quantum algorithms:

In quantum information theory, by the *maximally mixed state* of a quantum systems represented by a finite-dimensional Hilbert space $\mathscr{H}$ one means the mixed state whose density matrix is a multiple of the identity matrix on $\mathscr{H}$.

Hence if $\big(\left\vert w \right\rangle\big)_{w \colon W}$ is any orthonormal linear basis for $\mathscr{H}$, then the maximally mixed state is (in bra-ket notation) given by

$\frac{1}{dim(\mathscr{H})}
\,
\underset{w}{\sum}
\left\vert w \right\rangle
\left\langle w \right\vert
\;\;\colon\;\;
\mathscr{H} \otimes \mathscr{H}^\ast
\,,$

representing the uniform probability distribution on $W$.

A quantum channel which preserves the maximally mixed state is called a *unital quantum channel*.

A quantum channel with an environmental representation given by coupling to a maximally mixed state of the environment is called a *unistochastic quantum channel* or (ambiguously) *noisy quantum operation*. Such operation on single qbits constitute the “DQC1-model” of quantum computation.

See references at *unistochastic quantum channel*.

Created on September 28, 2023 at 10:44:53. See the history of this page for a list of all contributions to it.