From 5e608db9be92d9bc245d8c46a3489d8469c5d5a6 Mon Sep 17 00:00:00 2001 From: Marco Azimonti Date: Tue, 28 May 2024 22:06:56 +0900 Subject: [PATCH] updated README.md with preset experiments description --- README.md | 38 ++++++++++++++++++++++++++++ epr_experiment.py | 7 +++-- screenshots/entangled_electrons.png | Bin 0 -> 522236 bytes screenshots/entangled_photons.png | Bin 0 -> 557854 bytes 4 files changed, 43 insertions(+), 2 deletions(-) create mode 100644 screenshots/entangled_electrons.png create mode 100644 screenshots/entangled_photons.png diff --git a/README.md b/README.md index e13b550..4e06b83 100644 --- a/README.md +++ b/README.md @@ -62,6 +62,44 @@ Both apparatus measure at the same time. A button allows random selection of the This script provides a comprehensive tool for simulating and analyzing the fundamental aspects of quantum entanglement and the EPR paradox. +### Preset Experiments + +#### 1. Entangled Electrons with Stern-Gerlach Magnets + +The detectors are three Stern-Gerlach magnets: + +- One oriented along the z-axis +- Two in the zx plane with ±120° rotation + +The particles are two entangled electrons in the singlet state: + +``` +| Psi > = 1 / sqrt(2) * ( | up down > - | down up > ) +``` + +![Entangled electrons with Stern-Gerlach magnets experiment](screenshots/entangled_electrons.png) + +#### 2. Entangled Photons with Polarizers + +The apparatus consists of two polarizers directing two photons to three photodetectors: + +- One oriented along the z-axis +- Two in the zx plane with 22.5° and 45° rotation + +The particles are two entangled photons in the second triplet state: + +``` +| Psi > = 1 / sqrt(2) * ( | up up > + | down down > ) +``` + +Note: In the real world, light polarization is typically measured in degrees, and the angle θ can be from 0° to 360°. In the Hilbert space, the angles are typically represented by the state vectors on the Bloch sphere, where θ ranges from 0 to π. Since vertical and horizontal polarizations are orthogonal and correspond to π/2 in real-world measurements and π on the Bloch sphere, the relationship between the real-world polarization angle `θ_real` and the Hilbert space angle `θ_Hilbert` is given by: + +``` +θ_Hilbert = 2 * θ_real +``` + +![Entangled photons with polarizers experiment](screenshots/entangled_photons.png) + ## Getting Started To get started with these simulations: diff --git a/epr_experiment.py b/epr_experiment.py index 5c3ba77..abcac34 100644 --- a/epr_experiment.py +++ b/epr_experiment.py @@ -958,8 +958,11 @@ def main(): # In the Hilbert space, the angles are typically represented by # the state vectors on the Bloch sphere, # where θ ranges from 0 to π. - # The conversion from real-world polarization angle θreal to - # the Hilbert space angle θHilbert is given by: + # Since vertical and horizontal polarizations are orthogonal + # and correspond to π/2 in real-world measurements and π + # on the Bloch sphere, the relationship between the real-world + # polarization angle `θ_real` and the Hilbert space angle + # `θ_Hilbert` is given by: # θHilbert = 2 * θreal cfg.bloch_t = 2 cfg.bloch_p = 1 diff --git a/screenshots/entangled_electrons.png b/screenshots/entangled_electrons.png new file mode 100644 index 0000000000000000000000000000000000000000..c8de27d4b645a39d0330a48379947f8c0bef6776 GIT binary patch literal 522236 zcmeFYXIK+m*FOqMQBhD)kQxvb3q??hw5X_vicwJMgepxyde4A}fQW#CfCvGUCPL^) zjYzlsB|Skj*!*>zg+3P+fHMtFEoM$SF<<{d2t z2O1Sm@-1?=q@}$GVHY}0+7Ws7oJ;Ly|A^y~XI*tkrv~kvC#oM{6>E3Dl5xmDH0Yki zGv$Vn6w$*Xn$7!m?oDGoeU|gKuya+oz@aIg{mCMbGlI%;USUiza1 zE?(NzyxLuvy9=R3KdyhQgN3DxKZ5w_`+gl){%`l>y2ZY2W-D7f)5=zMe%ocPA}RGW z^z304wTSuyk}MZ9BwYPYD6!^hx@itxZsFZ^fKPn!)!VmCnp?ZRJ-g0*P(r8Awt*WN_8ns$;Caa#0pDzsk~^L!*@!mRqg0fRe*xZ1vYS1!Puc4=D7D_Bu4!xdj_;`H z8ME(}9r9Xg6$QsGmA>>QZ+A=6S{W z)Kr1fDapY#G4AdmA8ZpFR`NH zeN^+%b@uM38)CdIdn_-?#7Iu@gkJ2rBNfN8TYPsZ-!R+Z%g67qm-09SVV>Q-Jez*z 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