFA recognizing it has at last $m$ states, but $L_{m}$ can be recognized by a 1QCFA for any error bound $ε>0$ with $\bf{O}(\log{m})$ quantum states and 12 classical states.

quant-ph↗

arXiv2011

Two-tape finite automata with quantum and classical states

{\it Two-way finite automata with quantum and classical states} (2QCFA) were introduced by Ambainis and Watrous, and {\it two-way two-tape deterministic finite automata} (2TFA) were introduced by Rabin and Scott. In this paper we study 2TFA and propose a new computing model called {\it two-way two-tape finite automata with quantum and classical states} (2TQCFA). First, we give efficient 2TFA algorithms for recognizing languages which can be recognized by 2QCFA. Second, we give efficient 2TQCFA algorithms to recognize several languages whose status vis-a-vis 2QCFA have been posed as open questions, such as $L_{square}=\{a^{n}b^{n^{2}}\mid n\in \mathbf{N}\}$. Third, we show that $\{a^{n}b^{n^{k}}\mid n\in \mathbf{N}\}$ can be recognized by {\it $(k+1)$-tape deterministic finite automata} ($(k+1)$TFA). Finally, we introduce {\it $k$-tape automata with quantum and classical states} ($k$TQCFA) and prove that $\{a^{n}b^{n^{k}}\mid n\in \mathbf{N}\}$ can be recognized by $k$TQCFA.

quant-ph↗

arXiv2010

Decidability of the Equivalence of Multi-Letter Quantum Finite Automata

Multi-letter {\it quantum finite automata} (QFAs) were a quantum variant of classical {\it one-way multi-head finite automata} (J. Hromkovič, Acta Informatica 19 (1983) 377-384), and it has been shown that this new one-way QFAs (multi-letter QFAs) can accept with no error some regular languages $(a+b)^{*}b$ that are unacceptable by the previous one-way QFAs. In this paper, we study the decidability of the equivalence of multi-letter QFAs, and the main technical contributions are as follows: (1) We show that any two automata, a $k_{1}$-letter QFA ${\cal A}_1$ and a $k_{2}$-letter QFA ${\cal A}_2$, over the same input alphabet $Σ$ are equivalent if and only if they are $(n^2m^{k-1}-m^{k-1}+k)$-equivalent, where $m=|Σ|$ is the cardinality of $Σ$, $k=\max(k_{1},k_{2})$, and $n=n_{1}+n_{2}$, with $n_{1}$ and $n_{2}$ being the numbers of states of ${\cal A}_{1}$ and ${\cal A}_{2}$, respectively. When $k=1$, we obtain the decidability of equivalence of measure-once QFAs in the literature. It is worth mentioning that our technical method is essentially different from that for the decidability of the case of single input alphabet (i.e., $m=1$). (2) However, if we determine the equivalence of multi-letter QFAs by checking all strings of length not more than $ n^2m^{k-1}-m^{k-1}+k$, then the worst time complexity is exponential, i.e., $O(n^6m^{n^2m^{k-1}-m^{k-1}+2k-1})$. Therefore, we design a polynomial-time $O(m^{2k-1}n^{8}+km^kn^{6})$ algorithm for determining the equivalence of any two multi-letter QFAs. Here, the time complexity is concerning the number of states in the multi-letter QFAs, and $k$ is thought of as a constant.

cs.FL↗

arXiv2010

Characterizations of one-way general quantum finite automata

In this paper we study a generalized model named one-way general quantum finite automata} (1gQFA), in which each symbol in the input alphabet induces a trace-preserving quantum operation, instead of a unitary transformation. Two different kinds of 1gQFA will be studied: measure-once one-way general quantum finite automata} (MO-1gQFA), and measure-many one-way general quantum finite automata (MM-1gQFA). We prove that MO-1gQFA recognize, with bounded error, precisely the set of all regular languages. We prove that MM-1gQFA also recognize only regular languages with bounded error. Thus, MM-1gQFA and MO-1gQFA have the same language recognition power, which is greatly different from the conventional case in which the number of times the measurement is performed in the computation generally affects the language recognition power of one-way QFA. Finally, we present a sufficient and necessary condition for two MM-1gQFA to be equivalent.

quant-ph↗

arXiv2010

Reply to "Comment on 'Semiquantum-key distribution using less than four quantum states' "

Recently Boyer and Mor pointed out the first conclusion of Lemma 1 in our original paper is not correct, and therefore, the proof of Theorem 5 based on Lemma 1 is wrong. Furthermore, they gave a direct proof for Theorem 5 and affirmed the conclusions in our original paper. In this reply, we admit the first conclusion of Lemma 1 is not correct, but we need to point out the second conclusion of Lemma 1 is correct. Accordingly, all the proofs for Lemma 2, Lemma 3, and Theorems 3--6 are only based on the the second conclusion of Lemma 1 and therefore are correct.

quant-ph↗

arXiv2010

Arbitrated quantum signature schemes without using entangled states

A digital signature is a mathematical scheme for demonstrating the authenticity of a digital message or document. For signing quantum messages, some arbitrated quantum signature schemes have being proposed. However, in the existing literature, arbitrated quantum signature schemes depend on entanglement. In this paper, we present two arbitrated quantum signature schemes without utilizing entangled states in the signing phase and the verifying phase. The first proposed scheme can preserve the merits in the existing schemes. Then, we point out, in this scheme and the prior schemes, there exists a problem that Bob can repudiate the integrality of the signatures. To conquer this problem, we construct another arbitrated quantum signature scheme without using quantum entangled states but using a public board. The new scheme has three advantages: it does not utilize entangled states while it can preserve all merits in the existing schemes; the integrality of the signature can avoid being disavowed by the receiver; and, it provides a higher efficiency in transmission and reduces the complexity of implementation. Furthermore, we present a technique such that the quantum message can keep secret to the arbitrator in a arbitrated quantum signature scheme.

quant-ph↗

arXiv2009

Simultaneous Dense Coding

We present a dense coding scheme between one sender and two receivers, which guarantees that the receivers simultaneously obtain their respective messages. In our scheme, the quantum entanglement channel is first locked by the sender so that the receivers cannot learn their messages unless they collaborate to perform the unlocking operation. We also show that the quantum Fourier transform can act as the locking operator both in simultaneous dense coding and teleportation.

quant-ph↗

arXiv2009

Minimum-error discrimination of quantum states: New bounds and comparison

The minimum-error probability of ambiguous discrimination for two quantum states is the well-known {\it Helstrom limit} presented in 1976. Since then, it has been thought of as an intractable problem to obtain the minimum-error probability for ambiguously discriminating arbitrary $m$ quantum states. In this paper, we obtain a new lower bound on the minimum-error probability for ambiguous discrimination and compare this bound with six other bounds in the literature. Moreover, we show that the bound between ambiguous and unambiguous discrimination does not extend to ensembles of more than two states. Specifically, the main technical contributions are described as follows: (1) We derive a new lower bound on the minimum-error probability for ambiguous discrimination among arbitrary $m$ mixed quantum states with given prior probabilities, and we present a necessary and sufficient condition to show that this lower bound is attainable. (2) We compare this new lower bound with six other bounds in the literature in detail, and, in some cases, this bound is optimal. (3) It is known that if $m=2$, the optimal inconclusive probability of unambiguous discrimination $Q_{U}$ and the minimum-error probability of ambiguous discrimination $Q_{E}$ between arbitrary given $m$ mixed quantum states have the relationship $Q_{U}\geq 2Q_{E}$. In this paper, we show that, however, if $m>2$, the relationship $Q_{U}\geq 2Q_{E}$ may not hold again in general, and there may be no supremum of $Q_{U}/Q_{E}$ for more than two states, which may also reflect an essential difference between discrimination for two-states and multi-states. (4) A number of examples are constructed.

quant-ph↗

arXiv2009

Hierarchy and equivalence of multi-letter quantum finite automata

Multi-letter {\it quantum finite automata} (QFAs) were a new one-way QFA model proposed recently by Belovs, Rosmanis, and Smotrovs (LNCS, Vol. 4588, Springer, Berlin, 2007, pp. 60-71), and they showed that multi-letter QFAs can accept with no error some regular languages ($(a+b)^{*}b$) that are unacceptable by the one-way QFAs. In this paper, we continue to study multi-letter QFAs. We mainly focus on two issues: (1) we show that $(k+1)$-letter QFAs are computationally more powerful than $k$-letter QFAs, that is, $(k+1)$-letter QFAs can accept some regular languages that are unacceptable by any $k$-letter QFA. A comparison with the one-way QFAs is made by some examples; (2) we prove that a $k_{1}$-letter QFA ${\cal A}_1$ and another $k_{2}$-letter QFA ${\cal A}_2$ are equivalent if and only if they are $(n_{1}+n_{2})^{4}+k-1$-equivalent, and the time complexity of determining the equivalence of two multi-letter QFAs using this method is $O(n^{12}+k^{2}n^{4}+kn^{8})$, where $n_{1}$ and $n_{2}$ are the numbers of states of ${\cal A}_{1}$ and ${\cal A}_{2}$, respectively, and $k=\max(k_{1},k_{2})$. Some other issues are addressed for further consideration.

cs.CC↗

arXiv2008

Research report: State complexity of operations on two-way quantum finite automata

This paper deals with the size complexity of minimal {\it two-way quantum finite automata} (2qfa's) necessary for operations to perform on all inputs of each fixed length. Such a complexity measure, known as state complexity of operations, is useful in measuring how much information is necessary to convert languages. We focus on intersection, union, reversals, and catenation operations and show some upper bounds of state complexity of operations on 2qfa's. Also, we present a number of non-regular languages and prove that these languages can be accepted by 2qfa's with one-sided error probabilities within linear time. Notably, these examples show that our bounds obtained for these operations are not tight, and therefore worth improving. We give an instance to show that the upper bound of the state number for the simulation of one-way deterministic finite automata by two-way reversible finite automata is not tight in general.

cs.DM↗

arXiv2007

Minimum-error discrimination between mixed quantum states

We derive a general lower bound on the minimum-error probability for {\it ambiguous discrimination} between arbitrary $m$ mixed quantum states with given prior probabilities. When $m=2$, this bound is precisely the well-known Helstrom limit. Also, we give a general lower bound on the minimum-error probability for discriminating quantum operations. Then we further analyze how this lower bound is attainable for ambiguous discrimination of mixed quantum states by presenting necessary and sufficient conditions related to it. Furthermore, with a restricted condition, we work out a upper bound on the minimum-error probability for ambiguous discrimination of mixed quantum states. Therefore, some sufficient conditions are obtained for the minimum-error probability attaining this bound. Finally, under the condition of the minimum-error probability attaining this bound, we compare the minimum-error probability for {\it ambiguously} discriminating arbitrary $m$ mixed quantum states with the optimal failure probability for {\it unambiguously} discriminating the same states.

quant-ph↗

arXiv2007

Fuzzy Discrete Event Systems under Fuzzy Observability and a test-algorithm

In order to more effectively cope with the real-world problems of vagueness, impreciseness, and subjectivity, fuzzy discrete event systems (FDESs) were proposed recently. Notably, FDESs have been applied to biomedical control for HIV/AIDS treatment planning and sensory information processing for robotic control. Qiu, Cao and Ying independently developed supervisory control theory of FDESs. We note that the controllability of events in Qiu's work is fuzzy but the observability of events is crisp, and, the observability of events in Cao and Ying's work is also crisp although the controllability is not completely crisp since the controllable events can be disabled with any degrees. Motivated by the necessity to consider the situation that the events may be observed or controlled with some membership degrees, in this paper, we establish the supervisory control theory of FDESs with partial observations, in which both the observability and controllability of events are fuzzy instead. We formalize the notions of fuzzy controllability condition and fuzzy observability condition. And Controllability and Observability Theorem of FDESs is set up in a more generic framework. In particular, we present a detailed computing flow to verify whether the controllability and observability conditions hold. Thus, this result can decide the existence of supervisors. Also, we use this computing method to check the existence of supervisors in the Controllability and Observability Theorem of classical discrete event systems (DESs), which is a new method and different from classical case. A number of examples are elaborated on to illustrate the presented results.

cs.LO↗

arXiv2007

Local Entanglement Is Not Necessary for Perfect Discrimination between Unitary Operations Acting on Two-Qudits by LOCC

Recently, the problem of discriminating multipartite unitary operations by local operations and classical communication (LOCC) has attracted significant attention. The latest work in the literature on this problem showed that two multipartite unitary operations can always be perfectly distinguished by LOCC when a finite number of runs are allowable. However, in these schemes, local entanglement (an entangled state holden by one party) was required, which seems to imply that local entanglement is necessary for perfect discrimination between unitary operations by LOCC. In this article, we show that a perfect discrimination between two unitary operations acting on a two-qudits can always be achieved without exploiting any entanglement. As a result, we conclude that local entanglement is not necessary for perfect discrimination between unitary operations acting on two-qudits by LOCC.

quant-ph↗