74 research outputs found
Entanglement-assisted zero-error capacity is upper-bounded by the Lovász ϑ function
The zero-error capacity of a classical channel is expressed in terms of the independence number of some graph and its tensor powers. This quantity is hard to compute even for small graphs such as the cycle of length seven, so upper bounds such as the Lovász theta function play an important role in zero-error communication. In this paper, we show that the Lovász theta function is an upper bound on the zero-error capacity even in the presence of entanglement between the sender and receiver
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
Maximal Entanglement - A New Measure of Entanglement
Maximal correlation is a measure of correlation for bipartite distributions.
This measure has two intriguing features: (1) it is monotone under local
stochastic maps; (2) it gives the same number when computed on i.i.d. copies of
a pair of random variables. This measure of correlation has recently been
generalized for bipartite quantum states, for which the same properties have
been proved. In this paper, based on maximal correlation, we define a new
measure of entanglement which we call maximal entanglement. We show that this
measure of entanglement is faithful (is zero on separable states and positive
on entangled states), is monotone under local quantum operations, and gives the
same number when computed on tensor powers of a bipartite state.Comment: 8 pages, presented at IWCIT 201
- …