We consider the problem of implementing two-party interactive quantum

communication over noisy channels, a necessary endeavor if we wish to

fully reap quantum advantages for communication.\ \

\

For an arbitrary protocol with n messages, designed for

noiseless qudit channels, our main result is a simulation method that fails with probability less than

$2^{-\Theta(n\epsilon)}$ and uses a qudit channel $n(1 + \Theta

(\sqrt{\epsilon}))$ times, of which an $\epsilon$ fraction can be

corrupted adversarially.

\

The simulation is thus capacity achieving to leading order, and

we conjecture that it is optimal up to a constant factor in\

the $\sqrt{\epsilon}$ term.\ \

\

Furthermore, the simulation is in a model that does not require

pre-shared resources such as randomness or entanglement between the

communicating parties.

\

Surprisingly, this outperforms the best-known overhead of $1 +

O(\sqrt{\epsilon \log \log 1/\epsilon})$ in the corresponding

\emph{classical} model, which is also conjectured to be optimal

\ \ \ [Haeupler, FOCS\&$\#$39;14].

\

Our work also improves over the best previously known quantum result

where the overhead is a non-explicit large constant [Brassard \emph{et

\ \ al.}, FOCS\&$\#$39;14] for low $\epsilon$.

},
url = {http://acm-stoc.org/stoc2018/STOC-2018-Accepted.html},
author = {Debbie Leung and Ashwin Nayak and Ala Shayeghi and Dave Touchette and Penghui Yao and Nengkun Yu}
}
@article {1244,
title = {A framework for bounding nonlocality of state discrimination},
journal = {Communications in Mathematical Physics},
volume = {323},
year = {2013},
month = {2013/9/4},
pages = {1121 - 1153},
abstract = { We consider the class of protocols that can be implemented by local quantum
operations and classical communication (LOCC) between two parties. In
particular, we focus on the task of discriminating a known set of quantum
states by LOCC. Building on the work in the paper "Quantum nonlocality without
entanglement" [BDF+99], we provide a framework for bounding the amount of
nonlocality in a given set of bipartite quantum states in terms of a lower
bound on the probability of error in any LOCC discrimination protocol. We apply
our framework to an orthonormal product basis known as the domino states and
obtain an alternative and simplified proof that quantifies its nonlocality. We
generalize this result for similar bases in larger dimensions, as well as the
"rotated" domino states, resolving a long-standing open question [BDF+99].
},
doi = {10.1007/s00220-013-1784-0},
url = {http://arxiv.org/abs/1206.5822v1},
author = {Andrew M. Childs and Debbie Leung and Laura Mancinska and Maris Ozols}
}
@article {1246,
title = {Interpolatability distinguishes LOCC from separable von Neumann measurements},
journal = {Journal of Mathematical Physics},
volume = {54},
year = {2013},
month = {2013/06/25},
pages = {112204},
abstract = { Local operations with classical communication (LOCC) and separable operations
are two classes of quantum operations that play key roles in the study of
quantum entanglement. Separable operations are strictly more powerful than
LOCC, but no simple explanation of this phenomenon is known. We show that, in
the case of von Neumann measurements, the ability to interpolate measurements
is an operational principle that sets apart LOCC and separable operations.
},
doi = {10.1063/1.4830335},
url = {http://arxiv.org/abs/1306.5992v1},
author = {Andrew M. Childs and Debbie Leung and Laura Mancinska and Maris Ozols}
}
@article {1242,
title = {Characterization of universal two-qubit Hamiltonians},
year = {2010},
month = {2010/04/09},
abstract = { Suppose we can apply a given 2-qubit Hamiltonian H to any (ordered) pair of
qubits. We say H is n-universal if it can be used to approximate any unitary
operation on n qubits. While it is well known that almost any 2-qubit
Hamiltonian is 2-universal (Deutsch, Barenco, Ekert 1995; Lloyd 1995), an
explicit characterization of the set of non-universal 2-qubit Hamiltonians has
been elusive. Our main result is a complete characterization of 2-non-universal
2-qubit Hamiltonians. In particular, there are three ways that a 2-qubit
Hamiltonian H can fail to be universal: (1) H shares an eigenvector with the
gate that swaps two qubits, (2) H acts on the two qubits independently (in any
of a certain family of bases), or (3) H has zero trace. A 2-non-universal
2-qubit Hamiltonian can still be n-universal for some n >= 3. We give some
partial results on 3-universality. Finally, we also show how our
characterization of 2-universal Hamiltonians implies the well-known result that
almost any 2-qubit unitary is universal.
},
url = {http://arxiv.org/abs/1004.1645v2},
author = {Andrew M. Childs and Debbie Leung and Laura Mancinska and Maris Ozols}
}