J. R. Gittings | Searcharxiv

arXiv2003

An efficient numerical method for calculating the entanglement of formation of arbitrary mixed quantum states of any dimension

We present a conjugate gradient method for calculating the entanglement of formation of arbitrary mixed quantum states of any dimension and with any bipartite division of the Hilbert space. The development of the gradient used by the algorithm, its implications for the number of states required in the optimal decomposition, and the way that conjugate gradient minimization has been adapted for this particular problem are outlined. We have found that the algorithm exhibits linear convergence for general mixed states, and that it correctly reproduces the known results for pairs of qubits and for isotropic states. The results of an example application of the code are discussed: calculating the entanglement of formation of a Psi+ Bell state of two qutrits when one of those qutrits is subject to various decoherence channels. The results for qutrits are contrasted with those for qubits: for the types of decoherence considered here, qutrit entanglement appears to be more robust than qubit entanglement.

quant-ph↗

arXiv2002

Describing mixed spin-space entanglement of pure states of indistinguishable particles using an occupation number basis

Quantum mechanical entanglement is a resource for quantum computation, quantum teleportation, and quantum cryptography. The ability to quantify this resource correctly has thus become of great interest to those working in the field of quantum information theory. In this paper, we show that all existing entanglement measures but one fail important tests of fitness when applied to n particle, m site states of indistinguishable particles, where n,m>=2. The accepted method of measuring the entanglement of a bipartite system of distinguishable particles is to use the von Neumann entropy of the reduced density matrix of one half of the system. We show that expressing the full density matrix using a site-spin occupation number basis, and reducing with respect to that basis, gives an entanglement which meets all currently known fitness criteria for systems composed of either distinguishable or indistinguishable particles. We consider an output state from a previously published thought experiment, a state which is entangled in both spin and spatial degrees of freedom, and show that the site entropy measure gives the correct total entanglement. We also show how the spin-space entanglement transfer occurring within the apparatus can be understood in terms of the transfer of probability from single-occupancy to double-occupancy sectors of the density matrix.

quant-ph↗