Jordan products of quantum channels and their compatibility
- URL: http://arxiv.org/abs/2009.03279v1
- Date: Thu, 3 Sep 2020 18:00:03 GMT
- Title: Jordan products of quantum channels and their compatibility
- Authors: Mark Girard, Martin Pl\'avala, Jamie Sikora
- Abstract summary: Given two quantum channels, we examine the task of determining whether they are compatible.
We show it is equivalent to the quantum state marginal problem, i.e., every quantum state marginal problem can be recast as the compatibility of two channels.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Given two quantum channels, we examine the task of determining whether they
are compatible - meaning that one can perform both channels simultaneously but,
in the future, choose exactly one channel whose output is desired (while
forfeiting the output of the other channel). We show several results concerning
this task. First, we show it is equivalent to the quantum state marginal
problem, i.e., every quantum state marginal problem can be recast as the
compatibility of two channels, and vice versa. Second, we show that compatible
measure-and-prepare channels (i.e., entanglement-breaking channels) do not
necessarily have a measure-and-prepare compatibilizing channel. Third, we
extend the notion of the Jordan product of matrices to quantum channels and
present sufficient conditions for channel compatibility. These Jordan products
and their generalizations might be of independent interest. Last, we formulate
the different notions of compatibility as semidefinite programs and numerically
test when families of partially dephasing-depolaring channels are compatible.
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