# Articles for subject Quantum

• Density Operator 3 States some time ago
The description of physical states as vectors in a Hilbert space can be extended to a probabilistic description when we don’t have complete information. It turns out we are forced to use such a description in certain situations.
• The Mermin-Peres magic square is a neat demonstration of measurement contextuality.
• Projectors are linear operators with the property that the square of the operator is the operator.
• Observables and Projective measurements. The Born rule. Expectation and variance of observables and uncertainty principle.
• Quantum mechanics can be encapsulated by a set of postulates. In this set we will take the Hilbert space $$\mathcal{H}$$ as the primary object.
• Inner-products and norms are defined. Equipping a vector space with an inner-product gives an inner-product-space, and let’s us define bases.
• The Dirac braket notation is popular in Quantum Mechanics but at its core this is just an elegant notation for vectors of complex numbers. It’s introduced in a finite dimensional complex vector space.
• For some example noisy 1-qubit channels we give their representation in terms of Kraus Operators, the dynamical matrix and the process matrix.