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Anil Shaji

Publications and source records attributed to Anil Shaji.

64 records · Page 4Linked to original sources
arXiv2006

Dynamics of Two Qubits: Decoherence and an Entanglement Optimization Protocol

The evolution of two qubits coupled by a general nonlocal interaction is studied in two distinct regimes. In the first regime the purity of the individual qubits is interchanged through the entanglement shared by the two. We illustrate how this can be a mechanism for decoherence. In the second regime, the interaction entangles two initially pure qubits. The dynamical maps for the reduced unitary evolution of both initially simply separable and not-simply-separable states are found. We outline a protocol for optimizing the entanglement generation subject to constraints.

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arXiv2006

Doubly constrained bounds on the entanglement of formation

We derive bounds on the entanglement of formation of states of a 4xN bipartite system using two entanglement monotones constructed from operational separability criteria. The bounds are used simultaneously as constraints on the entanglement of formation. One monotone is the negativity, which is based on the Peres positive-partial-transpose criterion. For the other, we formulate a monotone based on a separability criterion introduced by Breuer (H.-P. Breuer, e-print quant-ph/0605036).

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arXiv2006

On Decoherence in Quantum Clock Synchronization

We study two quantum versions of the Eddington clock-synchronization protocol in the presence of decoherence. The first protocol uses maximally entangled states to achieve the Heisenberg limit for clock synchronization. The second protocol achieves the limit without using entanglement. We show the equivalence of the two protocols under any single-qubit decoherence model that does not itself provide synchronization information.

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arXiv2005

Mapping the Schrodinger picture of open quantum dynamics

For systems described by finite matrices, an affine form is developed for the maps that describe evolution of density matrices for a quantum system that interacts with another. This is established directly from the Heisenberg picture. It separates elements that depend only on the dynamics from those that depend on the state of the two systems. While the equivalent linear map is generally not completely positive, the homogeneous part of the affine maps is, and is shown to be composed of multiplication operations that come simply from the Hamiltonian for the larger system. The inhomogeneous part is shown to be zero if and only if the map does not increase the trace of the square of any density matrix. Properties are worked out in detail for two-qubit examples.

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arXiv2005

Maps for Lorentz transformations of spin

Lorentz transformations of spin density matrices for a particle with positive mass and spin 1/2 are described by maps of the kind used in open quantum dynamics. They show how the Lorentz transformations of the spin depend on the momentum. Since the spin and momentum generally are entangled, the maps generally are not completely positive and act in limited domains. States with two momentum values are considered, so the maps are for the spin qubit entangled with the qubit made from the two momentum values, and results from the open quantum dynamics of two coupled qubits can be applied. Inverse maps are used to show that every Lorentz transformation completely removes the spin polarization, and so completely removes the information, from a number of spin density matrices. The size of the spin polarization that is removed is calculated for particular cases.

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arXiv2005

Partial positive scaling transform: a separability criterion

The problem of constructing a necessary and sufficient condition for establishing the separability of continuous variable systems is revisited. Simon [R. Simon, Phys. Rev. Lett. 84, 2726 (2000)] pointed out that such a criterion may be constructed by drawing a parallel between the Peres' partial transpose criterion for finite dimensional systems and partial time reversal transformation for continuous variable systems. We generalize the partial time reversal transformation to a partial scaling transformation and re-examine the problem using a tomographic description of the continuous variable quantum system. The limits of applicability of the entanglement criteria obtained from partial scaling and partial time reversal are explored.

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arXiv2004

Dynamics of initially entangled open quantum systems

Linear maps of matrices describing evolution of density matrices for a quantum system initially entangled with another are identified and found to be not always completely positive. They can even map a positive matrix to a matrix that is not positive, unless we restrict the domain on which the map acts. Nevertheless, their form is similar to that of completely positive maps. Only some minus signs are inserted in the operator-sum representation. Each map is the difference of two completely positive maps. The maps are first obtained as maps of mean values and then as maps of basis matrices. These forms also prove to be useful. An example for two entangled qubits is worked out in detail. Relation to earlier work is discussed.

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arXiv2003

Non-relativistic proofs of the spin-statistics connection

A recent paper by Peshkin [1] has drawn attention again to the problem of understanding the spin statistics connection in non-relativistic quantum mechanics. Allen and Mondragon [2] has pointed out correctly some of the flaws in Peshkin's arguments which are based on the single valuedness under rotation of the wave functions of systems of identical particles. We examine carefully the claim that is made in the title of [2] that there can be ``no spin-statistics connection in non-relativistic quantum mechanics''. We show that we can derive the spin statistics connection for non-relativistic quantum field theories which have equations of motion of the Hamiltonian type based on SU(2) invariance of the Lagrangian. The formalism and machinary of non-relativistic quantum field theory as opposed to usual quantum mechanics is necessary for constructing our proof.

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arXiv2003

Structure and Parametrization of Generic Stochastic Maps of Density Matrices

The most general evolution of the density matrix of a quantum system with a finite-dimensional state space is by stochastic maps which take a density matrix linearly into the set of density matrices. These dynamical stochastic maps form a linear convex set that may be viewed as supermatrices. The property of hermiticity of density matrices renders an associated supermatrix hermitian and hence diagonalizable. The positivity of the density matrix does not make the associated supermatrix positive though. If the map itself is positive, it is called completely positive and they have a simple parameterization. This is extended to all positive (not completely positive) maps. A general dynamical map that does not preserve the norm of the density matrices it acts on can be thought of as the contraction of a norm-preserving map of an extended system. The reconstruction of such extended dynamics is also given.

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