404 research outputs found
Quantum data processing and error correction
This paper investigates properties of noisy quantum information channels. We
define a new quantity called {\em coherent information} which measures the
amount of quantum information conveyed in the noisy channel. This quantity can
never be increased by quantum information processing, and it yields a simple
necessary and sufficient condition for the existence of perfect quantum error
correction.Comment: LaTeX, 20 page
A New Quantum Data Processing Inequality
Quantum data processing inequality bounds the set of bipartite states that
can be generated by two far apart parties under local operations; Having access
to a bipartite state as a resource, two parties cannot locally transform it to
another bipartite state with a mutual information greater than that of the
resource state. But due to the additivity of quantum mutual information under
tensor product, the data processing inequality gives no bound when the parties
are provided with arbitrary number of copies of the resource state. In this
paper we introduce a measure of correlation on bipartite quantum states, called
maximal correlation, that is not additive and gives the same number when
computed for multiple copies. Then by proving a data processing inequality for
this measure, we find a bound on the set of states that can be generated under
local operations even when an arbitrary number of copies of the resource state
is available.Comment: 12 pages, fixed an error in the statement of Theorem 2 (thanks to
Dong Yang
Strong Subadditivity Lower Bound and Quantum Channels
We derive the strong subadditivity of the von Neumann entropy with a strict
lower bound dependent on the distribution of quantum correlation in the system.
We investigate the structure of states saturating the bounded subadditivity and
explore its consequences for the quantum data processing inequality. The
quantum data processing achieves a lower bound associated with the locally
inaccessible information.Comment: 6 pages, 2 figure
The best Fisher is upstream: data processing inequalities for quantum metrology
We apply the classical data processing inequality to quantum metrology to
show that manipulating the classical information from a quantum measurement
cannot aid in the estimation of parameters encoded in quantum states. We
further derive a quantum data processing inequality to show that coherent
manipulation of quantum data also cannot improve the precision in estimation.
In addition, we comment on the assumptions necessary to arrive at these
inequalities and how they might be avoided providing insights into enhancement
procedures which are not provably wrong.Comment: Comments encourage
Algebraic and information-theoretic conditions for operator quantum error-correction
Operator quantum error-correction is a technique for robustly storing quantum
information in the presence of noise. It generalizes the standard theory of
quantum error-correction, and provides a unified framework for topics such as
quantum error-correction, decoherence-free subspaces, and noiseless subsystems.
This paper develops (a) easily applied algebraic and information-theoretic
conditions which characterize when operator quantum error-correction is
feasible; (b) a representation theorem for a class of noise processes which can
be corrected using operator quantum error-correction; and (c) generalizations
of the coherent information and quantum data processing inequality to the
setting of operator quantum error-correction.Comment: 4 page
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