Session Communication and Integration

The scenario-based specification of a large distributed system is usually naturally decomposed into various modules. The integration of specification modules contrasts to the parallel composition of program components, and includes various ways such as scenario concatenation, choice, and nesting. The recent development of multiparty session types for process calculi provides useful techniques to accommodate the protocol modularisation, by encoding fragments of communication protocols in the usage of private channels for a class of agents. In this paper, we extend forgoing session type theories by enhancing the session integration mechanism. More specifically, we propose a novel synchronous multiparty session type theory, in which sessions are separated into the communicating and integrating levels. Communicating sessions record the message-based communications between multiple agents, whilst integrating sessions describe the integration of communicating ones. A two-level session type system is developed for pi-calculus with syntactic primitives for session establishment, and several key properties of the type system are studied. Applying the theory to system description, we show that a channel safety property and a session conformance property can be analysed. Also, to improve the utility of the theory, a process slicing method is used to help identify the violated sessions in the type checking.Comment: A short version of this paper is submitted for revie

Reasoning about Cardinal Directions between Extended Objects

Direction relations between extended spatial objects are important commonsense knowledge. Recently, Goyal and Egenhofer proposed a formal model, known as Cardinal Direction Calculus (CDC), for representing direction relations between connected plane regions. CDC is perhaps the most expressive qualitative calculus for directional information, and has attracted increasing interest from areas such as artificial intelligence, geographical information science, and image retrieval. Given a network of CDC constraints, the consistency problem is deciding if the network is realizable by connected regions in the real plane. This paper provides a cubic algorithm for checking consistency of basic CDC constraint networks, and proves that reasoning with CDC is in general an NP-Complete problem. For a consistent network of basic CDC constraints, our algorithm also returns a 'canonical' solution in cubic time. This cubic algorithm is also adapted to cope with cardinal directions between possibly disconnected regions, in which case currently the best algorithm is of time complexity O(n^5)

Optimal universal programmable detectors for unambiguous discrimination

We discuss the problem of designing unambiguous programmable discriminators for any n unknown quantum states in an m-dimensional Hilbert space. The discriminator is a fixed measurement that has two kinds of input registers: the program registers and the data register. The quantum state in the data register is what users want to identify, which is confirmed to be among the n states in program registers. The task of the discriminator is to tell the users which state stored in the program registers is equivalent to that in the data register. First, we give a necessary and sufficient condition for judging an unambiguous programmable discriminator. Then, if $m=n$, we present an optimal unambiguous programmable discriminator for them, in the sense of maximizing the worst-case probability of success. Finally, we propose a universal unambiguous programmable discriminator for arbitrary n quantum states.Comment: 7 page

Parallel Quantum Algorithm for Hamiltonian Simulation

We study how parallelism can speed up quantum simulation. A parallel quantum algorithm is proposed for simulating the dynamics of a large class of Hamiltonians with good sparse structures, called uniform-structured Hamiltonians, including various Hamiltonians of practical interest like local Hamiltonians and Pauli sums. Given the oracle access to the target sparse Hamiltonian, in both query and gate complexity, the running time of our parallel quantum simulation algorithm measured by the quantum circuit depth has a doubly (poly-)logarithmic dependence $\operatorname{polylog}\log(1/\epsilon)$ on the simulation precision $\epsilon$. This presents an exponential improvement over the dependence $\operatorname{polylog}(1/\epsilon)$ of previous optimal sparse Hamiltonian simulation algorithm without parallelism. To obtain this result, we introduce a novel notion of parallel quantum walk, based on Childs' quantum walk. The target evolution unitary is approximated by a truncated Taylor series, which is obtained by combining these quantum walks in a parallel way. A lower bound $\Omega(\log \log (1/\epsilon))$ is established, showing that the $\epsilon$-dependence of the gate depth achieved in this work cannot be significantly improved. Our algorithm is applied to simulating three physical models: the Heisenberg model, the Sachdev-Ye-Kitaev model and a quantum chemistry model in second quantization. By explicitly calculating the gate complexity for implementing the oracles, we show that on all these models, the total gate depth of our algorithm has a $\operatorname{polylog}\log(1/\epsilon)$ dependence in the parallel setting.Comment: Minor revision. 55 pages, 6 figures, 1 tabl

Unambiguous discrimination of mixed quantum states

In this paper, we consider the problem of unambiguous discrimination between a set of mixed quantum states. We first divide the density matrix of each mixed state into two parts by the fact that it comes from ensemble of pure quantum states. The first part will not contribute anything to the discrimination, the second part has support space linearly independent to each other. Then the problem we consider can be reduced to a problem in which the strategy of set discrimination can be used in designing measurements to discriminate mixed states unambiguously. We find a necessary and sufficient condition of unambiguous mixed state discrimination, and also point out that searching the optimal success probability of unambiguous discrimination is mathematically the well-known semi-definite programming problem. A upper bound of the optimal success probability is also presented. Finally, We generalize the concept of set discrimination to mixed state and point out that the problem of discriminating it unambiguously is equivalent to that of unambiguously discriminating mixed states.Comment: 7 page

Socioeconomic inequality in health care use among cancer patients in China : evidence from the China Health and Retirement Longitudinal Study

Background: Cancer is a major public health problem worldwide and the leading cause of death in China, with increasing incidence and mortality rates. This study sought to assess socioeconomic-related inequalities in health care use among cancer patients in China and to analyze factors associated with this disparity. Methods: This study used data collected for the China Health and Retirement Longitudinal Study in 2018. Patients who reported having cancer were included. The annual per capita household expenditure was classified into five groups by the quintile method. We calculated the distribution of actual, need-predicted, and need-standardized health care use across different socioeconomic groups among patients with cancer. The concentration index (CI) was used to evaluate inequalities in health care use. Influencing factors of inequalities were measured with the decomposition method. Results: A total of 392 people diagnosed with cancer were included in this study. The proportion of cancer patients who utilized outpatient and inpatient services was 23.47% and 40.82%, respectively, and the CIs for actual outpatient and inpatient service use were 0.1419 and 0.1960. The standardized CIs (CI for outpatient visits = 0.1549; CI for inpatient services = 0.1802) were also both positive, indicating that affluent cancer patients used more health services. The annual per capita household expenditure was the greatest factor favoring the better-off, which contributed as much as 78.99% and 83.92% to the inequality in outpatient and inpatient services use, followed by high school education (26.49% for outpatient services) and living in a rural village (34.53% for inpatient services). Urban Employee Basic Medical Insurance exacerbated the inequality in inpatient services (21.97%) while having a negative impact on outpatient visits (−22.19%). Conclusions: There is a pro-rich inequality in outpatient and inpatient services use among cancer patients in China. A lower socioeconomic status is negatively associated with cancer care use. Hence, more targeted financial protection for poor people would relieve cancer patients of the burden caused by the high cost of cancer care