231 research outputs found
Is Communication Complexity Physical?
Recently, Brassard et. al. conjectured that the fact that the maximal
possible correlations between two non-local parties are the quantum-mechanical
ones is linked to a reasonable restriction on communication complexity. We
provide further support for the conjecture in the multipartite case. We show
that any multipartite communication complexity problem could be reduced to
triviality, had Nature been more non-local than quantum-mechanics by a quite
small gap for any number of parties. Intriguingly, the multipartite
nonlocal-box that we use to show the result corresponds to the generalized Bell
inequality that manifests maximal violation in respect to a local
hidden-variable theory
Fault-Tolerant Thresholds for Encoded Ancillae with Homogeneous Errors
I describe a procedure for calculating thresholds for quantum computation as
a function of error model given the availability of ancillae prepared in
logical states with independent, identically distributed errors. The thresholds
are determined via a simple counting argument performed on a single qubit of an
infinitely large CSS code. I give concrete examples of thresholds thus
achievable for both Steane and Knill style fault-tolerant implementations and
investigate their relation to threshold estimates in the literature.Comment: 14 pages, 5 figures, 3 tables; v2 minor edits, v3 completely revised,
submitted to PR
Spin torque, tunnel-current spin polarization and magnetoresistance in MgO magnetic tunnel junctions
We examine the spin torque (ST) response of magnetic tunnel junctions (MTJs)
with ultra-thin MgO tunnel barrier layers to investigate the relationship
between the spin-transfer torque and the tunnel magnetoresistance (TMR) under
finite bias. We find that the spin torque per unit current exerted on the free
layer decreases by less than 10% over a bias range where the TMR decreases by
over 40%. We examine the implications of this result for various spin-polarized
tunneling models and find that it is consistent with magnetic-state-dependent
effective tunnel decay lengths.Comment: 4 pages, 3 figure
Quantum complexities of ordered searching, sorting, and element distinctness
We consider the quantum complexities of the following three problems:
searching an ordered list, sorting an un-ordered list, and deciding whether the
numbers in a list are all distinct. Letting N be the number of elements in the
input list, we prove a lower bound of \frac{1}{\pi}(\ln(N)-1) accesses to the
list elements for ordered searching, a lower bound of \Omega(N\log{N}) binary
comparisons for sorting, and a lower bound of \Omega(\sqrt{N}\log{N}) binary
comparisons for element distinctness. The previously best known lower bounds
are {1/12}\log_2(N) - O(1) due to Ambainis, \Omega(N), and \Omega(\sqrt{N}),
respectively. Our proofs are based on a weighted all-pairs inner product
argument.
In addition to our lower bound results, we give a quantum algorithm for
ordered searching using roughly 0.631 \log_2(N) oracle accesses. Our algorithm
uses a quantum routine for traversing through a binary search tree faster than
classically, and it is of a nature very different from a faster algorithm due
to Farhi, Goldstone, Gutmann, and Sipser.Comment: This new version contains new results. To appear at ICALP '01. Some
of the results have previously been presented at QIP '01. This paper subsumes
the papers quant-ph/0009091 and quant-ph/000903
Toward an Energy Efficient Language and Compiler for (Partially) Reversible Algorithms
We introduce a new programming language for expressing reversibility,
Energy-Efficient Language (Eel), geared toward algorithm design and
implementation. Eel is the first language to take advantage of a partially
reversible computation model, where programs can be composed of both reversible
and irreversible operations. In this model, irreversible operations cost energy
for every bit of information created or destroyed. To handle programs of
varying degrees of reversibility, Eel supports a log stack to automatically
trade energy costs for space costs, and introduces many powerful control logic
operators including protected conditional, general conditional, protected
loops, and general loops. In this paper, we present the design and compiler for
the three language levels of Eel along with an interpreter to simulate and
annotate incurred energy costs of a program.Comment: 17 pages, 0 additional figures, pre-print to be published in The 8th
Conference on Reversible Computing (RC2016
Experimental quantum tossing of a single coin
The cryptographic protocol of coin tossing consists of two parties, Alice and
Bob, that do not trust each other, but want to generate a random bit. If the
parties use a classical communication channel and have unlimited computational
resources, one of them can always cheat perfectly. Here we analyze in detail
how the performance of a quantum coin tossing experiment should be compared to
classical protocols, taking into account the inevitable experimental
imperfections. We then report an all-optical fiber experiment in which a single
coin is tossed whose randomness is higher than achievable by any classical
protocol and present some easily realisable cheating strategies by Alice and
Bob.Comment: 13 page
On the distinguishability of random quantum states
We develop two analytic lower bounds on the probability of success p of
identifying a state picked from a known ensemble of pure states: a bound based
on the pairwise inner products of the states, and a bound based on the
eigenvalues of their Gram matrix. We use the latter to lower bound the
asymptotic distinguishability of ensembles of n random quantum states in d
dimensions, where n/d approaches a constant. In particular, for almost all
ensembles of n states in n dimensions, p>0.72. An application to distinguishing
Boolean functions (the "oracle identification problem") in quantum computation
is given.Comment: 20 pages, 2 figures; v2 fixes typos and an error in an appendi
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