Vol.14
No.3&4, March
1, 2014
Research Articles:
Classical simulations of Abeliangroup normalizer circuits with
intermediate measurements (pp01810216)
Juan
BermejoVega and Maarten Van den Nest
Quantum normalizer circuits were recently introduced as
generalizations of Clifford circuits: a normalizer circuit over a
finite Abelian group G is composed of the quantum Fourier
transform (QFT) over G, together with gates which compute
quadratic functions and automorphisms. In \cite{VDNest_12_QFTs} it was
shown that every normalizer circuit can be simulated efficiently
classically. This result provides a nontrivial example of a family of
quantum circuits that cannot yield exponential speedups in spite
of usage of the QFT, the latter being a central quantum algorithmic
primitive. Here we extend the aforementioned result in several ways.
Most importantly, we show that normalizer circuits supplemented with
intermediate measurements can also be simulated efficiently classically,
even when the computation proceeds adaptively. This yields a
generalization of the GottesmanKnill theorem (valid for nqubit
Clifford operations) to quantum circuits described by arbitrary finite
Abelian groups. Moreover, our simulations are twofold: we present
efficient classical algorithms to sample the measurement probability
distribution of any adaptivenormalizer computation, as well as to
compute the amplitudes of the state vector in every step of it. Finally
we develop a generalization of the stabilizer formalism relative
to arbitrary finite Abelian groups: for example we characterize how to
update stabilizers under generalized Pauli measurements and provide a
normal form of the amplitudes of generalized stabilizer states using
quadratic functions and subgroup cosets.
Security of high speed quantum key distribution with finite
detector dead time (pp02170235)
Viacheslav
Burenkov, Bing Qi, Ben Fortescue, and HoiKwong Lo
The security of a high speed quantum key distribution system with
finite detector dead time $\tau$ is analyzed. When the transmission rate
becomes higher than the maximum count rate of the individual detectors
($1/\tau$), security issues affect the scheme for sifting bits.
Analytical calculations and numerical simulations of the
BennettBrassard BB84 protocol are performed. We study Rogers et al.'s
scheme (further information is available in [D. J. Rogers, J. C.
Bienfang, A. Nakassis, H. Xu, and C. W. Clark, New J. Phys.~{\bf 9}, 319
(2007)]) in the presence of an active eavesdropper Eve who has the power
to perform an interceptresend attack. It is shown that Rogers et al.'s
scheme is no longer guaranteed to be secure. More specifically, Eve can
induce a basisdependent detection efficiency at the receiver's end.
Modified key sifting schemes that are basisindependent and thus secure
in the presence of dead time and an active eavesdropper are then
introduced. We analyze and compare these secure sifting schemes for this
active Eve scenario, and calculate and simulate their key generation
rate. It is shown that the maximum key generation rate is $1/(2\tau)$
for passive basis selection, and $1/\tau$ for active basis selection.
The security analysis for finite detector dead time is also extended to
the decoy state BB84 protocol for one particular secure sifting scheme.
Twoparty QPC with polarizationentangled Bell states and the
coherent states
(pp02360254)
XiaoMing
Xiu, Li Dong, HongZhi Shen, YaJun Gao, and X. X. Yi
We propose a protocol of quantum privacy comparison with
polarizationentangled EinsteinPodolskyRosen (Bell) states and the
coherent states. One of two legitimate participants, Alice, prepares
polarizationentangled Bell states and keeps one photon of each photon
pair and sends the other photons to the third party, Charlie. Receiving
the photons, Charlie performs singlephoton transformation operations on
them and then sends them to the other legitimate participant, Bob. Three
participants adopt parity analysis method to check the distribution
security of Bell states. Exploiting polarization beam splitters and
nonlinear interactions mediated by the probe coherent states in Kerr
media, Alice and Bob check the parities of their photons using the bases
of $\{\ket H, \ket V\}$ or $\{\ket +, \ket \}$. On the basis of the
parity analysis outcomes and Charlie's publicized information, they can
analyze the security of the distributed quantum channel. Confirming
secure distribution of the shared Bell states, two participants perform
respective parity measurements on the privacy photons and own photons of
Bell states, and then send the results to Charlie. According to
information provided by two legitimate participants and his singlequbit
transformation operations, Charlie compares the privacy information of
Alice and Bob and publicizes the conclusion.
Dynamics of multiqubit states in noninertial frames for quantum
communication applications
(pp02550264)
Alaa Sagheer and
Hala Hamdoun
In this paper, some properties of multiqubit states traveling in
noninertial frames are investigated, where we assume that all particles
are accelerated. These properties are including fidelities, capacities
and entanglement of the accelerated channels for three different states,
namely, GreebergerHorneZeilinger (GHZ) state, GHZlike state and
Wstate. It is shown here that all these properties are decreased as the
accelerations of the moving particles are increased. The obtained
results show that the GHZstate is the most robust state comparing to
the others, where the degradation rate is less than that for the other
states particularly in the second Rindler region. Also, it is shown here
that the entangled property doesn't change in the accelerated frames.
Additionally, the paper shows that the degree of entanglement decreases
as the accelerations of the particles increase in the first Rindler
region. However in the second region, where all subsystems are
disconnected at zero acceleration, entangled states are generated as the
acceleration increases.
Steadystate entanglement by engineered quasilocal Markovian
dissipation
(pp02650294)
Francesco Ticozzi
and Lorenza Viola
We characterize timeindependent Markovian dynamics that drive a
finitedimensional multipartite quantum system into a target (pure)
entangled steady state, subject to physical locality constraints. New
control schemes are introduced in situations where the desired
stabilization task {\em cannot} be attained solely based on quasilocal
dissipative means, as considered in previous analysis. The new schemes
either allow for Hamiltonian control or, if the latter is not an option,
suitably restrict the set of admissible initial states. In both cases,
we provide explicit algorithms for constructing a Markovian master
equation that achieves the intended objective and show how this
genuinely extends the manifold of stabilizable states. In particular, we
present dissipative quasilocal control protocols for deterministically
engineering multipartite GHZ ``cat'' states and W states on $n$ qubits.
For GHZ states, we show that no scalable procedure exists for achieving
stabilization from arbitrary initial states, whereas this is possible
for a target W state by a suitable combination of a twobody Hamiltonian
and dissipators. Interestingly, for both entanglement classes, we show
that quasilocal stabilization may be {\em scalably} achieved
conditional to initialization of the system in a large, appropriately
chosen subspace.
Quantum solution to a three player Kolkata restaurant problem
using entangled qutrits
(pp02950305)
Puya Sharif and
Hoshang Heydari
Three player quantum Kolkata restaurant problem is modelled using
three entangled qutrits. This first use of three level quantum states in
this context is a step towards a $N$choice generalization of the
$N$player quantum minority game. It is shown that a better than
classical payoff is achieved by a Nash equilibrium solution where the
space of available strategies is spanned by subsets of SU(3) and the
players share a tripartite entangled initial state.
Faster phase estimation
(pp03060328)
Krysta M. Svore,
Matthew B. Hastings, and Michael Freedman
We develop several algorithms for performing quantum phase
estimation based on basic measurements and classical postprocessing. We
present a pedagogical review of quantum phase estimation and simulate
the algorithm to numerically determine its scaling in circuit depth and
width. We show that the use of purely random measurements requires a
number of measurements that is optimal up to constant factors, albeit at
the cost of exponential classical postprocessing; the method can also
be used to improve classical signal processing. We then develop a
quantum algorithm for phase estimation that yields an asymptotic
improvement in runtime, coming within a factor of $\log^*$ of the
minimum number of measurements required while still requiring only
minimal classical postprocessing. The corresponding quantum circuit
requires asymptotically lower depth and width (number of qubits) than
quantum phase estimation.
High performance error correction for quantum key distribution
using polar codes
(pp03290338)
Paul Jouguet and
Sebastien KunzJacques
We study the use of polar codes for both discrete and continuous
variables Quantum Key Distribution (QKD). Although very large blocks
must be used to obtain the efficiency required by quantum key
distribution, and especially continuous variables quantum key
distribution, their implementation on generic x86 Central Processing
Units (CPUs) is practical. Thanks to recursive decoding, they exhibit
excellent decoding speed, much higher than large, irregular Low Density
Parity Check (LDPC) codes implemented on similar hardware, and
competitive with implementations of the same codes on highend Graphic
Processing Units (GPUs).
Systems of Imprimitivity for the Clifford group
(pp03390360)
D.M. Appleby,
Ingemar Bengtsson, Stephen Brierley, Asa Ericsson, Markus Grassl, and
JanAke Larsson
It is known that if the dimension is a
perfect square the Clifford group can be represented by monomial
matrices. Another way of expressing this result is to say that when the
dimension is a perfect square the standard representation of the
Clifford group has a system of imprimitivity consisting of one
dimensional subspaces. We generalize this result to the case of an
arbitrary dimension. Let k be the squarefree part of the
dimension. Then we show that the standard representation of the Clifford
group has a system of imprimitivity consisting of $k$dimensional
subspaces. To illustrate the use of this result we apply it to the
calculation of SICPOVMs (symmetric informationally complete positive
operator valued measures), constructing exact solutions in dimensions 8
(handcalculation) as well as 12 and 28 (machinecalculation).
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