Exhaustive Generation of Orthomodular Lattices with Exactly One Non-Quantum State

正交模逻辑的自然演绎系统

A natural deduction system for orthomodular logic

本文提出正交模逻辑的自然演绎系统，证明其非线性非交换性，赋予矢列物理语义并将蕴涵解释为满足演绎定理的 Sasaki 箭头，进而扩展至两个可靠的谓词逻辑系统。

Bose-Einstein condensation processes with nontrivial geometric multiplicites realized via ${\cal PT}-$symmetric and exactly solvable linear-Bose-Hubbard building blocks

It is well known that using the conventional non-Hermitian but ${\cal PT}-$symmetric Bose-Hubbard Hamiltonian with real spectrum one can realize the Bose-Einstein condensation (BEC) process in an exceptional-point limit of order $N$. Such an exactly solvable simulation of the BEC-type phase transition is, unfortunately, incomplete because the standard version of the model only offers an extreme form of the limit characterized by a minimal geometric multiplicity $K=1$. In our paper we describe a rescaled and partitioned direct-sum modification of the linear version of the Bose-Hubbard model whi…

A presentation of Quantum Logic based on an "and then" connective

When a physicist performs a quantic measurement, new information about the system at hand is gathered. This paper studies the logical properties of how this new information is combined with previous information. It presents Quantum Logic as a propositional logic under two connectives: negation and the "and then" operation that combines old and new information. The "and then" connective is neither commutative nor associative. Many properties of this logic are exhibited, and some small elegant subset is shown to imply all the properties considered. No independence or completeness result is claim…

Classification of quantum phases and topology of logical operators in an exactly solved model of quantum codes

Searches for possible new quantum phases and classifications of quantum phases have been central problems in physics. Yet, they are indeed challenging problems due to the computational difficulties in analyzing quantum many-body systems and the lack of a general framework for classifications. While frustration-free Hamiltonians, which appear as fixed point Hamiltonians of renormalization group transformations, may serve as representatives of quantum phases, it is still difficult to analyze and classify quantum phases of arbitrary frustration-free Hamiltonians exhaustively. Here, we address the…

Quantum phase transitions mediated by clustered non-Hermitian degeneracies

A broad family of phase transitions in the closed as well as open quantum systems is known to be mediated by a non-Hermitian degeneracy (a.k.a. exceptional point, EP) of the Hamiltonian. In the EP limit, in general, the merger of an $N-$plet of the energy eigenvalues is accompanied by a parallel (though not necessarily complete) degeneracy of eigenstates (forming an EP-asociated $K-$plet; in mathematics, $K$ is called the geometric multiplicity of the EP). In the literature, unfortunately, only the benchmark matrix models with $K=1$ can be found. In our paper the gap is filled: the EP-mediated…

量子网络中，界面容量与架构补充决定纠缠产生速度

Interface Capacity and Architectural Replenishment Determine Entanglement-Generation Speed in Quantum Networks

该研究明确量子网络中纠缠产生速度由界面容量与架构补充能力共同决定，推导了费米子高斯动力学下的纠缠速度界，通过优化验证了架构对饱和深度的分类及VEEF方法的有效性。