395 research outputs found
Quantum Nonlocal Boxes Exhibit Stronger Distillability
The hypothetical nonlocal box (\textsf{NLB}) proposed by Popescu and Rohrlich
allows two spatially separated parties, Alice and Bob, to exhibit stronger than
quantum correlations. If the generated correlations are weak, they can
sometimes be distilled into a stronger correlation by repeated applications of
the \textsf{NLB}. Motivated by the limited distillability of \textsf{NLB}s, we
initiate here a study of the distillation of correlations for nonlocal boxes
that output quantum states rather than classical bits (\textsf{qNLB}s). We
propose a new protocol for distillation and show that it asymptotically
distills a class of correlated quantum nonlocal boxes to the value , whereas in contrast, the optimal non-adaptive
parity protocol for classical nonlocal boxes asymptotically distills only to
the value 3.0. We show that our protocol is an optimal non-adaptive protocol
for 1, 2 and 3 \textsf{qNLB} copies by constructing a matching dual solution
for the associated primal semidefinite program (SDP). We conclude that
\textsf{qNLB}s are a stronger resource for nonlocality than \textsf{NLB}s. The
main premise that develops from this conclusion is that the \textsf{NLB} model
is not the strongest resource to investigate the fundamental principles that
limit quantum nonlocality. As such, our work provides strong motivation to
reconsider the status quo of the principles that are known to limit nonlocal
correlations under the framework of \textsf{qNLB}s rather than \textsf{NLB}s.Comment: 25 pages, 7 figure
Commuting Quantum Circuits with Few Outputs are Unlikely to be Classically Simulatable
We study the classical simulatability of commuting quantum circuits with n
input qubits and O(log n) output qubits, where a quantum circuit is classically
simulatable if its output probability distribution can be sampled up to an
exponentially small additive error in classical polynomial time. First, we show
that there exists a commuting quantum circuit that is not classically
simulatable unless the polynomial hierarchy collapses to the third level. This
is the first formal evidence that a commuting quantum circuit is not
classically simulatable even when the number of output qubits is exponentially
small. Then, we consider a generalized version of the circuit and clarify the
condition under which it is classically simulatable. Lastly, we apply the
argument for the above evidence to Clifford circuits in a similar setting and
provide evidence that such a circuit augmented by a depth-1 non-Clifford layer
is not classically simulatable. These results reveal subtle differences between
quantum and classical computation.Comment: 19 pages, 6 figures; v2: Theorems 1 and 3 improved, proofs modifie
Feedback og debriefing
I denne artikel omtales feedback anvendt i den lægevidenskabelige uddannelse. Konteksten er simulationsøvelser, hvor akutte, sjældne eller komplekse hændelser trænes ved simulation.Det læringsmæssige potentiale i simulationsøvelser er meget stort og maksimeres ved at anvende en form for feedback, der betegnes debriefing. Debriefing indeholder dels en faglig del, dels en betydende emotionel del. Inddragelse af den emotionelle komponent er nødvendig hvis den nødvendige refleksion skal føre til læring. Principperne anvendt ved debriefing, som den beskrives her, kan bringes til anvendelse i andre fag og sammenhænge, for eksempel ved tekstfeedback
Higher Order Decompositions of Ordered Operator Exponentials
We present a decomposition scheme based on Lie-Trotter-Suzuki product
formulae to represent an ordered operator exponential as a product of ordinary
operator exponentials. We provide a rigorous proof that does not use a
time-displacement superoperator, and can be applied to non-analytic functions.
Our proof provides explicit bounds on the error and includes cases where the
functions are not infinitely differentiable. We show that Lie-Trotter-Suzuki
product formulae can still be used for functions that are not infinitely
differentiable, but that arbitrary order scaling may not be achieved.Comment: 16 pages, 1 figur
On the Minimum Degree up to Local Complementation: Bounds and Complexity
The local minimum degree of a graph is the minimum degree reached by means of
a series of local complementations. In this paper, we investigate on this
quantity which plays an important role in quantum computation and quantum error
correcting codes. First, we show that the local minimum degree of the Paley
graph of order p is greater than sqrt{p} - 3/2, which is, up to our knowledge,
the highest known bound on an explicit family of graphs. Probabilistic methods
allows us to derive the existence of an infinite number of graphs whose local
minimum degree is linear in their order with constant 0.189 for graphs in
general and 0.110 for bipartite graphs. As regards the computational complexity
of the decision problem associated with the local minimum degree, we show that
it is NP-complete and that there exists no k-approximation algorithm for this
problem for any constant k unless P = NP.Comment: 11 page
Necessary Condition for the Quantum Adiabatic Approximation
A gapped quantum system that is adiabatically perturbed remains approximately
in its eigenstate after the evolution. We prove that, for constant gap, general
quantum processes that approximately prepare the final eigenstate require a
minimum time proportional to the ratio of the length of the eigenstate path to
the gap. Thus, no rigorous adiabatic condition can yield a smaller cost. We
also give a necessary condition for the adiabatic approximation that depends on
local properties of the path, which is appropriate when the gap varies.Comment: 5 pages, 1 figur
Multipartite Nonlocal Quantum Correlations Resistant to Imperfections
We use techniques for lower bounds on communication to derive necessary
conditions in terms of detector efficiency or amount of super-luminal
communication for being able to reproduce with classical local hidden-variable
theories the quantum correlations occurring in EPR-type experiments in the
presence of noise. We apply our method to an example involving n parties
sharing a GHZ-type state on which they carry out measurements and show that for
local-hidden variable theories, the amount of super-luminal classical
communication c and the detector efficiency eta are constrained by eta 2^(-c/n)
= O(n^(-1/6)) even for constant general error probability epsilon = O(1)
Grover's Quantum Search Algorithm for an Arbitrary Initial Mixed State
The Grover quantum search algorithm is generalized to deal with an arbitrary
mixed initial state. The probability to measure a marked state as a function of
time is calculated, and found to depend strongly on the specific initial state.
The form of the function, though, remains as it is in the case of initial pure
state. We study the role of the von Neumann entropy of the initial state, and
show that the entropy cannot be a measure for the usefulness of the algorithm.
We give few examples and show that for some extremely mixed initial states
carrying high entropy, the generalized Grover algorithm is considerably faster
than any classical algorithm.Comment: 4 pages. See http://www.cs.technion.ac.il/~danken/MSc-thesis.pdf for
extended discussio
Minimum Degree up to Local Complementation: Bounds, Parameterized Complexity, and Exact Algorithms
The local minimum degree of a graph is the minimum degree that can be reached
by means of local complementation. For any n, there exist graphs of order n
which have a local minimum degree at least 0.189n, or at least 0.110n when
restricted to bipartite graphs. Regarding the upper bound, we show that for any
graph of order n, its local minimum degree is at most 3n/8+o(n) and n/4+o(n)
for bipartite graphs, improving the known n/2 upper bound. We also prove that
the local minimum degree is smaller than half of the vertex cover number (up to
a logarithmic term). The local minimum degree problem is NP-Complete and hard
to approximate. We show that this problem, even when restricted to bipartite
graphs, is in W[2] and FPT-equivalent to the EvenSet problem, which
W[1]-hardness is a long standing open question. Finally, we show that the local
minimum degree is computed by a O*(1.938^n)-algorithm, and a
O*(1.466^n)-algorithm for the bipartite graphs
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