Programmability of covariant quantum channels
- URL: http://arxiv.org/abs/2012.00717v2
- Date: Fri, 25 Jun 2021 07:18:34 GMT
- Title: Programmability of covariant quantum channels
- Authors: Martina Gschwendtner, Andreas Bluhm, Andreas Winter
- Abstract summary: A programmable quantum processor uses the states of a program register to specify one element of a set of quantum channels.
We show how to remove redundancy in the program and prove that the resulting program register has minimum Hilbert space dimension.
- Score: 0.0
- License: http://creativecommons.org/licenses/by-nc-nd/4.0/
- Abstract: A programmable quantum processor uses the states of a program register to
specify one element of a set of quantum channels which is applied to an input
register. It is well-known that such a device is impossible with a
finite-dimensional program register for any set that contains infinitely many
unitary quantum channels (Nielsen and Chuang's No-Programming Theorem), meaning
that a universal programmable quantum processor does not exist. The situation
changes if the system has symmetries. Indeed, here we consider group-covariant
channels. If the group acts irreducibly on the channel input, these channels
can be implemented exactly by a programmable quantum processor with finite
program dimension (via teleportation simulation, which uses the
Choi-Jamiolkowski state of the channel as a program). Moreover, by leveraging
the representation theory of the symmetry group action, we show how to remove
redundancy in the program and prove that the resulting program register has
minimum Hilbert space dimension. Furthermore, we provide upper and lower bounds
on the program register dimension of a processor implementing all
group-covariant channels approximately.
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