# Shengyang ZhongPeking University | PKU · Department of Philosophy

Shengyang Zhong

PhD

## About

20

Publications

4,890

Reads

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58

Citations

Citations since 2017

Introduction

Additional affiliations

October 2018 - January 2025

March 2016 - present

Education

September 2011 - September 2015

September 2009 - June 2011

September 2005 - June 2009

## Publications

Publications (20)

In this paper we show that some orthogeometries, i.e. projective geometries each defined using a ternary collinearity relation and equipped with a binary orthogonality relation, which are extensively studied in mathematics and quantum theory, correspond to Kripke frames, each defined using a binary relation, satisfying a few conditions. To be preci...

This paper presents a formalization of the state-property duality in quantum physics. On the side of properties, Piron shows that Piron lattices, originally called irreducible propositional systems, capture the essential structure formed by the testable properties of quantum systems. On the side of states, we define quantum Kripke frames to capture...

From the Hilbert space formalism we note that five simple conditions are satisfied by the orthogonality relation between the (pure) states of a quantum system. We argue, by proving a mathematical theorem, that they capture the essentials of this relation. Based on this, we investigate the rationale behind these conditions in the form of six physica...

In this paper, by slightly generalizing an observation of Dalla Chiara and Giunti-ni in their chapter on quantum logic in Handbook of Philosophical Logic, we propose a relational semantics for propositional language with negation and conjunction, which unifies the relational semantics of intuitionistic logic and that of ortho-logic. We study the se...

From the Hilbert space formalism we note that five simple conditions are satisfied by the orthogonality relation between the (pure) states of a quantum system. We argue, by proving a mathematical theorem, that they capture the essentials of this relation. Based on this, we investigate the rationale behind these conditions in the form of six physica...

In the chapter on quantum logic in Volume 6 of Handbook of Philosophical Logic, Dalla Chiara and Giuntini make an interesting observation that there is a unified relational semantics underlying both the {¬,∧}-fragment of intuitionistic logic and ortho-logic. In this paper, we contribute to a systematic investigation of this relational semantics by...

In these notes we discuss the problem of characterizing linear maps of trace 0. The most famous result is the Shoda-Albert-Muckenhoupt Theorem ([1]). It says that each linear map of trace 0 is a commutator, and it holds for finite-dimensional vector spaces over any fields. Here we present two characterizations of linear maps of trace 0 from the per...

It is well known that the non-orthogonality relation between the (pure) states of a quantum system is reflexive and symmetric, and the modal logic \(\mathbf {KTB}\) is sound and complete with respect to the class of sets each equipped with a reflexive and symmetric binary relation. In this paper, we consider two properties of the non-orthogonality...

We give a characterization of ortho-frames whose lattices of bi-orthogonally closed sets form complete orthomodular lattices. There have been several such characterizations in the literature. As far as I know, the first one is Theorem 1 in [2]. The characterization here makes use of a generalization of the notion of representatives proposed in [3]...

This paper provides a categorical equivalence between two types of quantum structures. One is a complete orthomodular lattice, which is used for reasoning about testable properties of a quantum system. The other is an orthomodular dynamic algebra, which is a quantale used for reasoning about quantum actions. The result extends to more restrictive l...

This talk assumes basic knowledge of category theory. The slides are in English. The video (in Chinese) can be found at: http://v.youku.com/v_show/id_XMTY3MTQwNjQyOA==.html?from=s1.8-1-1.2&spm=a2h0k.8191407.0.0

The slides are in English. The video (in Chinese) can be found at: http://v.youku.com/v_show/id_XMTY3MTM5NjM2OA==.html?from=s1.8-1-1.2&spm=a2h0k.8191407.0.0

The slides are in English. The video (in Chinese) can be found at: http://v.youku.com/v_show/id_XMTY3MTM4MzgzNg==.html?from=s1.8-1-1.2&spm=a2h0k.8191407.0.0

The slides are in English. The video (in Chinese) can be found at: http://v.youku.com/v_show/id_XMTY3MTM3MjAzNg==.html?from=s1.8-1-1.2&spm=a2h0k.8191407.0.0

The slides are in English. The video (in Chinese) can be found at: http://v.youku.com/v_show/id_XMTY3MTM2OTk0MA==.html?from=s1.8-1-1.2&spm=a2h0k.8191407.0.0

(Version 20160816) This is the errata of my PhD thesis Orthogonality and Quantum Geometry. It contains a corrected proof of Proposition 5.4.3, besides some typos.

In this paper we show a duality between two approaches to represent quantum structures abstractly and to model the logic and dynamics therein. One approach puts forward a “quantum dynamic frame” (Baltag et al. in Int J Theor Phys, 44(12):2267–2282, 2005), a labelled transition system whose transition relations are intended to represent projections...

We introduce a probabilistic modal (dynamic-epistemic) quantum logic PLQP for reasoning about quantum algorithms. We illustrate its expressivity by using it to encode the correctness of the well-known quantum search algorithm, as well as of a quantum protocol known to solve one of the paradigmatic tasks from classical distributed computing (the lea...

We propose an expressive but decidable logic for reasoning about quantum systems. The logic is endowed with tensor operators to capture properties of composite systems, and with probabilistic predication formulas P
≥ r
(s), saying that a quantum system in state s will yield the answer ‘yes’ (i.e. it will collapse to a state satisfying property P) w...

## Projects

Project (1)

This project studies the geometry formed by the (pure) states of a quantum system under the non-orthogonality relation, including its mathematical properties, its logical theories in various formal languages and its significance in physics and philosophy.