21 research outputs found
Svetlichny's inequality and genuine tripartite nonlocality in three-qubit pure states
The violation of the Svetlichny's inequality (SI) [Phys. Rev. D, 35, 3066
(1987)] is sufficient but not necessary for genuine tripartite nonlocal
correlations. Here we quantify the relationship between tripartite entanglement
and the maximum expectation value of the Svetlichny operator (which is bounded
from above by the inequality) for the two inequivalent subclasses of pure
three-qubit states: the GHZ-class and the W-class. We show that the maximum for
the GHZ-class states reduces to Mermin's inequality [Phys. Rev. Lett. 65, 1838
(1990)] modulo a constant factor, and although it is a function of the three
tangle and the residual concurrence, large number of states don't violate the
inequality. We further show that by design SI is more suitable as a measure of
genuine tripartite nonlocality between the three qubits in the the W-class
states, and the maximum is a certain function of the bipartite entanglement
(the concurrence) of the three reduced states, and only when their certain sum
attains a certain threshold value, they violate the inequality.Comment: Modified version, 5 pages, 2 figures, REVTeX
Quantum Random Walks do not need a Coin Toss
Classical randomized algorithms use a coin toss instruction to explore
different evolutionary branches of a problem. Quantum algorithms, on the other
hand, can explore multiple evolutionary branches by mere superposition of
states. Discrete quantum random walks, studied in the literature, have
nonetheless used both superposition and a quantum coin toss instruction. This
is not necessary, and a discrete quantum random walk without a quantum coin
toss instruction is defined and analyzed here. Our construction eliminates
quantum entanglement from the algorithm, and the results match those obtained
with a quantum coin toss instruction.Comment: 6 pages, 4 figures, RevTeX (v2) Expanded to include relation to
quantum walk with a coin. Connection with Dirac equation pointed out. Version
to be published in Phys. Rev.
Universal state inversion and concurrence in arbitrary dimensions
Wootters [Phys. Rev. Lett. 80, 2245 (1998)] has given an explicit formula for
the entanglement of formation of two qubits in terms of what he calls the
concurrence of the joint density operator. Wootters's concurrence is defined
with the help of the superoperator that flips the spin of a qubit. We
generalize the spin-flip superoperator to a "universal inverter," which acts on
quantum systems of arbitrary dimension, and we introduce the corresponding
concurrence for joint pure states of (D1 X D2) bipartite quantum systems. The
universal inverter, which is a positive, but not completely positive
superoperator, is closely related to the completely positive universal-NOT
superoperator, the quantum analogue of a classical NOT gate. We present a
physical realization of the universal-NOT superoperator.Comment: Revtex, 25 page
Two-Level Atom in an Optical Parametric Oscillator: Spectra of Transmitted and Fluorescent Fields in the Weak Driving Field Limit
We consider the interaction of a two-level atom inside an optical parametric oscillator. In the weak-driving-field limit, we essentially have an atom-cavity system driven by the occasional pair of correlated photons, or weakly squeezed light. We find that we may have holes, or dips, in the spectrum of the fluorescent and transmitted light. This occurs even in the strong-coupling limit when we find holes in the vacuum-Rabi doublet. Also, spectra with a subnatural linewidth may occur. These effects disappear for larger driving fields, unlike the spectral narrowing obtained in resonance fluorescence in a squeezed vacuum; here it is important that the squeezing parameter N tends to zero so that the system interacts with only one correlated pair of photons at a time. We show that a previous explanation for spectral narrowing and spectral holes for incoherent scattering is not applicable in the present case, and propose an alternative explanation. We attribute these anomalous effects to quantum interference in the two-photon scattering of the system
Characterization of the Positivity of the Density Matrix in Terms of the Coherence Vector Representation
A parameterization of the density operator, a coherence vector
representation, which uses a basis of orthogonal, traceless, Hermitian matrices
is discussed. Using this parameterization we find the region of permissible
vectors which represent a density operator. The inequalities which specify the
region are shown to involve the Casimir invariants of the group. In particular
cases, this allows the determination of degeneracies in the spectrum of the
operator. The identification of the Casimir invariants also provides a method
of constructing quantities which are invariant under {\it local} unitary
operations. Several examples are given which illustrate the constraints
provided by the positivity requirements and the utility of the coherence vector
parameterization.Comment: significantly rewritten and submitted for publicatio
Physics
Theoretical investigations of separability and entanglement of bipartite quantum system
Quantum Random Walks without Coin Toss
We construct a quantum random walk algorithm, based on the Dirac operator instead of the Laplacian. The algorithm explores multiple evolutionary branches by superposition of states, and does not require the coin toss instruction of classical randomised algorithms. We use this algorithm to search for a marked vertex on a hypercubic lattice in arbitrary dimensions. Our numerical and analytical results match the scaling behaviour of earlier algorithms that use a coin toss instruction