Geometric model for the electron spin correlation

• URL: http://arxiv.org/abs/2108.07869v3
• Date: Thu, 14 Apr 2022 03:07:00 GMT
• Title: Geometric model for the electron spin correlation
• Authors: Ana Mar\'ia Cetto
• Abstract summary: The formula for the spin correlation of the bipartite singlet spin state, $C_Q(boldsymbola,boldsymbolb)$, is derived on the basis of a probability distribution $rho(phi)$ that is generic. A geometric model that reproduces the spin correlation serves to validate our approach.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: The quantum formula for the spin correlation of the bipartite singlet spin state, $C_{Q}(\boldsymbol{a},\boldsymbol{b})$, is derived on the basis of a probability distribution $\rho(\phi)$ that is generic, i. e., independent of $(\boldsymbol{a},\boldsymbol{b})$. In line with a previous result obtained within the framework of the quantum formalism, the probability space is partitioned according to the sign of the product $A=\alpha\beta$ of the individual spin projections $\alpha$ and $\beta$ onto $\boldsymbol{a}$ and $\boldsymbol{b}$. A specific partitioning and a corresponding set of realizations {$ \phi$} are associated with every measurement setting $(\boldsymbol{a},\boldsymbol{b})$; this precludes the transfer of $\alpha$ or $\beta$ from $C_{Q}(\boldsymbol{a},\boldsymbol{b})$ to $C_{Q}(\boldsymbol{a},\boldsymbol{b'})$, for $\boldsymbol{b'}\neq\boldsymbol{b}.$ A geometric model that reproduces the spin correlation serves to validate our approach, giving a concrete meaning to the quantum result in terms of a (local random variable) probability distribution.

Related papers

• A Unified Framework for Uniform Signal Recovery in Nonlinear Generative Compressed Sensing [68.80803866919123]
  Under nonlinear measurements, most prior results are non-uniform, i.e., they hold with high probability for a fixed $mathbfx*$ rather than for all $mathbfx*$ simultaneously. Our framework accommodates GCS with 1-bit/uniformly quantized observations and single index models as canonical examples. We also develop a concentration inequality that produces tighter bounds for product processes whose index sets have low metric entropy.
  arXiv  Detail & Related papers  (2023-09-25T17:54:19Z)
• Fitting an ellipsoid to a quadratic number of random points [10.208117253395342]
  We consider the problem $(mathrmP)$ of fitting $n$ standard Gaussian random vectors in $mathbbRd$ to the boundary of a centered ellipsoid, as $n, d to infty$. This problem is conjectured to have a sharp feasibility transition: for any $varepsilon > 0$, if $n leq (1 - varepsilon) d2 / 4$ then $(mathrmP)$ has a solution with high probability.
  arXiv  Detail & Related papers  (2023-07-03T17:46:23Z)
• A random matrix model for random approximate $t$-designs [1.534667887016089]
  A random matrix model is proposed to describe the probability distribution of $delta(nu_mathcalS,t)$ for any $t$. We show that our model satisfies the so-called spectral gap conjecture, i.e. we prove that with the probability $1$ there is $tinmathbbZ_+$ such that $sup satisfieskinmathbbZ_+delta(k)=delta(t)$.
  arXiv  Detail & Related papers  (2022-10-14T14:50:06Z)
• Near-optimal fitting of ellipsoids to random points [68.12685213894112]
  A basic problem of fitting an ellipsoid to random points has connections to low-rank matrix decompositions, independent component analysis, and principal component analysis. We resolve this conjecture up to logarithmic factors by constructing a fitting ellipsoid for some $n = Omega(, d2/mathrmpolylog(d),)$. Our proof demonstrates feasibility of the least squares construction of Saunderson et al. using a convenient decomposition of a certain non-standard random matrix.
  arXiv  Detail & Related papers  (2022-08-19T18:00:34Z)
• Mean Estimation in High-Dimensional Binary Markov Gaussian Mixture Models [12.746888269949407]
  We consider a high-dimensional mean estimation problem over a binary hidden Markov model. We establish a nearly minimax optimal (up to logarithmic factors) estimation error rate, as a function of $|theta_*|,delta,d,n$.
  arXiv  Detail & Related papers  (2022-06-06T09:34:04Z)
• Beyond the Berry Phase: Extrinsic Geometry of Quantum States [77.34726150561087]
  We show how all properties of a quantum manifold of states are fully described by a gauge-invariant Bargmann. We show how our results have immediate applications to the modern theory of polarization.
  arXiv  Detail & Related papers  (2022-05-30T18:01:34Z)
• Adversarial Examples in Random Neural Networks with General Activations [14.12513604585194]
  adversarial examples are ubiquitous in two-layers networks with sub-exponential width and ReLU or smooth activations. We show that an adversarial example $boldsymbol x'$ can be found with high probability along the direction of the gradient.
  arXiv  Detail & Related papers  (2022-03-31T17:36:15Z)
• Matrix concentration inequalities and efficiency of random universal sets of quantum gates [0.0]
  For a random set $mathcalS subset U(d)$ of quantum gates we provide bounds on the probability that $mathcalS$ forms a $delta$-approximate $t$-design. We show that for $mathcalS$ drawn from an exact $t$-design the probability that it forms a $delta$-approximate $t$-design satisfies the inequality $mathbbPleft(delta geq x right)leq 2D_t
  arXiv  Detail & Related papers  (2022-02-10T23:44:09Z)
• Random matrices in service of ML footprint: ternary random features with no performance loss [55.30329197651178]
  We show that the eigenspectrum of $bf K$ is independent of the distribution of the i.i.d. entries of $bf w$. We propose a novel random technique, called Ternary Random Feature (TRF) The computation of the proposed random features requires no multiplication and a factor of $b$ less bits for storage compared to classical random features.
  arXiv  Detail & Related papers  (2021-10-05T09:33:49Z)
• Spectral properties of sample covariance matrices arising from random matrices with independent non identically distributed columns [50.053491972003656]
  It was previously shown that the functionals $texttr(AR(z))$, for $R(z) = (frac1nXXT- zI_p)-1$ and $Ain mathcal M_p$ deterministic, have a standard deviation of order $O(|A|_* / sqrt n)$. Here, we show that $|mathbb E[R(z)] - tilde R(z)|_F
  arXiv  Detail & Related papers  (2021-09-06T14:21:43Z)
• Optimal Combination of Linear and Spectral Estimators for Generalized Linear Models [59.015960528781115]
  We show how to optimally combine $hatboldsymbol xrm L$ and $hatboldsymbol xrm s$. In order to establish the limiting distribution of $(boldsymbol x, hatboldsymbol xrm L, hatboldsymbol xrm s)$, we design and analyze an Approximate Message Passing (AMP) algorithm.
  arXiv  Detail & Related papers  (2020-08-07T18:20:05Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.