Aikaterini Mandilara

Generalized PT symmetry and real spectra

The fact that eigenvalues of PT-symmetric Hamiltonians H can be real for some values of ap arameter and complex for others is explained by showing that the matrix elements ofH ,a ndhence the secular equation, are real, not only for PT but also for an ya ntiunitary operator A satisfying A 2k = 1w ith k odd. The argument is illustrated by a 2 × 2m atrix Hamiltonian, and two examples of the generalization are given.

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 unexcited 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.

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.

Nilpotent polynomial approach to four-qubit entanglement

We apply the general formalism of nilpotent polynomials (Mandilara et al 2006 Phys. Rev. A 74 022331) to the problem of pure-state multipartite entanglement classification in four qubits. In addition to establishing contact with the 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 four-partite entanglement is also suggested, and its behaviour numerically tested on random pure states.

Extending Hudson’s theorem to mixed quantum states

According to Hudson’s theorem, any pure quantum state with a positive Wigner function is necessarily a Gaussian state. Here, we make a step toward the extension of this theorem to mixed quantum states by finding upper and lower bounds on the degree of non-Gaussianity of states with positive Wigner functions. The bounds are expressed in the form of parametric functions relating the degree of non-Gaussianity of a state, its purity, and the purity of the Gaussian state characterized by the same covariance matrix. Although our bounds are not tight, they permit us to visualize the set of states with positive Wigner functions.

Entanglement studies in a simple two-electron atomic model

With a model of a one-dimensional two-electron atom we study the entanglement properties between two particles with non-overlapping wavefunctions that interact via the Coulombic, long-range potential. We calculate the two-electron eigenstates and monitor the bipartite entanglement using the von Neumann entropy. We observe non-trivial entangled states as we approach the double-excited state and Bell-like states at the single-ionization potential.

Elliptical orbits in the Bloch sphere

As is well known, when an SU(2) operation acts on a two-level system, its Bloch vector rotates without change of magnitude. Considering a system composed of two two-level systems, it is proven that for a class of nonlocal interactions of the two subsystems including (with ) and the Heisenberg interaction, the geometric description of the motion is particularly simple: each of the two Bloch vectors follows an elliptical orbit within the Bloch sphere. The utility of this result is demonstrated in two applications, the first of which bears on quantum control via quantum interfaces. By employing nonunitary control operations, we extend the idea of controllability to a set of points which are not necessarily connected by unitary transformations. The second application shows how the orbit of the coherence vector can be used to assess the entangling power of Heisenberg exchange interaction.

Quantum uncertainty relation saturated by the eigenstates of the harmonic oscillator

We rederive the Schrodinger-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 relation.

Purity- and Gaussianity-bounded uncertainty relations

Bounded uncertainty relations provide the minimum value of the uncertainty assuming some additional information on the state. We derive analytically an uncertainty relation bounded by a pair of constraints, those of purity and Gaussianity. In a limiting case this uncertainty relation reproduces the puritybounded derived by Man’ko and Dodonov and the Gaussianity-bounded one (Mandilara and Cerf 2012 Phys. Rev. A 86 030102R).

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. [L. M. Duan, Phys. Rev. Lett. 84, 2722 (2000)PRLTAO0031-900710.1103/PhysRevLett.84.2722] and Simon [R. Simon, Phys. Rev. Lett. 84, 2726 (2000)PRLTAO0031-900710.1103/PhysRevLett.84.2726], 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 [A. Mandilara and N. J. Cerf, Phys. Rev. A 86, 030102 (2012)PLRAAN1050-294710.1103/PhysRevA.86.030102]. We exhibit families of non-Gaussian entangled states whose entanglement remains undetected by the Duan-Simon criterion.