Vol.13
No.3&4, March 1, 2013
Research Articles:
Sufficient condition on noise correlations for scalable quantum
computing
(pp01810194)
John Preskill
I study the effectiveness of faulttolerant quantum computation against
correlated Hamiltonian noise, and derive a sufficient condition for
scalability. Arbitrarily long quantum computations can be executed
reliably provided that noise terms acting collectively on $k$ system
qubits are sufficiently weak, and decay sufficiently rapidly with
increasing $k$ and with increasing spatial separation of the qubits.
Magicstate distillation with the fourqubit code
(pp01950209)
Adam M. Meier, Bryan Eastin, and Emanuel Knill
The distillation of magic states is an oftencited technique for
enabling universal quantum computing once the error probability for a
special subset of gates has been made negligible by other means. We
present a routine for magicstate distillation that reduces the required
overhead for a range of parameters of practical interest. Each iteration
of the routine uses a fourqubit errordetecting code to distill the
$+1$ eigenstate of the Hadamard gate at a cost of ten input states per
two improved output states. Use of this routine in combination with the
$15$to$1$ distillation routine described by Bravyi and Kitaev allows
for further improvements in overhead.
Optimal classspecific witnesses for threequbit entanglement from GreenbergerHorneZeilinger symmetry
(pp02100220)
Christopher Eltschka and Jens Siewert
Recently, a new type of symmetry for threequbit quantum states was
introduced, the socalled GreenbergerHorneZeilinger (GHZ) symmetry. It
includes the operations which leave the threequbit standard GHZ state
unchanged. This symmetry is powerful as it yields families of mixed
states that are, on the one hand, complex enough from the physics point
of view and, on the other hand, simple enough mathematically so that
their properties can be characterized analytically. We show that by
using the properties of GHZsymmetric states it is straightforward to
derive optimal witnesses for detecting classspecific entanglement in
arbitrary threequbit states.
Reduction from noninjective hidden shift problem to injective hidden shift problem
(pp02210230)
Mirmojtaba Gharibi
We introduce a simple tool that can be used to reduce noninjective
instances of the hidden shift problem over arbitrary group to injective
instances over the same group. In particular, we show that the
averagecase noninjective hidden shift problem admit this reduction. We
show similar results for (noninjective) hidden shift problem for bent
functions. We generalize the notion of influence and show how it relates
to applicability of this tool for doing reductions. In particular, these
results can be used to simplify the main results by Gavinsky, Roetteler,
and Roland about the hidden shift problem for the Booleanvalued
functions and bent functions, and also to generalize their results to
nonBoolean domains (thereby answering an open question that they pose).
Gaming the quantum
(pp02310244)
Faisal Shah Khan and Simon J.D. Phoenix
In the time since the merger of quantum mechanics and game theory was
proposed formally in 1999, the two distinct perspectives apparent in
this merger of applying quantum mechanics to game theory, referred to
henceforth as the theory of ``quantized games'', and of applying game
theory to quantum mechanics, referred to henceforth as ``gaming the
quantum'', have become synonymous under the single illdefined term
``quantum game''. Here, these two perspectives are delineated and a
gametheoretically proper description of what makes a multiplayer,
noncooperative game quantum mechanical, is given. Within the context of
this description, finding Nash equilibrium in a zerosum quantum game is
exhibited to be equivalent to finding a solution to a simultaneous
distance minimization problem in the state space of quantum objects,
thus setting up a framework for a game theory inspired study of
``equilibrium'' behavior of quantum physical systems such as those
utilized in quantum information processing and computation.
Can bipartite classical information resources be activated?
(pp02450265)
Giuseppe Prettico and Antonio Acin
Nonadditivity is one of the distinctive traits of Quantum Information
Theory: the combined use of quantum objects may be more advantageous
than the sum of their individual uses. Nonadditivity effects have been
proven, for example, for quantum channel capacities, entanglement
distillation or state estimation. In this work, we consider whether nonadditivity
effects can be found in Classical Information Theory. We work in the
secretkey agreement scenario in which two honest parties, having access
to correlated classical data that are also correlated to an
eavesdropper, aim at distilling a secret key. Exploiting the analogies
between the entanglement and the secretkey agreement scenario, we
provide some evidence that the secretkey rate may be a nonadditive
quantity. In particular, we show that correlations with conjectured
bound information become secretkey distillable when combined. Our
results constitute a new instance of the subtle relation between the
entanglement and secretkey agreement scenario.
Spin squeezing of oneaxis twisting model in the presence of phase
dephasing
(pp02660280)
ChenGuang Ji,YongChun Liu, and GuangRi Jin
We present a detailed analysis of spin squeezing of the oneaxis
twisting model with a manybody phase dephasing, which is induced by
external field fluctuation in a twomode BoseEinstein condensates. Even
in the presence of the dephasing, our analytical results show that the
optimal initial state corresponds to a coherent spin state $\theta_{0},
\phi_0\rangle$ with the polar angle $\theta_0=\pi/2$. If the dephasing
rate $\gamma\ll S^{1/3}$, where $S$ is total atomic spin, we find that
the smallest value of squeezing parameter (i.e., the strongest
squeezing) obeys the same scaling with the ideal oneaxis twisting case,
namely $\xi^2\propto S^{2/3}$. While for a moderate dephasing, the
achievable squeezing obeys the power rule $S^{2/5}$, which is slightly
worse than the ideal case. When the dephasing rate $\gamma>S^{1/2}$, we
show that the squeezing is weak and neglectable.
Cooling distant atoms into steady entanglement via coupled cavities
(pp02810289)
Li Tuo Shen, Xin Yu Chen, ZhenBiao Yang, HuaiZhi Wu, and ShiBiao
Zheng
We propose a scheme for generating steadystate entanglement between two
distant atomic qubits in the coupledcavity system via laser cooling.
With suitable choice of the laser frequencies, the target entangled
state is the only ground state that is not excited by the lasers due to
large detunings. The laser excitations of other ground states, together
with dissipative processes, drive the system to the target state which
is the unique steady state of the system. Numerical simulation shows
that the maximally entangled state with high fidelity can be produced
with presently available
cooperativity.
Efficient quantum communication under collective noise
(pp02900323)
Michael Skotiniotis,
Wolfgang Dur, and Barbara Kraus
We introduce a new quantum communication protocol for the transmission
of quantum information under collective noise. Our protocol utilizes a
decoherencefree subspace in such a way that an optimal asymptotic
transmission rate is achieved, while at the same time encoding and
decoding operations can be efficiently implemented. The encoding and
decoding circuit requires a number of elementary gates that scale
linearly with the number of transmitted qudits, $m$. The logical depth
of our encoding and decoding operations is constant and depends only on
the channel in question. For channels described by an arbitrary discrete
group $G$, i.e.~with a discrete number, $\lvert G\rvert$, of possible
noise operators, perfect transmission at a rate $m/(m+r)$ is achieved
with an overhead that scales at most as $\mathcal{O}(d^r)$ where the
number of auxiliary qudits, $r$, depends solely on the group in
question. Moreover, this overhead is independent of the number of
transmitted qudits, $m$. For certain groups, e.g.~cyclic groups, we find
that the overhead scales only linearly with the number of group elements
$G$.
Optical detection of quantum entanglement between two quantum dots
mear a metal nanoparticle
(pp03240333)
Yong He and KaDi Zhu
We theoretically study the interaction between two semiconductor quantum
dots (SQDs) and a metal nanoparticle\ (MNP) within the quantum
description. The plasmon field produced in the MNP excited by the
external field can play the platform of F\"{o}rster energy transfer
between two SQDs which gives rise to the generation of entangled states.
The Fano effect can be shown in the energy absorption spectrum of MNP,
which originates from constructive or destructive interference between
two competing optical pathways. Since the generated entangled state is
in one pathway, the steadystate concurrence of entanglement can be
evaluated by the observation of Fano profile. Because the concurrence of
two SQDs is determined by both the pump intensity and the energy
difference, one can properly choose these two parameters for detecting
the nonnegligible entanglement. When the pump intensity is very strong,
there is no entanglement. The method to observe entanglement with the
Fano profile, so, has a limited range of applicability. The optical
observation is a novel approach to reveal entanglement. It may be used
to optically detect quantum entanglement in many solidstate systems.
Multipartite entanglement in XOR games
(pp03340360)
Jop Briet, Harry Buhrman, Troy Lee, and Thomas Vidick
We study multipartite entanglement in the context of XOR games. In
particular, we study the ratio of the entangled and classical \emph{biases},
which measure the maximum advantage of a quantum or classical strategy
over a uniformly random strategy. For the case of twoplayer XOR games,
Tsirelson proved that this ratio is upper bounded by the celebrated
Grothendieck constant. In contrast, \PG proved the existence of
entangled states that give quantum players an unbounded advantage over
classical players in a threeplayer XOR game. We show that the
multipartite entangled states that are most often seen in today's
literature can only lead to a bias that is a constant factor larger than
the classical bias. These states include GHZ states, any state
localunitarily equivalent to combinations of GHZ and maximally
entangled states shared between different subsets of the players (e.g.,
stabilizer states), as well as generalizations of GHZ states of the form
$\sum_i \alpha_i \ket{i}\cdots\ket{i}$ for arbitrary amplitudes $\alpha_i$.
Our results have the following surprising consequence: \emph{classical}
threeplayer XOR games do not follow an XOR parallel repetition theorem,
even a very weak one. Besides this, we discuss implications of our
results for communication complexity and hardness of approximation. Our
proofs are based on novel applications of extensions of Grothendieck's
inequality, due to Blei and Tonge, and Carne, generalizing Tsirelson's
use of Grothendieck's inequality to bound the bias of twoplayer XOR
games.
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