Archives for Entanglement
Projection Operators and Symmetry
Projection Operators and Group Theory 1. How Projection Operators Relate to Group Theory Projection operators appear in quantum mechanics whenever we have symmetries described by a group \( G \).…
Projection Operators along with examples. Gleason’s theorem next
Projection Operators and Measurement Outcomes Projection Operators and Measurement Outcomes 1. Single-Particle Spin Measurement Consider a quantum system where a spin-\( 1/2 \) particle (, an electron) is measured along…
Projection Operators and Hidden Variables in QM
Gleason’s Theorem and Hidden Variables 1. Projection Operators A projection operator \( P \) is a Hermitian operator satisfying: P² = P These operators represent measurement outcomes in quantum…
Derivation of the Classical and Quantum Correlation Functions in EPR , Bell’s Theorem
Derivation of Correlation Functions Hidden Variable Theory Correlation In a local hidden variable (LHV) theory, measurement results depend on pre-existing hidden variables (denoted λ) rather than quantum superposition. Each particle…
Quantum Mechanical Correlation in Bell’s Theorem
Quantum Correlations and Hidden Variable Predictions 1. Correlations Predicted by Quantum Mechanics For two entangled spin-1/2 particles, the quantum state is: |ψ⟩ = (1/√2) ( |↑⟩₁ |↓⟩₂ - |↓⟩₁ |↑⟩₂…
Bell’s Theorem and the Two-Particle EPR Example
Bell’s Theorem and the Two-Particle EPR Example Bell's theorem directly refutes the EPR argument by showing that quantum mechanics produces correlations that cannot be explained by any local hidden variable…
Is ‘ Information ‘ subjective?
Does information has a subjective nature/aspect to it? Do we define something as being informative because we ourselves can perceive it? The perception can be either with lab instruments or…
The Separability Problem in Quantum Mechanics for Mixed States
Separability Problem in Quantum Mechanics for Mixed States The **separability problem** in quantum mechanics refers to the task of determining whether a given **mixed quantum state** is **separable** or **entangled**.…
Bell’s Paper – Section 4 – The Proof
### Section IV: Contradiction (Detailed Explanation) In Section IV, Bell presents the formal proof of why a hidden variable theory cannot reproduce the quantum mechanical predictions for certain measurements on…
Trying to Understand Bell’s EPR Paper
Sections 2 and 3 in the paper - I had some trouble deciphering. ### Section II: Formulation In this section, Bell formulates the Einstein-Podolsky-Rosen (EPR) paradox mathematically. He uses the…