277 research outputs found
Substituting a qubit for an arbitrarily large number of classical bits
We show that a qubit can be used to substitute for an arbitrarily large
number of classical bits. We consider a physical system S interacting locally
with a classical field phi(x) as it travels directly from point A to point B.
The field has the property that its integrated value is an integer multiple of
some constant. The problem is to determine whether the integer is odd or even.
This task can be performed perfectly if S is a qubit. On the otherhand, if S is
a classical system then we show that it must carry an arbitrarily large amount
of classical information. We identify the physical reason for such a huge
quantum advantage, and show that it also implies a large difference between the
size of quantum and classical memories necessary for some computations. We also
present a simple proof that no finite amount of one-way classical communication
can perfectly simulate the effect of quantum entanglement.Comment: 8 pages, LaTeX, no figures. v2: added result on entanglement
simulation with classical communication; v3: minor correction to main proof,
change of title, added referenc
Improved Quantum Communication Complexity Bounds for Disjointness and Equality
We prove new bounds on the quantum communication complexity of the
disjointness and equality problems. For the case of exact and non-deterministic
protocols we show that these complexities are all equal to n+1, the previous
best lower bound being n/2. We show this by improving a general bound for
non-deterministic protocols of de Wolf. We also give an O(sqrt{n}c^{log^*
n})-qubit bounded-error protocol for disjointness, modifying and improving the
earlier O(sqrt{n}log n) protocol of Buhrman, Cleve, and Wigderson, and prove an
Omega(sqrt{n}) lower bound for a large class of protocols that includes the
BCW-protocol as well as our new protocol.Comment: 11 pages LaTe
Spin-torque driven magnetic vortex self-oscillations in perpendicular magnetic fields
We have employed complete micromagnetic simulations to analyze dc current
driven self-oscillations of a vortex core in a spin-valve nanopillar in a
perpendicular field by including the coupled effect of the spin-torque and the
magnetostatic field computed self-consistently for the entire spin-valve. The
vortex in the thicker nanomagnet moves along a quasi-elliptical trajectory that
expands with applied current, resulting in blue-shifting of the frequency,
while the magnetization of the thinner nanomagnet is non-uniform due to the
bias current. The simulations explain the experimental magnetoresistance-field
hysteresis loop and yield good agreement with the measured frequency vs.
current behavior of this spin-torque vortex oscillator.Comment: 10 pages, 3 figures, to be appear on AP
Causality and Cirel'son bounds
An EPR-Bell type experiment carried out on an entangled quantum system can
produce correlations stronger than allowed by local realistic theories. However
there are correlations that are no-signaling and are more non local than the
quantum correlations. Here we show that any correlations more non local than
those achievable in an EPR-Bell type experiment necessarily allow -in the
context of the quantum formalism- both for signaling and for generation of
entanglement. We use our approach to rederive Cirel'son bound for the CHSH
expression, and we derive a new Cirel'son type bound for qutrits. We discuss in
detail the interpretation of our approach.Comment: 5 page
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
Classical and quantum partition bound and detector inefficiency
We study randomized and quantum efficiency lower bounds in communication
complexity. These arise from the study of zero-communication protocols in which
players are allowed to abort. Our scenario is inspired by the physics setup of
Bell experiments, where two players share a predefined entangled state but are
not allowed to communicate. Each is given a measurement as input, which they
perform on their share of the system. The outcomes of the measurements should
follow a distribution predicted by quantum mechanics; however, in practice, the
detectors may fail to produce an output in some of the runs. The efficiency of
the experiment is the probability that the experiment succeeds (neither of the
detectors fails).
When the players share a quantum state, this gives rise to a new bound on
quantum communication complexity (eff*) that subsumes the factorization norm.
When players share randomness instead of a quantum state, the efficiency bound
(eff), coincides with the partition bound of Jain and Klauck. This is one of
the strongest lower bounds known for randomized communication complexity, which
subsumes all the known combinatorial and algebraic methods including the
rectangle (corruption) bound, the factorization norm, and discrepancy.
The lower bound is formulated as a convex optimization problem. In practice,
the dual form is more feasible to use, and we show that it amounts to
constructing an explicit Bell inequality (for eff) or Tsirelson inequality (for
eff*). We give an example of a quantum distribution where the violation can be
exponentially bigger than the previously studied class of normalized Bell
inequalities.
For one-way communication, we show that the quantum one-way partition bound
is tight for classical communication with shared entanglement up to arbitrarily
small error.Comment: 21 pages, extended versio
Nonlocality as a Benchmark for Universal Quantum Computation in Ising Anyon Topological Quantum Computers
An obstacle affecting any proposal for a topological quantum computer based
on Ising anyons is that quasiparticle braiding can only implement a finite
(non-universal) set of quantum operations. The computational power of this
restricted set of operations (often called stabilizer operations) has been
studied in quantum information theory, and it is known that no
quantum-computational advantage can be obtained without the help of an
additional non-stabilizer operation. Similarly, a bipartite two-qubit system
based on Ising anyons cannot exhibit non-locality (in the sense of violating a
Bell inequality) when only topologically protected stabilizer operations are
performed. To produce correlations that cannot be described by a local hidden
variable model again requires the use of a non-stabilizer operation. Using
geometric techniques, we relate the sets of operations that enable universal
quantum computing (UQC) with those that enable violation of a Bell inequality.
Motivated by the fact that non-stabilizer operations are expected to be highly
imperfect, our aim is to provide a benchmark for identifying UQC-enabling
operations that is both experimentally practical and conceptually simple. We
show that any (noisy) single-qubit non-stabilizer operation that, together with
perfect stabilizer operations, enables violation of the simplest two-qubit Bell
inequality can also be used to enable UQC. This benchmarking requires finding
the expectation values of two distinct Pauli measurements on each qubit of a
bipartite system.Comment: 12 pages, 2 figure
Tighter Relations Between Sensitivity and Other Complexity Measures
Sensitivity conjecture is a longstanding and fundamental open problem in the
area of complexity measures of Boolean functions and decision tree complexity.
The conjecture postulates that the maximum sensitivity of a Boolean function is
polynomially related to other major complexity measures. Despite much attention
to the problem and major advances in analysis of Boolean functions in the past
decade, the problem remains wide open with no positive result toward the
conjecture since the work of Kenyon and Kutin from 2004.
In this work, we present new upper bounds for various complexity measures in
terms of sensitivity improving the bounds provided by Kenyon and Kutin.
Specifically, we show that deg(f)^{1-o(1)}=O(2^{s(f)}) and C(f) < 2^{s(f)-1}
s(f); these in turn imply various corollaries regarding the relation between
sensitivity and other complexity measures, such as block sensitivity, via known
results. The gap between sensitivity and other complexity measures remains
exponential but these results are the first improvement for this difficult
problem that has been achieved in a decade.Comment: This is the merged form of arXiv submission 1306.4466 with another
work. Appeared in ICALP 2014, 14 page
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