Swarnamala Sirsi

Quasi-Probability Distributions for Arbitrary Spin-j Particles

Quasi-probability distribution functions fjWW, fjMM for quantum spin-j systems are derived based on the Wigner-Weyl, Margenau-Hill approaches. A probability distribution fjsph which is nonzero only on the surface of the sphere of radius √j(j+1) is obtained by expressing the characteristic function in terms of the spherical moments. It is shown that the Wigner-Weyl distribution function turns out to be a distribution over the sphere in the classical limit.

Non-oriented spin-1 systems

A maximal state of spin polarisation of a spin-1 system with all eight degrees of freedom (namely, three distinct axes and two non-zero scalars) is realised when a spin-1 nucleus with nonzero electric quadrupole moment is embedded in a suitable crystal lattice generating an electric quadrupole field and is exposed to an external constant magnetic field whose direction does not coincide with any of the principal axes characterising the electric quadrupole field. In the absence of the magnetic field only five of the eight degrees of freedom (i.e. two distinct axes and a nonzero scalar) are realised if the asymmetry parameter eta not=0. If eta =0 the two axes coalesce. This suggestion is made to stimulate experimental efforts to produce polarised multiaxial spin-1 targets.

Trivariate Quasiprobability Distributions for Polarized Spin-1 Nuclei

Quasiprobability distributions are derived for arbitrarily polarized spin-1 nuclei using the Margenau–Hill and the Wigner–Weyl correspondence rules.

Joint probabilities for an aligned spin-1 system

Following Margenau and Hill (1961) we adduce arguments to show that an aligned spin-1 system (for e.g. 2H or 14N nuclei in external electric quadrupole fields) can be viewed in terms of bivariate probability distributions obtained by identifying the associated characteristic function.

SU(2) invariants of symmetric qubit states

We express the density matrix for the N-qubit symmetric state or spin-j state (j = N/2) in terms of the well-known Fano statistical tensor parameters. Employing the multi-axial representation, where the spin-j density matrix is shown to be characterized by j(2j + 1) axes and 2j real scalars, we enumerate the number of invariants constructed out of these axes and scalars. We calculate these invariants explicitly in the particular case of the pure and mixed spin-1 state.

Visualization of an entangled channel spin-1 system

Covariance matrix formalism gives powerful entanglement criteria for continuous as well as finite dimensional systems. We use this formalism to study a mixed channel spin-1 system which is well known in nuclear reactions. A spin-j state can be visualized as being made up of 2j spinors which are represented by a constellation of 2j points on a Bloch sphere using Majorana construction. We extend this formalism to visualize an entangled mixed spin-1 system.

Spin squeezing of mixed systems

The notion of spin squeezing has been discussed in this paper using the density matrix formalism. Extending the definition of squeezing for pure states given by Kitagawa and Ueda in an appropriate manner and employing the spherical tensor representation, we show that mixed spin states which are non-oriented and possess vector polarization indeed exhibit squeezing. We construct a mixed state of a spin 1 system using two spin ½ states and study its squeezing behaviour as a function of the individual polarizations of the two spinors.

Nonlocality in Einstein–Podolsky–Rosen Spin Correlations

We study the nonlocal nature of EPR correlations of two spin j particles entangled in a singlet state using the quantum-mechanical joint probabilities.

Geometric multiaxial representation of N-qubit mixed symmetric separable states

Study of an N qubit mixed symmetric separable states is a long standing challenging problem as there exist no unique separability criterion. In this regard, we take up the N-qubit mixed symmetric separable states for a detailed study as these states are of experimental importance and offer elegant mathematical analysis since the dimension of the Hilbert space reduces from 2N to N + 1. Since there exists a one to one correspondence between spin-j system and an N-qubit symmetric state, we employ Fano statistical tensor parameters for the parametrization of spin density matrix. Further, we use geometric multiaxial representation (MAR) of density matrix to characterize the mixed symmetric separable states. Since separability problem is NP hard, we choose to study it in the continuum limit where mixed symmetric separable states are characterized by the P-distribution function λ (ᶿ, Φ) We show that the N-qubit mixed symmetric separable state can be visualized as a uniaxial system if the distribution function is independent of ᶿ, and Φ. We further choose distribution function to be the most general positive function on a sphere and observe that the statistical tensor parameters characterizing the N-qubit symmetric system are the expansion coefficients of the distribution function. As an example for the discrete case, we investigate the MAR of a uniformly weighted two qubit mixed symmetric separable state. We also observe that there exists a correspondence between separability and classicality of states.

POVM construction: A simple recipe with applications to symmetric states

We propose a simple method for constructing POVMs using any set of matrices which form an orthonormal basis for the space of complex matrices. Considering the orthonormal set of irreducible spherical tensors, we examine the properties of the construction on the