Vol.12
No.1&2, January 1, 2012
Research Articles:
Practical
fourdimensional quantum key distribution without entanglement
(pp00010008)
William T.
Buttler, Steven K. Lamoreaux, and Justin R. Torgerson
We describe a fourdimensional ($\mathcal{D} = 4$) singlephoton quantum
cryptography protocol with up to twenty ($\mathcal{D} \times (2^2 + 1)$)
possible states generated by a polarization, phase and timeencoding
transmitter. This protocol can be experimentally realized with existing
technology, drawing from time and polarizationencoded systems. The
protocol is error tolerant and has a maximum raw bit rate of two raw
bits per detection, which when combined with state detection efficiency
yields a qubit rate of up to one per transmission under ideal
assumptions, or up to twice the raw bit rate of twodimensional
protocols such as the wellknown BB84 protocol.
Bell violations
through independent bases games
(pp00090020)
Oded Regev
In a recent paper, Junge and Palazuelos presented two twoplayer games
exhibiting interesting properties. In their first game, entangled
players can perform notably better than classical players. The
quantitative gap between the two cases is remarkably large, especially
as a function of the number of inputs to the players. In their second
game, entangled players can perform notably better than players that are
restricted to using a maximally entangled state (of arbitrary
dimension). This was the first game exhibiting such a behavior. The
analysis of both games is heavily based on nontrivial results from
Banach space theory and operator space theory. Here we provide
alternative proofs of these two results. Our proofs are arguably
simpler, use elementary probabilistic techniques and standard quantum
information arguments, and also give better quantitative bounds.
Impossibility of
succinct quantum proofs for collisionfreeness
(pp00210028)
Scott Aaronson
We show that any quantum algorithm to decide whether a function f[n]
\rightarrow [n] is a permutation or far from a permutation\ must
make \Omega( n^{1/3}/w) queries to f, even if the
algorithm is given a wqubit quantum witness in support of f
being a permutation. This implies that there exists an oracle A
such that {SZK}^{A}\not \subset {QMA}^{A}, answering an
eightyearold open question of the author. \ Indeed, we show that
relative to some oracle, {SZK} is not in the counting class
{A}_0{PP} defined by Vyalyi. The proof is a fairly simple extension
of the quantum lower bound for the collision problem.
Blackbox
Hamiltonian simulation and unitary implementation
(pp00290062)
Andrew M.
Childs and Dominic W. Berry
We present general methods for simulating blackbox Hamiltonians using
quantum walks. These techniques have two main applications: simulating
sparse Hamiltonians and implementing blackbox unitary operations. In
particular, we give the best known simulation of sparse Hamiltonians
with constant precision. Our method has complexity linear in both the
sparseness $\sparseness$ (the maximum number of nonzero elements in a
column) and the evolution time $t$, whereas previous methods had
complexity scaling as $\sparseness^4$ and were superlinear in $t$. We
also consider the task of implementing an arbitrary unitary operation
given a blackbox description of its matrix elements. Whereas standard
methods for performing an explicitly specified $\UN\times\UN$ unitary
operation use $\tilde O(\UN^2)$ elementary gates, we show that a
blackbox unitary can be performed with bounded error using $O(\UN^{2/3}
(\log\log \UN)^{4/3})$ queries to its matrix elements. In fact, except
for pathological cases, it appears that most unitaries can be performed
with only $\tilde O(\sqrt{\UN})$ queries, which is optimal.
Mixed maximally
entangled states
(pp00630073)
Z. G. Li, M.
G. Zhao, S. M. Fei, H. Fan, and W. M. Liu
We find that the mixed maximally entangled states exist and prove that
the form of the mixed maximally entangled states is unique in terms of
the entanglement of formation. Moreover, even if the entanglement is
quantified by other entanglement measures, this conclusion is still
proven right. This result is a supplementary to the generally accepted
fact that all maximally entangled states are pure. These states possess
important properties of the pure maximally entangled states, for
example, these states can be used as a resource for faithful
teleportation and they can be distinguished perfectly by local
operations and classical communication.
Entanglement
distillation from quasifree fermions
(pp00740104)
Zoltan Kadar,
Michael Keyl, and Dirk Schlingemann
We develop a scheme to distill entanglement from bipartite Fermionic
systems in an arbitrary quasifree state. It can be applied if either one
system containing infinite onecopy entanglement is available or if an
arbitrary amount of equally prepared systems can be used. We show that
the efficiency of the proposed scheme is in general very good and in
some cases even optimal. Furthermore we apply it to Fermions hopping on
an infinite lattice and demonstrate in this context that an efficient
numerical analysis is possible for more than $10^6$ lattice sites.
On learning
finitestate quantum sources
(pp01050118)
Brendan Juba
We examine the complexity of learning the distributions produced by
finitestate quantum sources. We show how prior techniques for learning
hidden Markov models can be adapted to the {\em quantum generator} model
to find that the analogous state of affairs holds:
informationtheoretically, a polynomial number of samples suffice to
approximately identify the distribution, but computationally, the
problem is as hard as learning parities with noise, a notorious open
question in computational learning theory.
Relative state measures of
correlations in bipartite quantum systems
(pp01190137)
Pierre
Rudolfsson and Erik Sjoqvist
Everett's concept of relative state can be viewed as a map that contains
information about correlations between measurement outcomes on two
quantum systems. We demonstrate how geometric properties of the relative
state map can be used to develop operationally welldefined measures of
the total correlation in bipartite quantum systems of arbitrary state
space dimension. These measures are invariant under local unitary
transformations and nonincreasing under local operations. We show that
some known correlation measures have a natural interpretation in terms
of relative states.
Some bounds on
the minimum number of queries required for quantum channel perfect
discrimination (pp01380148)
Cheng Lu,
Jianxin Chen, and Runyao Duan
We prove a lower bound on the $q$maximal fidelities between two quantum
channels $\E_0$ and $\E_1$ and an upper bound on the $q$maximal
fidelities between a quantum channel $\E$ and an identity $\I$. Then we
apply these two bounds to provide a simple sufficient and necessary
condition for sequential perfect distinguishability between $\E$ and
$\I$ and provide both a lower bound and an upper bound on the minimum
number of queries required to sequentially perfectly discriminating $\E$
and $\I$. Interestingly, in the $2$dimensional case, both bounds
coincide. Based on the optimal perfect discrimination protocol presented
in \cite{DFY09}, we can further generalize the lower bound and upper
bound to the minimum number of queries to perfectly discriminating $\E$
and $I$ over all possible discrimination schemes. Finally the two lower
bounds are shown remain working for perfectly discriminating general two
quantum channels $\E_0$ and $\E_1$ in sequential scheme and over all
possible discrimination schemes respectively.
Recovery in
quantum error correction for general noise without measurement
(pp01490158)
ChiKwong Li,
Mikio Nakahara, YiuTung Poon, NungSing Sze, and Hiroyuki Tomita
It is known that one can do quantum error correction without syndrome
measurement, which is often done in operator quantum error correction (OQEC).
However, the physical realization could be challenging, especially when
the recovery process involves highrank projection operators and a
superoperator. We use operator theory to improve OQEC so that the
implementation can always be done by unitary gates followed by a partial
trace operation. Examples are given to show that our error correction
scheme outperforms the existing ones in various scenarios.
Nearly
deterministic controlledNOT gate with weak crossKerr nonlinearities
(pp01590170)
XiaoMing Xiu,
Li Dong, YaJun Gao, and X. X. Yi
On the basis of the probe coherent state and weak crossKerr
nonlinearities, we present a scheme of a nearly deterministic
ControlledNOT gate. In this construction, feedforward methods, quantum
nondemolition detectors and several optical elements are applied. It is
a potentially practical quantum gate with certain features. First, the
lack of auxiliary photons is allowable, which decreases consumption of
resources. Secondly, employment of the signal photon from either of
target output ports and three quantum nondemolition detectors enable the
success probability to approach unit and judge whether the signal
photons lose or not. Thirdly, the displacement measurement is adopted,
and thus the ControlledNOT gate works against photon loss of the probe
coherent state. Finally, in order to circumvent the effect of dephasing,
the monochromatic signal photons are exploited.
back to QIC online Front page
