nLab maximally mixed quantum state



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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 (|w) w:W\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

1dim()w|ww|: *, \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 WW.


Relation to quantum channels

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.