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Reinaldo O. Vianna

Publications and source records attributed to Reinaldo O. Vianna.

29 records · Page 2Linked to original sources
arXiv2012

Quantifying Quantum Correlations in Fermionic Systems using Witness Operators

We present a method to quantify quantum correlations in arbitrary systems of indistinguishable fermions using witness operators. The method associates the problem of finding the optimal entan- glement witness of a state with a class of problems known as semidefinite programs (SDPs), which can be solved efficiently with arbitrary accuracy. Based on these optimal witnesses, we introduce a measure of quantum correlations which has an interpretation analogous to the Generalized Robust- ness of entanglement. We also extend the notion of quantum discord to the case of indistinguishable fermions, and propose a geometric quantifier, which is compared to our entanglement measure. Our numerical results show a remarkable equivalence between the proposed Generalized Robustness and the Schliemann concurrence, which are equal for pure states. For mixed states, the Schliemann con- currence presents itself as an upper bound for the Generalized Robustness. The quantum discord is also found to be an upper bound for the entanglement.

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arXiv2011

Variational quantum tomography with incomplete information by means of semidefinite programs

We introduce a new method to reconstruct unknown quantum states out of incomplete and noisy information. The method is a linear convex optimization problem, therefore with a unique minimum, which can be efficiently solved with Semidefinite Programs. Numerical simulations indicate that the estimated state does not overestimate purity, and neither the expectation value of optimal entanglement witnesses. The convergence properties of the method are similar to compressed sensing approaches, in the sense that, in order to reconstruct low rank states, it needs just a fraction of the effort correspondig to an informationally complete measurement.

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arXiv2009

Viable entanglement detection of unknown mixed states in low dimensions

We explore procedures to detect entanglement of unknown mixed states, which can be experimentally viable. The heart of the method is a hierarchy of simple feasibility problems, which provides sufficient conditions to entanglement. Our numerical investigations indicate that the entanglement is detected with a cost which is much lower than full state tomography. The procedure is applicable to both free and bound entanglement, and involves only single copy measurements.

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arXiv2006

Study of the Distillability of Werner States Using Entanglement Witnesses and Robust Semidefinite Programs

We use Robust Semidefinite Programs and Entanglement Witnesses to study the distillability of Werner states. We perform exact numerical calculations which show 2-undistillability in a region of the state space which was previously conjectured to be undistillable. We also introduce bases which yield interesting expressions for the {\em distillability witnesses} and for a tensor product of Werner states with arbitrary number of copies.

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arXiv2006

Witnessed Entanglement

We present a new measure of entanglement for mixed states. It can be approximately computable for every state and can be used to quantify all different types of multipartite entanglement. We show that it satisfies the usual properties of a good entanglement quantifier and derive relations between it and other entanglement measures.

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arXiv2005

An algorithm to perform POVMs through Neumark theorem: application to the discrimination of non-orthogonal pure quantum states

We consider a protocol to perform the optimal quantum state discrimination of $N$ linearly independent non-orthogonal pure quantum states and present a computational code. Through the extension of the original Hilbert space, it is possible to perform an unitary operation yielding a final configuration, which gives the best discrimination without ambiguity by means of von Neumann measurements. Our goal is to introduce a detailed general mathematical procedure to realize this task by means of semidefinite programming and norm minimization. The former is used to fix which is the best detection probability amplitude for each state of the ensemble. The latter determines the matrix which leads the states to the final configuration. In a final step, we decompose the unitary transformation in a sequence of two-level rotation matrices.

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arXiv2004

A Robust Semidefinite Programming Approach to the Separability Problem

We express the optimization of entanglement witnesses for arbitrary bipartite states in terms of a class of convex optimization problems known as Robust Semidefinite Programs (RSDP). We propose, using well known properties of RSDP, several new sufficient tests for the separability of mixed states. Our results are then generalized to multipartite density operators.

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arXiv2004

The Semi-Quantum Computer

We discuss the performance of the Search and Fourier Transform algorithms on a hybrid computer constituted of classical and quantum processors working together. We show that this semi-quantum computer would be an improvement over a pure classical architecture, no matter how few qubits are available and, therefore, it suggests an easier implementable technology than a pure quantum computer with arbitrary number of qubits.

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