Comment on: Disproof of Bell's Theorem by Clifford Algebra Valued Local Variables

Comments on "Disproof of Bell's theorem"

In a series of very interesting papers [1-7], Joy Christian constructed a counterexample to Bell's theorem. This counterexample does not have the same assumptions as the original Bell's theorem, and therefore it does not represent a genuine disproof in a strict mathematical sense. However, assuming the physical relevance of the new assumptions, the counterexample is shown to be a contextual hidden variable theory. If Bell's theorem's importance is to rule out contextual hidden variable theories obeying relativistic locality, then Joy Christian's counterexample achieves its aim. If however cont…

Disproof of Bell's Theorem by Clifford Algebra Valued Local Variables

It is shown that Bell's theorem fails for the Clifford algebra valued local realistic variables. This is made evident by exactly reproducing quantum mechanical expectation value for the EPR-Bohm type spin correlations observable by means of a local, deterministic, Clifford algebra valued variable, without necessitating either remote contextuality or backward causation. Since Clifford product of multivector variables is non-commutative in general, the spin correlations derived within our locally causal model violate the CHSH inequality just as strongly as their quantum mechanical counterparts.

Disproof of Bell's Theorem

We illustrate an explicit counterexample to Bell's theorem by constructing a pair of spin variables in S^3 that exactly reproduces the EPR-Bohm correlation in a manifestly local-realistic manner.

Disproof of Bell's Theorem: Further Consolidations

The failure of Bell's theorem for Clifford algebra valued local variables is further consolidated by proving that the conditions of remote parameter independence and remote outcome independence are duly respected within the recently constructed exact, local realistic model for the EPR-Bohm correlations. Since the conjunction of these two conditions is equivalent to the locality condition of Bell, this provides an independent geometric proof of the local causality of the model, at the level of microstates. In addition to local causality, the model respects at least seven other conceptual and op…

Disproofs of Bell, GHZ, and Hardy Type Theorems and the Illusion of Entanglement

An elementary topological error in Bell's representation of the EPR elements of reality is identified. Once recognized, it leads to a topologically correct local-realistic framework that provides exact, deterministic, and local underpinning of at least the Bell, GHZ-3, GHZ-4, and Hardy states. The correlations exhibited by these states are shown to be exactly the classical correlations among the points of a 3 or 7-sphere, both of which are closed under multiplication, and hence preserve the locality condition of Bell. The alleged non-localities of these states are thus shown to result from mis…

Clifford 随机化乘积态的高效学习

Efficient Learning of Clifford-Scrambled Product States

本文提出从两拷贝 Bell 采样中高效学习 Clifford 随机化乘积态的方法，通过二次关系和二元线性代数构造解纠缠器，实现 O(n^2) 样本学习及 T 深度一电路的精确学习，并排除相关伪随机态。

用优雅型贝尔不等式和新的自证等价性认证马约拉纳费米子

Certifying Majorana Fermions with Elegant-Like Bell Inequalities and a New Self-Testing Equivalence

本文提出了一种新的贝尔不等式构造方法，能够精确计算量子界限，并用于设备无关认证马约拉纳费米子。

Non-Viability of a Counter-Argument to Bell's Theorem

It is demonstrated that a recently suggested model for the EPR-Bohm spin experiment, based on Clifford algebra valued local variables and observables, runs into very serious difficulties and can therefore not be taken as constituting a viable counter-example to Bell's theorem.

贝尔不等式、旋量与经典自旋矢量模型的不可能性

Bell, Spinors, and the Impossibility of a Classical Spin-Vector Model

该研究通过代数方法证明经典自旋矢量模型无法解释量子自旋关联性，揭示了贝尔不等式矛盾的根源。

Parity proofs of the Bell-Kochen-Specker theorem based on the 600-cell

The set of 60 real rays in four dimensions derived from the vertices of a 600-cell is shown to possess numerous subsets of rays and bases that provide basis-critical parity proofs of the Bell-Kochen-Specker (BKS) theorem (a basis-critical proof is one that fails if even a single basis is deleted from it). The proofs vary considerably in size, with the smallest having 26 rays and 13 bases and the largest 60 rays and 41 bases. There are at least 90 basic types of proofs, with each coming in a number of geometrically distinct varieties. The replicas of all the proofs under the symmetries of the 6…

自然量子比特代数：克莱因边界澄清与新的不可嵌入定理

Natural Qubit Algebra: clarification of the Clifford boundary and new non-embeddability theorem

本文提出自然量子比特代数，澄清克莱因边界并证明新的不可嵌入定理，通过代数方法重新表述贝尔-CHSH场景，并展示格罗弗和伯斯坦-瓦兹里尼相位 oracle 的紧凑符号描述结构。

局部Clifford算子的经典表示

Classical representation of local Clifford operators

本文提出局部Clifford算子的经典表示，用于描述n-GPM集之间的幺正共轭映射，并应用于证明广义Bell态集的LU-等价分类的完整性。

Does Geometric Algebra provide a loophole to Bell's Theorem? (with corrections)

In 2007, and in a series of later papers, Joy Christian claimed to refute Bell's theorem, presenting an alleged local realistic model of the singlet correlations using techniques from Geometric Algebra (GA). Several authors published papers refuting his claims, and Christian's ideas did not gain acceptance. However, he recently succeeded in publishing yet more ambitious and complex versions of his theory in fairly mainstream journals. How could this be? The mathematics and logic of Bell's theorem is simple and transparent and has been intensely studied and debated for over 50 years. Christian …

Local unitary classification for sets of generalized Bell states

In this paper, we study the local unitary classification for pairs (triples) of generalized Bell states, based on the local unitary equivalence of two sets. In detail, we firstly introduce some general unitary operators which give us more local unitary equivalent sets besides Clifford operators. And then we present two necessary conditions for local unitary equivalent sets which can be used to examine the local inequivalence. Following this approach, we completely classify all of pairs in $d\otimes d$ quantum system into $\prod_{j=1}^{n} (k_{j} + 1) $ LU-inequivalent pairs when the prime facto…

Optimized Entanglement Purification

We investigate novel protocols for entanglement purification of qubit Bell pairs. Employing genetic algorithms for the design of the purification circuit, we obtain shorter circuits achieving higher success rates and better final fidelities than what is currently available in the literature. We provide a software tool for analytical and numerical study of the generated purification circuits, under customizable error models. These new purification protocols pave the way to practical implementations of modular quantum computers and quantum repeaters. Our approach is particularly attentive to the…

高纠缠、高掺杂且可跨设备高效验证的量子态

Highly-entangled, highly-doped states that are efficiently cross-device verifiable

本文提出一类高纠缠且无法被对数非克利福德门电路近似的量子态，证明贝尔采样可实现高效的跨设备内积估计，且方案可扩展、鲁棒，适用于量子密码与验证。

Bell's Theorem Versus Local Realism in a Quaternionic Model of Physical Space

In the context of EPR-Bohm type experiments and spin detections confined to spacelike hypersurfaces, a local, deterministic and realistic model within a Friedmann-Robertson-Walker spacetime with a constant spatial curvature (S^3) is presented that describes simultaneous measurements of the spins of two fermions emerging in a singlet state from the decay of a spinless boson. Exact agreement with the probabilistic predictions of quantum theory is achieved in the model without data rejection, remote contextuality, superdeterminism or backward causation. A singularity-free Clifford-algebraic repre…