Vol.14
No.1&2, January 1, 2014
Research Articles:
Gateefficient
discrete simulations of continuoustime quantum query algorithms
(pp00010030)
Dominic
W. Berry, Richard Cleve, and Sevag Gharibian
We show how to efficiently simulate continuoustime quantum query
algorithms that run in time T in a manner that preserves the
query complexity (within a polylogarithmic factor) while also incurring
a small overhead cost in the total number of gates between queries. By
small overhead, we mean T within a factor that is polylogarithmic
in terms of T and a cost measure that reflects the cost of
computing the driving Hamiltonian. This permits any
continuoustime quantum algorithm based on an efficiently computable
driving Hamiltonian to be converted into a gateefficient algorithm with
similar running time.
Comparisons
between quantum state distinguishability measures
(pp00310038)
Koenraad M.R.
Audenaert
We provide a compendium of inequalities between several quantum
state distinguishability measures. For each measure these inequalities
consist of the sharpest possible upper and lower bounds in terms of
another measure. Some of these inequalities are already known, but new
or more general proofs are given, whereas other inequalities are new. We
also supply cases of equality to show that all inequalities are indeed
the sharpest possible.
Effects of
quantum error correction on entanglement sudden death
(pp00390055)
Muhammed
Yonac and Joseph H. Eberly
We investigate the effects of error correction on nonlocal quantum
coherence as a function of time, extending the study by Sainz and Bjork.
We consider error correction of amplitude damping, pure phase damping
and combinations of amplitude and phase damping as they affect both
fidelity and quantum entanglement. Initial twoqubit entanglement is
encoded in arbitrary real superpositions of both $\Phi$type and
$\Psi$type Bell states. Our main focus is on the possibility of delay
or prevention of ESD (early stage decoherence, or entanglement sudden
death). We obtain the onset times for ESD as a function of the
statesuperposition mixing angle. Error correction affects entanglement
and fidelity differently, and we exhibit initial entangled states for
which error correction increases fidelity but decreases entanglement,
and vice versa.
Quantum
algorithms for onedimensional infrastructures
(pp00560090)
Pradeep
Sarvepalli and Pawel M. Wocjan
Infrastructures are grouplike objects that make their appearance in
arithmetic geometry in the study of computational problems related to
number fields and function fields over finite fields. The most prominent
computational tasks of infrastructures are the computation of the
circumference of the infrastructure and the generalized discrete
logarithms. Both these problems are not known to have efficient
classical algorithms for an arbitrary infrastructure. Our main
contributions are polynomial time quantum algorithms for onedimensional
infrastructures that satisfy certain conditions. For instance, these
conditions are always fulfilled for infrastructures obtained from number
fields and function fields, both of unit rank one. Since quadratic
number fields give rise to such infrastructures, this algorithm can be
used to solve Pell's equation and the principal ideal problem. In this
sense we generalize Hallgren's quantum algorithms for quadratic number
fields, while also providing a polynomial speedup over them. Our more
general approach shows that these quantum algorithms can also be applied
to infrastructures obtained from complex cubic and totally complex
quartic number fields. Our improved way of analyzing the performance
makes it possible to show that these algorithms succeed with constant
probability independent of the problem size. In contrast, the lower
bound on the success probability due to Hallgren decreases as the fourth
power of the logarithm of the circumference. Our analysis also shows
that fewer qubits are required. We also contribute to the study of
infrastructures, and show how to compute efficiently within
infrastructures.
Codingbased
quantum private database query using entanglement
(pp00910106)
Fang Yu and
Daowen Qiu
We propose an efficient codingbased quantum protocol which uses
entanglement to help a user retrieve one out of $N$ items from a
database without revealing which one he/she is interested in. The query
is accomplished through an encodingdecoding process with the support of
a databasespecific unitary operation. For each query, $O(logN)$ time is
needed for communication and no more than one bit of information about
the database can be learnt by even a dishonest user. We prove rigorously
that the protocol is secure against a dishonest database which causes
little deviation on the original system. A theorem quantitatively
describes the tradeoff between information and disturbance in such a
setting. Examples are given to illustrate that both codingbased quantum
private database query protocols proposed so far, including ours and
Olejnik's, are insecure against dishonest databases which are free to
cause deviations. Compared to Olejnik's protocol, which utilizes
superposed states rather than entanglement, our protocol can prevent a
dishonestbutconscientious database, which tries to provide the user
right answers to his/her queries while eavesdropping, from learning
significant information when it evaded his/her detection. Finally, for
the purpose of enhancing user privacy, two extensions of the protocol
are proposed and discussed.
Nonlocal
entanglement concentration of separate nitrogenvacancy centers coupling
to microtoroidal resonators (pp01070121)
Chuan Wang,
Yong Zhang, Ming Lei, Guangsheng Jin, Haiqiang Ma, and Ru Zhang
Here we propose two practical protocols to concentrate entanglement
between separate nitrogenvacancy (NV) centers in less entangled state
via coupling to microtoroidal resonators. We construct the parity check
gate of the NV center and microtoroidal resonator systems via the
interaction with the ancillary photon inputoutput process near the
microtoroidal resonators. Thus the parity of the NV center state can be
readout by the measurement on the ancillary photon. Then we introduce
the parity check operations to entanglement concentration protocols.
Considering current techniques, we also discuss the feasibility of our
proposal and its experimental challenges.
Manytoone
remote information concentration for qudits and multipartite
entanglement (pp01220136)
XinWen Wang,
ShiQing Tang, LiJun Xie, DengYu Zhang, and LeMan Kuang
Telecloning and its reverse process, referred to as remote
information concentration (RIC), have attracted considerable interest
because of their potential applications in quantuminformation
processing. We here present a general scheme for RIC in $d$level
systems (qudits), in which the quantum information initially distributed
in many spatially separated qudits can be remotely and deterministically
concentrated to a single qudit via an entangled channel without
performing any global operations. We show that the entangled channel of
RIC can be different types of entangled states, including mixed states
as well as pure ones. More interestingly, these mixed states include a
bound entangled state which has a similar form to the generalized Smolin
state but has different characteristics from it. We also show that there
exists a multipartite entangled state which can be used to implement
both telecloning and RIC in the twolevel system. Our manytoone RIC
protocol could be slightly modified to perform some types of
manytomany RIC tasks.
Onestep
implementation of quantum comtrolledphase gate via quantum Zeno
dynamics (pp01370143)
WenAn Li and
LianFu Wei
We propose a scheme to implement a quantum controllablephase gate
via quantum Zeno dynamics. The two qubits are asymmetrically encoded by
two fourlevel atoms coupled via a quantized cavity mode. Under proper
conditions, the desirable logic operation can be implemented in one
step. Since the qubit is encoded by the ground and the metastable states
of the atom and the cavity mode is not really excited, our protocol is
robust against the spontaneous decays of the atoms and cavity.
Specifically, the feasibility of our generic proposal is demonstrated
with two nitrogenvacancy centers coupled to whisperinggallery
microresonator.
Quantum Systems
on Non$k$Hyperfinite Complexes: a generalization of classical
statistical mechanics on expander graphs
(pp01440180)
Michael H.
Freedman and Matthew B. Hastings
We construct families of cell complexes that generalize expander
graphs. These families are called non$k$hyperfinite, generalizing the
idea of a nonhyperfinite (NH) family of graphs. Roughly speaking, such
a complex has the property that one cannot remove a small fraction of
points and be left with an object that looks $k1$dimensional at large
scales. We then consider certain quantum systems on these complexes. A
future goal is to construct a family of Hamiltonians such that every low
energy state has topological order as part of an attempt to prove the
quantum PCP conjecture. This goal is approached by constructing a toric
code Hamiltonian with the property that every low energy state without
vertex defects has topological order, a property that would not hold for
any local system in any lattice $Z^d$ or indeed on any $1$hyperfinite
complex. Further, such NH complexes find application in quantum coding
theory. The hypergraph product codes\cite{hpc} of Tillich and Z\'{e}mor
are generalized using NH complexes.
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