Quantum Computing an der TU München

Because they preserve the norm of the vector.

Given an arbitrary basis of two states, an state can be represented in terms of it and it will be possible to measure as long as this new base is orthonormal

That the vectors that form the basis are unit vectors (modulus 1 in the euclidean distance) and orthogonal in their Hilbert space

Given an arbitrary basis that spans the space S, it allows us to obtain a new orthonormal basis that has as it's the first element the unit vector v and spans S still.

That if the domain an orthonormal space, the image will also be one (Therefore if input is an unit vector, so will the output)

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• The measurement of the second qubit gives always the same as the first one, showing correlation in the measurements.
• Bell demonstrated that the measurement correlation is greater than any possible in a classical system.

Every single-qubit gate can be broken in the product of three rotation matrixes. With a finite set of rotation angles α, β & γ, we can produce an arbitrary gate

It's the number of 1's in the binary representation of a number. This number can be odd or even and it's used as the most basic form of error correction.

cos(−𝜃)=+cos(𝜃)

sin(−𝜃)=−sin(𝜃)

The NAND gate. With them, you can build any other function.

is still an unitary matrix