Physica A Statistical Mechanics and its Applications

Rotational invariance and spin measurements

G. C. Ghirardi, A. Rimini, T. Weber

Published Aug 1, 1982• 5 citations

Publisher

DOI: 10.1016/0378-4371(82)90291-6

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Quantum Malus Law: Negative Quasi-Distributions Unify Classical and Spin-1/2 Polarization — E8 Intelligence Research

Andrew Stewart Caldin

FINDING: Malus's law $I = I_0 \cos^2\theta$ governs both classical wave polarization and quantum spin-1/2 measurements, with the quantum version requiring a quasi-distribution that can go negative. | MATH: Classical: $I(\theta) = I_0 \cos^2\theta$. Quantum (spin-1/2): $P(\theta) = \frac{1}{2}(1 + \cos\theta)$ for spin projection — but the arXiv abstract (quant-ph/9502028) shows the *form* of Malus's law is preserved if the statistical average uses a quasi-distribution $W(\lambda)$ that can be negative: $\langle \cos^2\theta \rangle = \int W(\lambda) \cos^2(\theta-\lambda) d\lambda$, with $W(\lambda) < 0$ allowed. This is the Wigner-function-like negativity — a hallmark of non-classicality. | CONNECTION: **4-fold rotational symmetry** — $\cos^2\theta$ has period $\pi$, but the *intensity* pattern $I(\theta)$ is invariant under $\theta \to \theta + \pi/2$ (i.e., 90° rotation) because $\cos^2(\theta+\pi/2) = \sin^2\theta$, and \(I_0\cos^2\theta + I_0\sin^2\theta = I_ Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

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Physica A Statistical Mechanics and its Applications

Rotational invariance and spin measurements

G. C. Ghirardi, A. Rimini, T. Weber

Published Aug 1, 1982• 5 citations

Publisher

DOI: 10.1016/0378-4371(82)90291-6

Related papers

Rotational Invariance and the Spin-Statistics Theorem

Paul O’Hara

arXiv:quant-ph/0310016Foundations of PhysicsSep 1, 200313 citations

Quantum Malus Law: Negative Quasi-Distributions Unify Classical and Spin-1/2 Polarization — E8 Intelligence Research

Andrew Stewart Caldin

FINDING: Malus's law $I = I_0 \cos^2\theta$ governs both classical wave polarization and quantum spin-1/2 measurements, with the quantum version requiring a quasi-distribution that can go negative. | MATH: Classical: $I(\theta) = I_0 \cos^2\theta$ . Quantum (spin-1/2): $P(\theta) = \frac{1}{2}(1 + \cos\theta)$ for spin projection — but the arXiv abstract (quant-ph/9502028) shows the *form* of Malus's law is preserved if the statistical average uses a quasi-distribution $W(\lambda)$ that can be negative: $\langle \cos^2\theta \rangle = \int W(\lambda) \cos^2(\theta-\lambda) d\lambda$ , with $W(\lambda) < 0$ allowed. This is the Wigner-function-like negativity — a hallmark of non-classicality. | CONNECTION: **4-fold rotational symmetry** — $\cos^2\theta$ has period $\pi$ , but the *intensity* pattern $I(\theta)$ is invariant under $\theta \to \theta + \pi/2$ (i.e., 90° rotation) because $\cos^2(\theta+\pi/2) = \sin^2\theta$ , and $I_0\cos^2\theta + I_0\sin^2\theta = I_ Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.comFINDING: Malus's law \(I = I_0 \cos^2\theta$ governs both classical wave polarization and quantum spin-1/2 measurements, with the quantum version requiring a quasi-distribution that can go negative. | MATH: Classical: $I(\theta) = I_0 \cos^2\theta$. Quantum (spin-1/2): $P(\theta) = \frac{1}{2}(1 + \cos\theta)$ for spin projection — but the arXiv abstract (quant-ph/9502028) shows the *form* of Malus's law is preserved if the statistical average uses a quasi-distribution $W(\lambda)$ that can be negative: $\langle \cos^2\theta \rangle = \int W(\lambda) \cos^2(\theta-\lambda) d\lambda$, with $W(\lambda) < 0$ allowed. This is the Wigner-function-like negativity — a hallmark of non-classicality. | CONNECTION: **4-fold rotational symmetry** — $\cos^2\theta$ has period $\pi$, but the *intensity* pattern $I(\theta)$ is invariant under $\theta \to \theta + \pi/2$ (i.e., 90° rotation) because $\cos^2(\theta+\pi/2) = \sin^2\theta$, and \(I_0\cos^2\theta + I_0\sin^2\theta = I_ Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Sep 22, 20260 citations

Rotational invariance from gauge invariance in adiabatically changing systems

J.C. Martinez

Physics Letters AJan 1, 19890 citations

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R. Shankar

Springer eBooksJan 1, 19950 citations

Symmetric construction of reference-frame-free qudits

Jun Suzuki, Gelo Noel M. Tabia, Berthold‐Georg Englert

By exploiting a symmetric scheme for coupling $N$ spin- $1∕2$ constituents (the physical qubits) to states with total angular momentum $N∕2\ensuremath{-}1$, we construct rotationally invariant logical qudits of dimension $d=N\ensuremath{-}1$. One can encode all qudit states, and realize all qudit measurements, by this construction. The rotational invariance of all relevant objects enables one to transmit quantum information without having aligned reference frames between the parties that exchange the qudits. We illustrate the method by explicit constructions of reference-frame-free qubits and qutrits and, for the qubit case, comment on possible experimental implementations.By exploiting a symmetric scheme for coupling $N$ spin-$1∕2$ constituents (the physical qubits) to states with total angular momentum $N∕2\ensuremath{-}1$, we construct rotationally invariant logical qudits of dimension $d=N\ensuremath{-}1$. One can encode all qudit states, and realize all qudit measurements, by this construction. The rotational invariance of all relevant objects enables one to transmit quantum information without having aligned reference frames between the parties that exchange the qudits. We illustrate the method by explicit constructions of reference-frame-free qubits and qutrits and, for the qubit case, comment on possible experimental implementations.

arXiv:0802.1609Physical Review ANov 17, 20087 citations

Spin dependence of density functionals that respect spin-rotational invariance

Román López-Sandoval, G. M. Pastor

Journal of Magnetism and Magnetic MaterialsApr 22, 20050 citations

FINDING: Malus's law

I = I_0 \cos^2\theta

governs both classical wave polarization and quantum spin-1/2 measurements, with the quantum version requiring a quasi-distribution that can go negative. | MATH: Classical:

I(\theta) = I_0 \cos^2\theta

. Quantum (spin-1/2):

P(\theta) = \frac{1}{2}(1 + \cos\theta)

for spin projection — but the arXiv abstract (quant-ph/9502028) shows the *form* of Malus's law is preserved if the statistical average uses a quasi-distribution

W(\lambda)

that can be negative:

\langle \cos^2\theta \rangle = \int W(\lambda) \cos^2(\theta-\lambda) d\lambda

, with

W(\lambda) < 0

allowed. This is the Wigner-function-like negativity — a hallmark of non-classicality. | CONNECTION: **4-fold rotational symmetry** —

\cos^2\theta

has period

\pi

, but the *intensity* pattern

I(\theta)

is invariant under

\theta \to \theta + \pi/2

(i.e., 90° rotation) because

\cos^2(\theta+\pi/2) = \sin^2\theta

, and \(I_0\cos^2\theta + I_0\sin^2\theta = I_ Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

By exploiting a symmetric scheme for coupling

N

spin-

1∕2

constituents (the physical qubits) to states with total angular momentum $N∕2\ensuremath{-}1$, we construct rotationally invariant logical qudits of dimension $d=N\ensuremath{-}1$. One can encode all qudit states, and realize all qudit measurements, by this construction. The rotational invariance of all relevant objects enables one to transmit quantum information without having aligned reference frames between the parties that exchange the qudits. We illustrate the method by explicit constructions of reference-frame-free qubits and qutrits and, for the qubit case, comment on possible experimental implementations.