arXiv subjects

Yun Shang

Publications and source records attributed to Yun Shang.

22 records · Page 2Linked to original sources

arXiv2018

Quantum communication protocols by quantum walks with two coins

We introduce some new perfect state transfer and teleportation schemes by quantum walks with two coins. Encoding the transferred information in coin 1 state and alternatively using two coin operators, we can perfectly recover the information on coin 1 state at target position only by at most two times of flipping operation. Based on quantum walks with two coins either on the line or on the $N$-circle, we can perfectly transfer any qubit state. In addition, using quantum walks with two coins either on complete graphs or regular graphs, we can first implement perfect qudit state transfer by quantum walks. Compared with existing schemes driven by one coin, more general graph structures can be used to perfectly transfer more general state. Moreover, the external control of coin operator during the transmitting process can be decreased greatly. Selecting coin 1 as the sender and coin 2 as the receiver, we also study how to realize generalized teleportation over long steps of walks by the above quantum walk models. Because quantum walks is an universal quantum computation model, our schemes may provide an universal platform for the design of quantum network and quantum computer.

quant-ph↗

arXiv2017

Pure state `really' informationally complete with rank-1 POVM

What is the minimal number of elements in a rank-1 positive-operator-valued measure (POVM) which can uniquely determine any pure state in $d$-dimensional Hilbert space $\mathcal{H}_d$? The known result is that the number is no less than $3d-2$. We show that this lower bound is not tight except for $d=2$ or 4. Then we give an upper bound of $4d-3$. For $d=2$, many rank-1 POVMs with four elements can determine any pure states in $\mathcal{H}_2$. For $d=3$, we show eight is the minimal number by construction. For $d=4$, the minimal number is in the set of $\{10,11,12,13\}$. We show that if this number is greater than 10, an unsettled open problem can be solved that three orthonormal bases can not distinguish all pure states in $\mathcal{H}_4$. For any dimension $d$, we construct $d+2k-2$ adaptive rank-1 positive operators for the reconstruction of any unknown pure state in $\mathcal{H}_d$, where $1\le k \le d$.

quant-ph↗

arXiv2012

Turing machines based on unsharp quantum logic

In this paper, we consider Turing machines based on unsharp quantum logic. For a lattice-ordered quantum multiple-valued (MV) algebra E, we introduce E-valued non-deterministic Turing machines (ENTMs) and E-valued deterministic Turing machines (EDTMs). We discuss different E-valued recursively enumerable languages from width-first and depth-first recognition. We find that width-first recognition is equal to or less than depth-first recognition in general. The equivalence requires an underlying E value lattice to degenerate into an MV algebra. We also study variants of ENTMs. ENTMs with a classical initial state and ENTMs with a classical final state have the same power as ENTMs with quantum initial and final states. In particular, the latter can be simulated by ENTMs with classical transitions under a certain condition. Using these findings, we prove that ENTMs are not equivalent to EDTMs and that ENTMs are more powerful than EDTMs. This is a notable difference from the classical Turing machines.

cs.LO↗

arXiv2010

Process Algebra as Abstract Data Types

In this paper we introduced an algebraic semantics for process algebra in form of abstract data types. For that purpose, we developed a particular type of algebra, the seed algebra, which describes exactly the behavior of a process within a labeled transition system. We have shown the possibility of characterizing the bisimulation of two processes with the isomorphism of their corresponding seed algebras. We pointed out that the traditional concept of isomorphism of algebra does not apply here, because there is even no one-one correspondence between the elements of two seed algebras. The lack of this one-one correspondence comes from the non-deterministic choice of transitions of a process. We introduce a technique of hidden operations to mask unwanted details of elements of a seed algebra, which only reflect non-determinism or other implicit control mechanism of process transition. Elements of a seed algebra are considered as indistinguishable if they show the same behavior after these unwanted details are masked. Each class of indistinguishable elements is called a non-hidden closure. We proved that bisimulation of two processes is equivalent to isomorphism of non-hidden closures of two seed algebras representing these two processes. We call this kind of isomorphism a deep isomorphism. We get different models of seed algebra by specifying different axiom systems for the same signature. Each model corresponds to a different kind of bisimulation. By proving the relations between these models we also established relations between 10 different bisimulations, which form a acyclic directed graph.

cs.PL↗