Pure State Density Operator Research Articles

Hyperpolarization and the physical boundary of Liouville space.

The quantum state of a spin ensemble is described by a density operator, which corresponds to a point in the Liouville space of orthogonal spin operators. Valid density operators are confined to a particular region of Liouville space, which we call the physical region and which is bounded by multidimensional figures called simplexes. Each vertex of a simplex corresponds to a pure-state density operator. We provide examples for spins , , and for coupled pairs of spins-1/2. We use the von Neumann entropy as a criterion for hyperpolarization. It is shown that the inhomogeneous master equation for spin dynamics leads to non-physical results in some cases, a problem that may be avoided by using the Lindbladian master equation.

Optical Tomograms of Multiple-Photon-Added Gaussian States via the Intermediate State Representation Theory

Optical tomogram of a quantum state can serve as an alternative to its density matrix since it contains all the information on this state. In this paper we use the explicit expression of the intermediate state |q, f, g〉(that is, an eigenvector of the coordinate and momentum operator fQ + gP) and the Radon transform between the Wigner operator Δ(p, q) and the pure-state density operator |q, f, g〉〈q, f, g| to calculate the specific tomograms for multiple-photon-added coherent states (MPACSs), thermal states (MPATSs) and displaced thermal states (MPADTSs). Their analytical tomograms are actually the finite-summation representations related to single-variable Hermite polynomials. Besides, the numerical results indicate that the larger photon-addition number can lead to the multi-peak tomographic distributions for these three states, and the measurable tomograms of MPACSs and MPADTSs exhibit π-periodic features but MPATSs can’t.

Optical Tomography for Single- and Two-Mode Squeezed Chaotic Fields

Different from the previous methods of obtaining optical tomography of quantum states, in this paper we use the Radon transform between the single- (two-)mode Wigner operator and the pure-state density operator |q〉 f,g f,g 〈q| (|η,τ 1,τ 2〉〈η,τ 1,τ 2|) to analytically obtain optical tomograms for single- (two-)mode squeezed chaotic fields, where the states |q〉 f,g (|η,τ 1,τ 2〉) refer to the newly introduced intermediate coordinate-momentum (entangled) states. More interestingly, we find that the tomograms of squeezed chaotic fields and those of coherent states are related by a integration. Thus, we establish a new convenient approach of obtaining tomograms for quantum states.

Obtaining Multimode Entangled State Representation by Generalized Radon Transformation of the Wigner Operator

In a preceding paper (Fan and Lv in J. Math. Phys. 50:102108, 2009), the phase-space integration corresponding to the straight line characteristic of two different real parameters λ,τ over the Wigner operator (i.e. the Radon transformation) leads to pure-state density operator |u〉λ,τ λ,τ〈u|, where |u〉λ,τ is just the coordinate-momentum intermediate representation. In this work we show that generalized Radon transformation of the Wigner operator yields multimode density operator of continuum variables. This provides us with a new approach for obtaining multimode entangled state representation. The Weyl ordering of the Wigner operator is used in our discussions.

Partial Trace Method for Deriving Density Operators of Light Field

With the help of technique of integration within an ordered product of operators we can fully display the partial trace method to deduce some new density operators of light field. The general form of single-mode density operator is derived in this way from a normalized two-mode generalized squeezed pure state density operator.

Explicit pure-state density operator structure for quantum tomography

The formulation of region operators named by D. Ellinas and A. J. Bracken [Phys. Rev. A 78, 052106 (2008)], which appears as the phase-space integration corresponding to the straight line over the Wigner operator, is manifestly improved and generalized. By virtue of the technique of integration within ordered (both normally ordered and Weyl ordered) product of operators, we show that the integration involved in the generalized region operator can be directly carried through to completion that leads to the explicit pure-state density operator |u⟩λ,τλ,τ⟨u|, where |u⟩λ,τ makes up the coordinate-momentum intermediate representation. This directly results in that the tomogram of a quantum state |ψ⟩ is just proportional to |⟨u|ψ⟩λ,τ|2, where ⟨u|ψ⟩λ,τ is the wave function of |ψ⟩ in the coordinate-momentum intermediate representation.

Husimi Function of Excited Squeezed Vacuum State

The q-p phase-space distribution function is a popular tool to study semiclassical physics and to describe the quantum aspects of a system. In this paper by using the pure state density operator formula of the Husimi operator Δh(q, p; κ) = |p,q〉κκ〈p,q| we deduce the Husimi function of the excited squeezed vacuum state. Then we study the behavior of Husimi distribution graphically.

Interference and entanglement: an intrinsic approach

An addition rule of impure density operators, which provides a pure state density operator, is formulated. Quantum interference including visibility property is discussed in the context of the density operator formalism. A measure of entanglement is then introduced as the norm of the matrix equal to the difference between a bipartite density matrix and the tensor product of partial traces. Entanglement for arbitrary quantum observables for multipartite systems is discussed. Star-product kernels are used to map the formulation of the addition rule of density operators onto the addition rule of symbols of the operators. Entanglement and nonlocalization of the pure state projector and allied operators are discussed. Tomographic and Weyl symbols (tomograms and Wigner functions) are considered as examples. The squeezed-states and some spin-states (two qubits) are studied to illustrate the formalism.

Density operator description of geometric phenomena in the ray space

A general gauge-invariant formalism for parallel transport, geodesics and geometric phase based on the pure state density operator is propounded. A single-query quantum search algorithm is proposed.

Geometric phase as a simple closed-form integral

For a general evolution of a quantal system, the geometric phase measured with reference to a given initial state is derived as an integral of a function of the pure state density operator by invoking the Pancharatnam connection continuously.

Natural Expansion of a Many-Electron Wave Function

It is shown that the validity of the natural expansion of a many-electron wave function can be established through extremum conditions applied to the diagonal elements of the pure-state density operator constructed from the state vector of the system in a tensor-product space of rank two. From this viewpoint, a variational definition of the two complementary reduced density operators can be given, and deductions can be drawn concerning the properties of the reduced density operators. It is therefore advantageous to regard the related expressions and many of the analytical properties of the reduced density matrices as arising from the solution of a two-space variational problem. A practical method of obtaining this expansion from a wave function of arbitrary form is developed. Functional equations analogous to this type of expansion in a tensor-product space of higher rank and with constraints of pairwise orthogonality are also derived.