与非单位秩投影子无关的量子情境性

单个量子比特是否存在上下文关系？

Is there contextuality for a single qubit?

它是由Cabello和Nakamura [A. Cabello，Phys. Rev. Lett. 90，190401（2003）]，Kochen-Specker定理适用于两个维度，如果使用正算子值测度。我们表明，在他们的模型中的语境是不是Kochen-Specker类型。而是没有跟踪执行测量的整个系统的结果。这与POVM元素和扩展希尔伯特空间上的投影仪之间没有一一对应的事实有关，并且当在Cabello和Nakamura的模型中使用时，相同的POVM元素必须源自两个不同的投影仪。此外，我们提出了上述模型的隐变量公式。

Contextuality under weak assumptions

The presence of contextuality in quantum theory was first highlighted by Bell, Kochen and Specker, who discovered that for quantum systems of three or more dimensions, measurements cannot be viewed as revealing pre-existing properties of the system. More precisely, no model can assign deterministic outcomes to the projectors of a quantum measurement in a way that depends only on the projector and not the context (the full set of projectors) in which it appeared, despite the fact that the Born rule probabilities associated with projectors are independent of the context. A more general, operatio…

Minimal proofs of state-independent contextuality

It has been recently shown that state-independent contextuality (SIC) is a fundamental resource linked with a type of nonlocality which cannot be improved by nonsignaling resources. Therefore, it is of fundamental importance to identify the simplest sets of quantum observables needed to prove SIC. We show that d+10 rank-1 projectors are sufficient to prove SIC for any physical system in dimension d>2. This result outperforms both the best Kochen-Specker proofs and the results presented by Yu and Oh in arXiv:1112.5513v1.

强O值语境性：排除量子理论的离散非确定性替代方案

Strong $O$-valued contextuality: ruling out discrete nondeterministic alternatives to quantum theory

研究排除量子理论离散非确定性替代方案，通过构建有限测量配置，采用状态依赖哈迪型测试和广义KS定理两种方式，扩展层理论框架引入强\(O\)值语境性，探讨对多值逻辑及相关协议的影响。

Contextuality in bosonic bunching

We show that under certain assumptions one can derive a variant of Specker's non-contextual inequality for a system of three indistinguishable bosonic particles. The inequality states that the sum of probabilities of three pairwise exclusive events is bounded by one. This inequality cannot be violated using standard quantum mechanical projectors. On the other hand, due to bosonic properties this bound is violated up to 3/2. We also argue that the violation of this inequality can be considered as a test of bosonic nature.

Construction of State-independent Proofs for Quantum Contextuality

Since the enlightening proofs of quantum contextuality first established by Kochen and Specker, and also by Bell, various simplified proofs have been constructed to exclude the non-contextual hidden variable theory of our nature at the microscopic scale. The conflict between the non-contextual hidden variable theory and quantum mechanics is commonly revealed by Kochen-Specker (KS) sets of yes-no tests, represented by projectors (or rays), via either logical contradictions or noncontextuality inequalities in a state-(in)dependent manner. Here we first propose a systematic and programmable const…

How (Maximally) Contextual is Quantum Mechanics?

Proofs of Bell-Kochen-Specker contextuality demonstrate that there exists sets of projectors that cannot each be assigned either 0 or 1 such that each basis formed from them contains exactly one 1-assigned projector. Instead, at least some of the projectors must have a valuation that depends on the \emph{context} in which they are measured. This motivates the question of \emph{how many} of the projectors must have contextual valuations. In this paper, we demonstrate a bound on what fraction of rank-1 projective measurements on a quantum system must be considered to have context-dependent valua…

Experimental demonstration of fully contextual quantum correlations on an NMR quantum information processor

The existence of contextuality in quantum mechanics is a fundamental departure from the classical description of the world. Currently, the quest to identify scenarios which cannot be more contextual than quantum theory is at the forefront of research in quantum contextuality. In this work, we experimentally test two inequalities, which are capable of revealing fully contextual quantum correlations, on a Hilbert space of dimension 8 and 4 respectively, on an NMR quantum information processor. The projectors associated with the contextuality inequalities are first reformulated in terms of Pauli …

The complete Heyting algebra of subsystems and contextuality

The finite set of subsystems of a finite quantum system with variables in ${\mathbb Z}(n)$, is studied as a Heyting algebra. The physical meaning of the logical connectives is discussed. It is shown that disjunction of subsystems is more general concept than superposition. Consequently the quantum probabilities related to projectors in the subsystems, are incompatible with associativity of the join in the Heyting algebra, unless if the variables belong to the same chain. This leads to contextuality, which in the present formalism has as contexts, the chains in the Heyting algebra. Logical Bell…

Hypergraph framework for irreducible noncontextuality inequalities from logical proofs of the Kochen-Specker theorem

Kochen-Specker (KS) theorem reveals the inconsistency between quantum theory and any putative underlying model of it satisfying the constraint of KS-noncontextuality. A logical proof of the KS theorem is one that relies only on the compatibility relations amongst a set of projectors (a KS set) to witness this inconsistency. These compatibility relations can be represented by a hypergraph, referred to as a contextuality scenario. Here we consider contextuality scenarios that we term KS-uncolourable, e.g., those which appear in logical proofs of the KS theorem. We introduce a hypergraph framewor…

Nonclassical Structures within the N-qubit Pauli Group

Structures that demonstrate nonclassicality are of foundational interest in quantum mechanics, and can also be seen as resources for numerous applications in quantum information processing - particularly in the Hilbert space of $N$ qubits. The theory of entanglement, quantum contextuality, and quantum nonlocality within the $N$-qubit Pauli group is further developed in this thesis. The Strong Kochen-Specker theorem and the structures that prove it are introduced and explored in detail. The pattern of connections between structures that show entanglement, contextuality, and nonlocality is expla…

Construction of Three-Qubit Kochen-Specker Sets

Contextuality is one of the fundamental deviations of quantum mechanics from classical physics. The Kochen-Specker (KS) theorem shows that non-contextual classical physics with hidden variables is inconsistent with the predictions of quantum mechanics. Parity proof is one of the many different approaches applied to prove KS theorem for quantum system with different dimensionality. This method of proof requires KS sets that composed of an odd number of bases and an even number of projectors. In most of the cases, the number of KS sets produced is large and its production is generally aided by c…

通过幺正扩张在量子硬件上实现辅助场量子蒙特卡罗

Auxiliary-Field Quantum Monte Carlo on Quantum Hardware via Unitary Dilation

本文提出近-term量子算法，通过随机场Ω驱动的一体传播子序列，利用随机Magnus展开将轨迹转换为分段常数生成器，并通过小辅助系统实现幺正演化，减少中途测量需求，验证了在Hubbard模型上的准确性和硬件执行能力。

不一致线性约束系统有限维量子解存在性的完整分类

A complete classification of the existence of finite-dimensional quantum solutions to inconsistent linear constraint systems

该论文完整分类了不一致线性约束系统的有限维量子解存在性，证明其存在当且仅当维度至少为3且模数与维度不互素，并构造了显式例子。