qspin 0.1

Quantum Spin

This is a little package that will help with learning how quantum spin and entanglement work. It is meant to complement some of the “theoretical minimum” lectures and other web resources.

• [https://en.wikipedia.org/wiki/Pauli_matrices]

• [https://en.wikipedia.org/wiki/Triplet_state]

• [https://en.wikipedia.org/wiki/Von_Neumann_entropy]

• Book: Quantum Mechanics - The Theoretical Minimum, Leanoard Susskind and Art Friedman, Basic Books, 2014. (mostly chapters 6&7)

• [http://theoreticalminimum.com/courses/quantum-mechanics/2012/winter/lecture-6] and 7

Eventually I hope to work this in to understanding quantum computing.

Examples of code use.

Out-of-the box tests:

from qspin import *
test_spin()
test_entangled()

Symbolic states, up, down and linear combinations to form mixed states

>>> u
1.0 |u>
>>> d
1.0 |d>
>>> u + d
1.0 |u>  + 1.0 |d>
>>> u + i*d
(1+0j) |u>  + 1j |d>

Operators

>>> sx
[[0 1]
 [1 0]]
>>> sy
[[ 0.+0.j -0.-1.j]
 [ 0.+1.j  0.+0.j]]
>>> sz
[[ 1  0]
 [ 0 -1]]
>>> sz*u
1.0 |u>
>>> sz*d
-1.0 |d>

Expected value (.H is Hermetian conjugate)

>> u.H*sz*u
1.0

Two-particle states, formed as tensor products

>>> uu = u**u
>>> ud = u**d
>>> du = d**u
>>> dd = d**d
>>> uu
1.0 |uu>
>>> ud
1.0 |ud>
>>> du
1.0 |du>
>>> dd
1.0 |dd>
>>> (ud - du).normalized()
0.707106781187 |ud>  - 0.707106781187 |du>

Same with two-particle operators - tensor products of single particle operators. s0 is the identity operator.

>>> sigx = s0**sx
>>> taux = sx**s0