19 research outputs found
Quantum uncertainty relation saturated by the eigenstates of the harmonic oscillator
We rederive the Schr¨odinger-Robertson uncertainty principle for the position and momentum of a quantum
particle. Our derivation does not directly employ commutation relations, but works by reduction to an eigenvalue
problem related to the harmonic oscillator, which can then be further exploited to find a larger class of constrained
uncertainty relations. We derive an uncertainty relation under the constraint of a fixed degree of Gaussianity and
prove that, remarkably, it is saturated by all eigenstates of the harmonic oscillator. This goes beyond the common
knowledge that the (Gaussian) ground state of the harmonic oscillator saturates the uncertainty relatio
Detection of non-Gaussian entangled states with an improved continuous-variable separability criterion
Currently available separability criteria for continuous-variable states are
generally based on the covariance matrix of quadrature operators. The
well-known separability criterion of Duan et al. [Phys. Rev. Lett. 84, 2722
(2000)] and Simon [Phys. Rev. Lett. 84, 2726 (2000)] , for example, gives a
necessary and sufficient condition for a two-mode Gaussian state to be
separable, but leaves many entangled non-Gaussian states undetected. Here, we
introduce an improvement of this criterion that enables a stronger entanglement
detection. The improved condition is based on the knowledge of an additional
parameter, namely the degree of Gaussianity, and exploits a connection with
Gaussianity-bounded uncertainty relations [Phys. Rev. A 86, 030102 (2012)]. We
exhibit families of non-Gaussian entangled states whose entanglement remains
undetected by the Duan-Simon criterion.Comment: Revised presentation, results unchanged. 10 pages, 6 figure
Control of multiatom entanglement in a cavity
We propose a general formalism for analytical description of multiatomic
ensembles interacting with a single mode quantized cavity field under the
assumption that most atoms remain un-excited on average. By combining the
obtained formalism with the nilpotent technique for the description of
multipartite entanglement we are able to overview in a unified fashion
different probabilistic control scenarios of entanglement among atoms or
examine atomic ensembles. We then apply the proposed control schemes to the
creation of multiatom states useful for quantum information.Comment: 11 pages, 1 figure. Finalized versio
Nilpotent polynomials approach to four-qubit entanglement
We apply the general formalism of nilpotent polynomials [Mandilara et al,
Phys. Rev. A 74, 022331 (2006)] to the problem of pure-state multipartite
entanglement classification in four qubits. In addition to establishing contact
with existing results, we explicitly show how the nilpotent formalism naturally
suggests constructions of entanglement measures invariant under the required
unitary or invertible class of local operations. A candidate measure of
fourpartite entanglement is also suggested, and its behavior numerically tested
on random pure states.Comment: 11 pages, 1 figure. Finalised versio
Quantum bit commitment under Gaussian constraints
Quantum bit commitment has long been known to be impossible. Nevertheless,
just as in the classical case, imposing certain constraints on the power of the
parties may enable the construction of asymptotically secure protocols. Here,
we introduce a quantum bit commitment protocol and prove that it is
asymptotically secure if cheating is restricted to Gaussian operations. This
protocol exploits continuous-variable quantum optical carriers, for which such
a Gaussian constraint is experimentally relevant as the high optical
nonlinearity needed to effect deterministic non-Gaussian cheating is
inaccessible.Comment: 9 pages, 6 figure
Quantum entanglement via nilpotent polynomials
We propose a general method for introducing extensive characteristics of quantum entanglement. The
method relies on polynomials of nilpotent raising operators that create entangled states acting on a reference
vacuum state. By introducing the notion of tanglemeter, the logarithm of the state vector represented in a
special canonical form and expressed via polynomials of nilpotent variables, we show how this description
provides a simple criterion for entanglement as well as a universal method for constructing the invariants
characterizing entanglement. We compare the existing measures and classes of entanglement with those emerging
from our approach. We derive the equation of motion for the tanglemeter and, in representative examples
of up to four-qubit systems, show how the known classes appear in a natural way within our framework. We
extend our approach to qutrits and higher-dimensional systems, and make contact with the recently introduced
idea of generalized entanglement. Possible future developments and applications of the method are discussed
Self-induced transparency of the optical phonons
We show that the self-induced transparency of optical phonons may appear in a systems consisting of a two level atoms interacting with elastic waves. The presence of the gap in phonon spectrum substantially enhances the pulse delay in respect to the acoustic self induced transparency phenomena. One of the main characteristics of the predicted phenomenon is the appearance of the critical velocity of the self-induced transparency pulse which, in the absorbing media, represents the upper limit which pulse may reach. Its magnitude is determined by the ratio of the phonon gap and the energy difference of the two level system. This feature opens a new way for the control of the speed of elastic waves. We believe that, in the view of the emerging new quantum technologies relying on creation and trapping of the coherent phonons interacting with artificial atoms, some practical implementations of interest for the storage and manipulation of quantum information may be realised on the basis of our work. (C) 2017 Elsevier Ltd. All rights reserved
Entanglement via nilpotent polynomials
This paper is an attempt to give a pedagogical presentation of the original work by Lorenza Viola, Andrei Smilga, and ourselvs published in Physical Review A 74, 022331 (2006). The readers are invited to consult that paper for more details as well as for the history of the entanglement concept and the relevant bibliography.SCOPUS: ch.binfo:eu-repo/semantics/publishe