431 research outputs found
Proving the power of postselection
It is a widely believed, though unproven, conjecture that the capability of
postselection increases the language recognition power of both probabilistic
and quantum polynomial-time computers. It is also unknown whether
polynomial-time quantum machines with postselection are more powerful than
their probabilistic counterparts with the same resource restrictions. We
approach these problems by imposing additional constraints on the resources to
be used by the computer, and are able to prove for the first time that
postselection does augment the computational power of both classical and
quantum computers, and that quantum does outperform probabilistic in this
context, under simultaneous time and space bounds in a certain range. We also
look at postselected versions of space-bounded classes, as well as those
corresponding to error-free and one-sided error recognition, and provide
classical characterizations. It is shown that would equal
if the randomized machines had the postselection capability.Comment: 26 pages. This is a heavily improved version of arXiv:1102.066
The computational complexity of PEPS
We determine the computational power of preparing Projected Entangled Pair
States (PEPS), as well as the complexity of classically simulating them, and
generally the complexity of contracting tensor networks. While creating PEPS
allows to solve PP problems, the latter two tasks are both proven to be
#P-complete. We further show how PEPS can be used to approximate ground states
of gapped Hamiltonians, and that creating them is easier than creating
arbitrary PEPS. The main tool for our proofs is a duality between PEPS and
postselection which allows to use existing results from quantum compexity.Comment: 5 pages, 1 figure. Published version, plus a few extra
Witnessing effective entanglement in a continuous variable prepare&measure setup and application to a QKD scheme using postselection
We report an experimental demonstration of effective entanglement in a
prepare&measure type of quantum key distribution protocol. Coherent
polarization states and heterodyne measurement to characterize the transmitted
quantum states are used, thus enabling us to reconstruct directly their
Q-function. By evaluating the excess noise of the states, we experimentally
demonstrate that they fulfill a non-separability criterion previously presented
by Rigas et al. [J. Rigas, O. G\"uhne, N. L\"utkenhaus, Phys. Rev. A 73, 012341
(2006)]. For a restricted eavesdropping scenario we predict key rates using
postselection of the heterodyne measurement results.Comment: 12 pages, 12 figures, 2 table
Complexity classification of two-qubit commuting hamiltonians
We classify two-qubit commuting Hamiltonians in terms of their computational
complexity. Suppose one has a two-qubit commuting Hamiltonian H which one can
apply to any pair of qubits, starting in a computational basis state. We prove
a dichotomy theorem: either this model is efficiently classically simulable or
it allows one to sample from probability distributions which cannot be sampled
from classically unless the polynomial hierarchy collapses. Furthermore, the
only simulable Hamiltonians are those which fail to generate entanglement. This
shows that generic two-qubit commuting Hamiltonians can be used to perform
computational tasks which are intractable for classical computers under
plausible assumptions. Our proof makes use of new postselection gadgets and Lie
theory.Comment: 34 page
Online Learning of Quantum States
Suppose we have many copies of an unknown -qubit state . We measure
some copies of using a known two-outcome measurement , then other
copies using a measurement , and so on. At each stage , we generate a
current hypothesis about the state , using the outcomes of
the previous measurements. We show that it is possible to do this in a way that
guarantees that , the error in our prediction for the next
measurement, is at least at most times. Even in the "non-realizable" setting---where
there could be arbitrary noise in the measurement outcomes---we show how to
output hypothesis states that do significantly worse than the best possible
states at most times on the first
measurements. These results generalize a 2007 theorem by Aaronson on the
PAC-learnability of quantum states, to the online and regret-minimization
settings. We give three different ways to prove our results---using convex
optimization, quantum postselection, and sequential fat-shattering
dimension---which have different advantages in terms of parameters and
portability.Comment: 18 page
Can Anomalous Amplification be Attained Without Postselection?
We present a parameter estimation technique based on performing joint
measurements of a weak interaction away from the weak-value-amplification
approximation. Two detectors are used to collect full statistics of the
correlations between two weakly entangled degrees of freedom. Without the need
of postselection, the protocol resembles the anomalous amplification of an
imaginary-weak-value-like response. The amplification is induced in the
difference signal of both detectors allowing robustness to different sources of
technical noise, and offering in addition the advantages of balanced signals
for precision metrology. All of the Fisher information about the parameter of
interest is collected, and a phase controls the amplification response. We
experimentally demonstrate the proposed technique by measuring polarization
rotations in a linearly polarized laser pulse. The effective sensitivity and
precision of a split detector is increased when compared to a conventional
continuous-wave balanced detection technique
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