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'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'14] for low $\epsilon$.

%B Annual ACM Symposium on the Theory of Computing STOC 2018
%8 2018/01/01
%G eng
%U http://acm-stoc.org/stoc2018/STOC-2018-Accepted.html
%0 Journal Article
%J Communications in Mathematical Physics
%D 2013
%T A framework for bounding nonlocality of state discrimination
%A Andrew M. Childs
%A Debbie Leung
%A Laura Mancinska
%A Maris Ozols
%X 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].
%B Communications in Mathematical Physics
%V 323
%P 1121 - 1153
%8 2013/9/4
%G eng
%U http://arxiv.org/abs/1206.5822v1
%N 3
%! Commun. Math. Phys.
%R 10.1007/s00220-013-1784-0
%0 Journal Article
%J Journal of Mathematical Physics
%D 2013
%T Interpolatability distinguishes LOCC from separable von Neumann measurements
%A Andrew M. Childs
%A Debbie Leung
%A Laura Mancinska
%A Maris Ozols
%X 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.
%B Journal of Mathematical Physics
%V 54
%P 112204
%8 2013/06/25
%G eng
%U http://arxiv.org/abs/1306.5992v1
%N 11
%! J. Math. Phys.
%R 10.1063/1.4830335
%0 Journal Article
%D 2010
%T Characterization of universal two-qubit Hamiltonians
%A Andrew M. Childs
%A Debbie Leung
%A Laura Mancinska
%A Maris Ozols
%X 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.
%8 2010/04/09
%G eng
%U http://arxiv.org/abs/1004.1645v2
%! Quantum Information and Computation 11