Fundamentals

Concepts:

• Photons
• Entanglement
• Bell’s theorem
• EPR paradox
• Locality
  • the idea that a particle can only be influenced by its immediate surroundings
• CHSH game
• Quantum state
  • Wave function representation - complex-valued function of any complete set of commuting or compatible degrees of freedom
    • Spin
    • Momentum
    • Position
    • e.g. one set could be the x,y,z spatial coordinates of an electron
• Qbit
• Observable
  • https://en.wikipedia.org/wiki/Observable#Incompatibility_of_observables_in_quantum_mechanics
• Uncertainty principle
  • Standard deviation of position and speed multipled together is always greater than reduced plank constant
  • https://en.wikipedia.org/wiki/Uncertainty_principle
• Reduced plank constant:
  • hbar = h/2pi
• Plank’s constant
  • Electro magnetic radiation
    • Classical: Synchronised oscillations of electro and magnetic fields
    • All bodies emit electromagnetic radiation
  • There was no model for the spectrum of radiation from bodies.
  • Plank discovered this constant while trying to come up with a model
  • Hypothesised:
    • Equations of motions for light produced a set of harmonic oscillators (sin waves)
    • The entropy of each oscillator varied with the temperature of the body
    • He defined spectral radiance per unit frequency of a body for frequency ν at absolute temperature T
    • But it gave a range of solutions.
    • Observation: radiated energy emitted at shorter wavelengths increases more rapidly with temperature than energy emitted at longer wavelengths
      • Imagine a firework sparkler. At lower temperatures, it glows a deep red, like embers barely burning. As it heats up, the glow turns orange and yellow, brightening like a sunrise. When it gets very hot, it blazes in blue and violet, dazzling and intense, with the shorter, sharper colors dominating the scene. The hotter it gets, the more the sparkler’s energy leaps into those vivid, high-energy hues, leaving the red glow far behind.
      • Red is the longest wavelength, blue is shortest in terms of our visible spectrum.
      • At lower temperatures, like the red glow, most energy is emitted at longer wavelengths (less intense). As the temperature rises, energy shifts toward orange and yellow, increasing rapidly at shorter wavelengths. At very high temperatures, like the blue and violet blaze, energy at shorter wavelengths dominates, growing much faster than at longer wavelengths.
    • to interpret UN [’the vibrational energy of N oscillators’] not as a continuous, infinitely divisible quantity, but as a discrete quantity composed of an integral number of finite equal parts. Let us call each such part the energy element ε;
    • He then basically wanted to solve it, so he plugged in a variable based on experimental data called h.
    • E = hf where f is the frequency
    • h is the plank constant
    • This gives you the scaling by frequency
    • Closely related to Boltzmann constant
• Boltzmann constant
  • The Boltzmann constant is a proportionality constant between the quantities temperature (with unit kelvin) and energy (with unit joule)
  • Relates average gas to temperature
• Ultraviolet catastrophy
• Action principles
  • (kinetic, potential) energy
  • accumulated value of energy function between two states = action
  • energy > force. force is 3d, energy is 1d.
• Conservation law
  • Invariants - things that stay the same despite system evolution
• Continuous symmetry
  • Pizza rotated = symmetric continuously
  • Vs. discrete symmetry - ie. cut into slice. Only if you only rotate by angles that match the slices, that’s discrete symmetry—specific stops along the way
  • Continuous symmetry is the seamless glide, where every point of motion keeps the essence intact
• Noether’s theorem
  • every continuous symmetry of an action in a system with conservative forces has a corresponding conservation law
• Conservative force
  • A force that is declarative/stateless - ie. has conservative function, will always be invariant
  • Non-conservative force example is friction. It dissipates energy, so it depends on the path taken.
  • For example, sliding an object across a surface requires more work over a longer path because friction resists motion throughout
• Local causality
• Local realism
• Single phosphorus donor
  • a hydrogen atom in a vacuum, possessing electron and nuclear spins of 1/2 that serve as natural qubits
  • record-long quantum coherence times
  • silicon host material can be isotopically purified to be nearly free of nuclear spin-carrying isotopes, resulting in exceptional coherence times

Papers:

• https://iopscience.iop.org/article/10.1088/2399-6528/aae224

Bell’s theorem

• Pair of particles

Uncertainty principle:

• standard deviation of position = square root variance from the mean
• standard deviation of momentum = square root variance from the mean
• stddev(position) * stddev(momentum) ≥ plank constant / 2
• 2 * stddev(position) * stddev(momentum) ≥ plank constant ?
• the more accurately one property is measured, the less accurately the other property can be known
• https://en.wikipedia.org/wiki/Uncertainty_principle
• https://en.wikipedia.org/wiki/Uncertainty_principle#Energy–time

For instance if you have a translation symmetry, this basically means that if you switch position x for position x’ in the equations describing your physical systems, the equations should still hold. This gives rise to a conserved quantity that is momentum

Similarly, if your equations are symmetric with respect to time translations, that is, you replace t with t + something in your equations and everything still holds, then your conserved quantity is energy

This creates conjugate pairs: position/momentum position wrt an axis of rotation/angular momentum, energy/time etc

Entanglement

Blog.

Right, so what does entanglement actually describe?

That you can have a quantum state - ie. a qbit consisting of two photons A and B

Send that photon down the line. A and B are now spatially disjoint

And then measure/observe B. And it appears A and B are correlated.

Such that when you measure B, you get a value. And when you measure that same property on A, you get a value which is correlated with B’s.

Even if they are separated by space.

The thing though is - you cannot transmit that information faster than light.

So what that means - measure B’s spin. This is somewhat correlated with A’s spin.

> Entanglement produces correlation between the measurements, the mutual information between the entangled particles can be exploited, but any transmission of information at faster-than-light speeds is impossible

Mutual information it quantifies the “amount of information” (in units such as shannons (bits), nats or hartleys) obtained about one random variable by observing the other random variable

I get it:

• to setup a qbit, you have two photons.
• send one photon to B.
• then measure photon A - its spin is 0.
• measure photon B - its spin is 1.

When we say “no signaling,” we mean that you cannot use the perfect correlation of entangled particles to send information between observers. Here’s why:

1. We Know the Correlation Rule: Yes, we know in advance there is a perfect correlation (e.g., if one particle’s spin is up, the other’s is down). However:

2. Measurement Outcomes Are Random: When you measure one particle, you get a random result (e.g., spin up or spin down). While the other particle’s result will perfectly correlate (e.g., opposite spin), this outcome isn’t pre-determined in a way that lets you encode or send specific information.

3. Classical Communication Required: To confirm the correlation, observers must compare their results. This comparison requires classical communication, which is constrained by the speed of light.

Thus, although we know the general correlation in advance, we cannot exploit it to transmit information because the specific measurement outcomes are unpredictable. This randomness preserves the no-signaling principle.

Why This Doesn’t Allow Communication

Imagine you want to send a message using this setup:

1. You think, “If I measure 0, they’ll know I’m sending a 0.” But you cannot choose to get a 0—it’s random.
2. The randomness of quantum mechanics prevents encoding meaningful information in the measurement outcomes, even with predetermined measurement times.

But I don’t understand

in the bell violation tests

they were seprated by 10,000x 1ly

and both tested it

if that’s possible

why not

Time.

Q: Does the entanglement operation or measurement of a spin increase entropy?

Measuring a spin collapses the wavefunction, reducing the system’s quantum coherence. This can lead to an increase in classical entropy (due to loss of coherence) and can depend on how the measurement process interacts with the environment (introducing decoherence).

Measurement increases entropy ie. ticks clock ie. passes time.

Literally - passage of time IS observation. there is no separation between action and time. they are the same concept.

But time is also spacetime? ie. spacetime is a single fabric. weird.