10,676 research outputs found
On the capacities of bipartite Hamiltonians and unitary gates
We consider interactions as bidirectional channels. We investigate the
capacities for interaction Hamiltonians and nonlocal unitary gates to generate
entanglement and transmit classical information. We give analytic expressions
for the entanglement generating capacity and entanglement-assisted one-way
classical communication capacity of interactions, and show that these
quantities are additive, so that the asymptotic capacities equal the
corresponding 1-shot capacities. We give general bounds on other capacities,
discuss some examples, and conclude with some open questions.Comment: V3: extensively rewritten. V4: a mistaken reference to a conjecture
by Kraus and Cirac [quant-ph/0011050] removed and a mistake in the order of
authors in Ref. [53] correcte
Quantum Proofs
Quantum information and computation provide a fascinating twist on the notion
of proofs in computational complexity theory. For instance, one may consider a
quantum computational analogue of the complexity class \class{NP}, known as
QMA, in which a quantum state plays the role of a proof (also called a
certificate or witness), and is checked by a polynomial-time quantum
computation. For some problems, the fact that a quantum proof state could be a
superposition over exponentially many classical states appears to offer
computational advantages over classical proof strings. In the interactive proof
system setting, one may consider a verifier and one or more provers that
exchange and process quantum information rather than classical information
during an interaction for a given input string, giving rise to quantum
complexity classes such as QIP, QSZK, and QMIP* that represent natural quantum
analogues of IP, SZK, and MIP. While quantum interactive proof systems inherit
some properties from their classical counterparts, they also possess distinct
and uniquely quantum features that lead to an interesting landscape of
complexity classes based on variants of this model.
In this survey we provide an overview of many of the known results concerning
quantum proofs, computational models based on this concept, and properties of
the complexity classes they define. In particular, we discuss non-interactive
proofs and the complexity class QMA, single-prover quantum interactive proof
systems and the complexity class QIP, statistical zero-knowledge quantum
interactive proof systems and the complexity class \class{QSZK}, and
multiprover interactive proof systems and the complexity classes QMIP, QMIP*,
and MIP*.Comment: Survey published by NOW publisher
- …