5,611 research outputs found
Entanglement criterion via general symmetric informationally complete measurements
We study the quantum separability problem by using general symmetric
informationally complete measurements and present a separability criterion for
arbitrary dimensional bipartite systems. We show by detailed examples that our
criterion is more powerful than the existing ones in entanglement detection.Comment: 8 pages, 5 figure
Quantum entanglement
All our former experience with application of quantum theory seems to say:
{\it what is predicted by quantum formalism must occur in laboratory}. But the
essence of quantum formalism - entanglement, recognized by Einstein, Podolsky,
Rosen and Schr\"odinger - waited over 70 years to enter to laboratories as a
new resource as real as energy.
This holistic property of compound quantum systems, which involves
nonclassical correlations between subsystems, is a potential for many quantum
processes, including ``canonical'' ones: quantum cryptography, quantum
teleportation and dense coding. However, it appeared that this new resource is
very complex and difficult to detect. Being usually fragile to environment, it
is robust against conceptual and mathematical tools, the task of which is to
decipher its rich structure.
This article reviews basic aspects of entanglement including its
characterization, detection, distillation and quantifying. In particular, the
authors discuss various manifestations of entanglement via Bell inequalities,
entropic inequalities, entanglement witnesses, quantum cryptography and point
out some interrelations. They also discuss a basic role of entanglement in
quantum communication within distant labs paradigm and stress some
peculiarities such as irreversibility of entanglement manipulations including
its extremal form - bound entanglement phenomenon. A basic role of entanglement
witnesses in detection of entanglement is emphasized.Comment: 110 pages, 3 figures, ReVTex4, Improved (slightly extended)
presentation, updated references, minor changes, submitted to Rev. Mod. Phys
Collectibility for Mixed Quantum States
Bounds analogous to entropic uncertainty relations allow one to design
practical tests to detect quantum entanglement by a collective measurement
performed on several copies of the state analyzed. This approach, initially
worked out for pure states only [Phys. Rev. Lett. 107, 150502 (2011)], is
extended here for mixed quantum states. We define collectibility for any mixed
states of a multipartite system. Deriving bounds for collectibility for
positive partially transposed states of given purity provides a new insight
into the structure of entangled quantum states. In case of two qubits the
application of complementary measurements and coincidence based detections
leads to a new test of entanglement of pseudopure states.Comment: 13 page
Quantum interactive proofs and the complexity of separability testing
We identify a formal connection between physical problems related to the
detection of separable (unentangled) quantum states and complexity classes in
theoretical computer science. In particular, we show that to nearly every
quantum interactive proof complexity class (including BQP, QMA, QMA(2), and
QSZK), there corresponds a natural separability testing problem that is
complete for that class. Of particular interest is the fact that the problem of
determining whether an isometry can be made to produce a separable state is
either QMA-complete or QMA(2)-complete, depending upon whether the distance
between quantum states is measured by the one-way LOCC norm or the trace norm.
We obtain strong hardness results by proving that for each n-qubit maximally
entangled state there exists a fixed one-way LOCC measurement that
distinguishes it from any separable state with error probability that decays
exponentially in n.Comment: v2: 43 pages, 5 figures, completely rewritten and in Theory of
Computing (ToC) journal forma
Automated design of robust discriminant analysis classifier for foot pressure lesions using kinematic data
In the recent years, the use of motion tracking systems for acquisition of functional biomechanical gait data, has received increasing interest due to the richness and accuracy of the measured kinematic information. However, costs frequently restrict the number of subjects employed, and this makes the dimensionality of the collected data far higher than the available samples. This paper applies discriminant analysis algorithms to the classification of patients with different types of foot lesions, in order to establish an association between foot motion and lesion formation. With primary attention to small sample size situations, we compare different types of Bayesian classifiers and evaluate their performance with various dimensionality reduction techniques for feature extraction, as well as search methods for selection of raw kinematic variables. Finally, we propose a novel integrated method which fine-tunes the classifier parameters and selects the most relevant kinematic variables simultaneously. Performance comparisons are using robust resampling techniques such as Bootstrapand k-fold cross-validation. Results from experimentations with lesion subjects suffering from pathological plantar hyperkeratosis, show that the proposed method can lead tocorrect classification rates with less than 10% of the original features
Partial separability and entanglement criteria for multiqubit quantum states
We explore the subtle relationships between partial separability and
entanglement of subsystems in multiqubit quantum states and give experimentally
accessible conditions that distinguish between various classes and levels of
partial separability in a hierarchical order. These conditions take the form of
bounds on the correlations of locally orthogonal observables. Violations of
such inequalities give strong sufficient criteria for various forms of partial
inseparability and multiqubit entanglement. The strength of these criteria is
illustrated by showing that they are stronger than several other well-known
entanglement criteria (the fidelity criterion, violation of Mermin-type
separability inequalities, the Laskowski-\.Zukowski criterion and the
D\"ur-Cirac criterion), and also by showing their great noise robustness for a
variety of multiqubit states, including N-qubit GHZ states and Dicke states.
Furthermore, for N greater than or equal to 3 they can detect bound entangled
states. For all these states, the required number of measurement settings for
implementation of the entanglement criteria is shown to be only N+1. If one
chooses the familiar Pauli matrices as single-qubit observables, the
inequalities take the form of bounds on the anti-diagonal matrix elements of a
state in terms of its diagonal matrix elements.Comment: 25 pages, 3 figures. v4: published versio
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