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Mingsheng Ying

Publications and source records attributed to Mingsheng Ying.

172 records · Page 10Linked to original sources
arXiv2005

Catalyst-assisted Probabilistic Entanglement Transformation

We are concerned with catalyst-assisted probabilistic entanglement transformations. A necessary and sufficient condition is presented under which there exist partial catalysts that can increase the maximal transforming probability of a given entanglement transformation. We also design an algorithm which leads to an efficient method for finding the most economical partial catalysts with minimal dimension. The mathematical structure of catalyst-assisted probabilistic transformation is carefully investigated.

quant-ph↗
arXiv2005

Efficiency of Deterministic Entanglement Transformation

We prove that sufficiently many copies of a bipartite entangled pure state can always be transformed into some copies of another one with certainty by local quantum operations and classical communication. The efficiency of such a transformation is characterized by deterministic entanglement exchange rate, and it is proved to be always positive and bounded from top by the infimum of the ratios of Renyi's entropies of source state and target state. A careful analysis shows that the deterministic entanglement exchange rate cannot be increased even in the presence of catalysts. As an application, we show that there can be two incomparable states with deterministic entanglement exchange rate strictly exceeding 1.

quant-ph↗
arXiv2005

The Existence of Quantum Entanglement Catalysts

Without additional resources, it is often impossible to transform one entangled quantum state into another with local quantum operations and classical communication. Jonathan and Plenio [Phys. Rev. Lett. 83, 3566(1999)] presented an interesting example showing that the presence of another state, called a catalyst, enables such a transformation without changing the catalyst. They also pointed out that in general it is very hard to find an analytical condition under which a catalyst exists. In this paper we study the existence of catalysts for two incomparable quantum states. For the simplest case of $2\times 2$ catalysts for transformations from one $4\times 4$ state to another, a necessary and sufficient condition for existence is found. For the general case, we give an efficient polynomial time algorithm to decide whether a $k\times k$ catalyst exists for two $n\times n$ incomparable states, where $k$ is treated as a constant.

quant-ph↗
arXiv2005

An Equivalence of Entanglement-Assisted Transformation and Multiple-Copy Entanglement Transformation

We examine the powers of entanglement-assisted transformation and multiple-copy entanglement transformation. First, we find a sufficient condition of when a given catalyst is useful in producing another specific target state. As an application of this condition, for any non-maximally entangled bipartite pure state and any integer $n$ not less than 4, we are able to explicitly construct a set of $n\times n$ quantum states which can be produced by using the given state as a catalyst. Second, we prove that for any positive integer $k$, entanglement-assisted transformation with $k\times k$-dimensional catalysts is useful in producing a target state if and only if multiple-copy entanglement transformation with $k$ copies of state is useful in producing the same target. Moreover, a necessary and sufficient condition for both of them is obtained in terms of the Schmidt coefficients of the target. This equivalence of entanglement-assisted transformation and multiple-copy entanglement transformation implies many interesting properties of entanglement transformation. Furthermore, these results are generalized to the case of probabilistic entanglement transformations.

quant-ph↗
arXiv2004

Quantum search algorithm by adiabatic evolution under a priori probability

Grover's algorithm is one of the most important quantum algorithms, which performs the task of searching an unsorted database without a priori probability. Recently the adiabatic evolution has been used to design and reproduce quantum algorithms, including Grover's algorithm. In this paper, we show that quantum search algorithm by adiabatic evolution has two properties that conventional quantum search algorithm doesn't have. Firstly, we show that in the initial state of the algorithm only the amplitude of the basis state corresponding to the solution affects the running time of the algorithm, while other amplitudes do not. Using this property, if we know a priori probability about the location of the solution before search, we can modify the adiabatic evolution to make the algorithm faster. Secondly, we show that by a factor for the initial and finial Hamiltonians we can reduce the running time of the algorithm arbitrarily. Especially, we can reduce the running time of adiabatic search algorithm to a constant time independent of the size of the database. The second property can be extended to other adiabatic algorithms.

quant-ph↗
arXiv2004

Comparability of multipartite entanglement

We prove, in a multipartite setting, that it's always feasible to exactly transform a genuinely $m$-partite entangled state with sufficient many copies to any other $m$-partite state via local quantum operation and classical communication. This result affirms the comparability of multipartite pure entangled states.

quant-ph↗
arXiv2004

Supervisory Control of Fuzzy Discrete Event Systems

In order to cope with situations in which a plant's dynamics are not precisely known, we consider the problem of supervisory control for a class of discrete event systems modelled by fuzzy automata. The behavior of such discrete event systems is described by fuzzy languages; the supervisors are event feedback and can disable only controllable events with any degree. The concept of discrete event system controllability is thus extended by incorporating fuzziness. In this new sense, we present a necessary and sufficient condition for a fuzzy language to be controllable. We also study the supremal controllable fuzzy sublanguage and the infimal controllable fuzzy superlanguage when a given pre-specified desired fuzzy language is uncontrollable. Our framework generalizes that of Ramadge-Wonham and reduces to Ramadge-Wonham framework when membership grades in all fuzzy languages must be either 0 or 1. The theoretical development is accompanied by illustrative numerical examples.

cs.DM↗
arXiv2004

A Theory of Computation Based on Quantum Logic (I)

The (meta)logic underlying classical theory of computation is Boolean (two-valued) logic. Quantum logic was proposed by Birkhoff and von Neumann as a logic of quantum mechanics more than sixty years ago. The major difference between Boolean logic and quantum logic is that the latter does not enjoy distributivity in general. The rapid development of quantum computation in recent years stimulates us to establish a theory of computation based on quantum logic. The present paper is the first step toward such a new theory and it focuses on the simplest models of computation, namely finite automata. It is found that the universal validity of many properties of automata depend heavily upon the distributivity of the underlying logic. This indicates that these properties does not universally hold in the realm of quantum logic. On the other hand, we show that a local validity of them can be recovered by imposing a certain commutativity to the (atomic) statements about the automata under consideration. This reveals an essential difference between the classical theory of computation and the computation theory based on quantum logic.

cs.LO↗
arXiv2003

Quantum operation, quantum Fourier transform and semi-definite programming

We analyze a class of quantum operations based on a geometrical representation of $d-$level quantum system (or qudit for short). A sufficient and necessary condition of complete positivity, expressed in terms of the quantum Fourier transform, is found for this class of operations. A more general class of operations on qudits is also considered and its completely positive condition is reduced to the well-known semi-definite programming problem.

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