7,403 research outputs found
Distribution of Standard deviation of an observable among superposed states
The standard deviation (SD) quantifies the spread of the observed values on a
measurement of an observable. In this paper, we study the distribution of SD
among the different components of a superposition state. It is found that the
SD of an observable on a superposition state can be well bounded by the SDs of
the superposed states. We also show that the bounds also serve as good bounds
on coherence of a superposition state. As a further generalization, we give an
alternative definition of incompatibility of two observables subject to a given
state and show how the incompatibility subject to a superposition state is
distributed.Comment: 14 pages, 3 figures, misprints are revise
Bell-type inequality and quantum nonlocality in four-qubit systems
We present a Bell-type inequality for four-qubit systems. Using the
inequality we investigate quantum nonlocality of a generic family of states
[Phys. Rev. A 65, 052112 (2002)] and several canonical
four-qubit entangled states. It has been demonstrated that the inequality is
maximally violated by so called "four-qubit maximal entangled state
" and it is also violated by the four-qubit W state and a
special family of states . Moreover, a useful
entanglement-nonlocality relationship for the family of states
is obtained.Comment: 6 pages, 2 figure
Preparation of -photon concatenated GHZ states for observing distinct quantum effects at macroscopic scale
As a class of multipartite entangled states, the multipartite concatenated
GHZ (C-GHZ) states remain superior stability under the influence of
decoherence. We propose two scalable experimental realization of the
multiphoton C-GHZ states based on the entanglers of multiphoton GHZ state.
Given a -photon GHZ state as an input state, if is odd, one can create
a -photon C-GHZ state. Also, generally, we design a scheme to prepare
-photon C-GHZ states from single-photon states by using entanglers
of -photon GHZ state and -control Toffoli gates.Comment: 5 pages, 3 figure
Optimal sampling ratios in comparative diagnostic trials
In this paper we focus on comparative diagnostic trials which are frequently
employed to compare two markers with continuous or ordinal results. We derive
explicit expressions for the optimal sampling ratio based on a common variance
structure shared by existing summary statistics of the receiver operating
characteristic (ROC) curve. Estimating the optimal ratio requires either pilot
data or parametric model assumptions; however, pilot data are often unavailable
at the planning stage of diagnostic trials. In the absence of pilot data, some
distributions have to be assumed for carrying out the calculation. An optimal
ratio from an incorrect distributional assumption may lead to an underpowered
study. We propose a two-stage procedure to adaptively estimate the optimal
ratio in comparative diagnostic trials without pilot data or assuming
parametric distributions. We illustrate the properties of the proposed method
through theoretical proofs and extensive simulation studies. We use an example
in cancer diagnostic studies to illustrate the application of our method. We
find that our method increases the power, or reduces the required overall
sample size dramatically
Violation of generalized Bell inequality and its optimal measurement settings
We provide a method to describe quantum nonlocality for -qubit systems. By
treating the correlation function as an -index tensor, we derive a
generalized Bell inequality. Taking generalized Greenberger-Horne-Zeilinger
(GHZ) state for example, we calculate quantum prediction under a series of
measurement settings involving various angle parameters. We reveal the exact
relationship between quantum prediction and the angle parameters. We show that
there exists a set of optimal measurement settings and find the corresponding
maximal quantum prediction for -qubit generalized GHZ states. As an example,
we consider an interesting situation involving only two angle parameters.
Finally, we obtain a criterion for the violation of the generalized Bell
inequality.Comment: 11 pages, 2 figure
Exploration of multiphoton entangled states by using weak nonlinearities
We propose a fruitful scheme for exploring multiphoton entangled states based
on linear optics and weak nonlinearities. Compared with the previous schemes
the present method is more feasible because there are only small phase shifts
instead of a series of related functions of photon numbers in the process of
interaction with Kerr nonlinearities. In the absence of decoherence we analyze
the error probabilities induced by homodyne measurement and show that the
maximal error probability can be made small enough even when the number of
photons is large. This implies that the present scheme is quite tractable and
it is possible to produce entangled states involving a large number of photons.Comment: 5 pages, 1 figur
On four-photon entanglement from parametric down-conversion process
We propose two schemes to generate four-photon polarization-entangled states
from the second-order emission of the spontaneous parametric down-conversion
process. By using linear optical elements and the coincidence-detection, the
four indistinguishable photons emitted from parametric down-conversion source
result in the Greenberger-Horne-Zeilinger (GHZ) state or the superposition of
two orthogonal GHZ states. For this superposition state, under particular phase
settings we analyze the quantum correlation function and the local hidden
variable (LHV) correlation. As a result, the Bell inequality derived from the
LHV correlation is violated with the visibility larger than 0.442. It means
that the present four-photon entangled state is therefore suitable for testing
the LHV theory.Comment: 5 pages, 2 figure
Entanglement measure and quantum violation of Bell-type inequality for a family of four-qubit entangled states
By calculating entanglement measures and quantum violation of Bell-type
inequality, we reveal the relationship between entanglement measure and the
amount of quantum violation for a family of four-qubit entangled states. It has
been demonstrated that the Bell-type inequality is completely violated by these
four-qubit entangled states. The plot of entanglement measure as a function of
the expectation value of Bell operator shows that entanglement measure first
decreases and then increases smoothly with increasing quantum violation.Comment: 5 pages, 3 figure
Exploration of photon-number entangled states using weak nonlinearities
A method for exploring photon-number entangled states with weak
nonlinearities is described. We show that it is possible to create and detect
such entanglement at various scales, ranging from microscopic to macroscopic
systems. In the present architecture, we suggest that the maximal phase shift
induced in the process of interaction between photons is proportional to photon
numbers. Also, in the absence of decoherence we analyze maximum error
probability and show its feasibility with current technology.Comment: 4 pages, 1 figur
Scalable symmetry detector and its applications by using beam splitters and weak nonlinearities
We describe a method to detect twin-beam multiphoton entanglement based on a
beam splitter and weak nonlinearities. For the twin-beam four-photon
entanglement, we explore a symmetry detector. It works not only for collecting
two-pair entangled states directly from the spontaneous parametric
down-conversion process, but also for purifying them by cascading these
symmetry detectors. Surprisingly, by calculating the iterative coefficient and
the success probability we show that with a few iterations the desired two-pair
can be obtained from a class of four-photon entangled states. We then
generalize the symmetry detector to -pair emissions and show that it is
capable of determining the number of the pairs emitted indistinguishably from
the spontaneous parametric down-conversion source, which may contribute to
explore multipair entanglement with a large number of photons.Comment: 6 pages, 3 figure
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