Thiago O. Maciel

Witnessed entanglement and the geometric measure of quantum discord

We establish relations between geometric quantum discord and entanglement quantifiers obtained by means of optimal witness operators. In particular, we prove a relation between negativity and geometric discord in the Hilbert-Schmidt norm, which is slightly different from a previous conjectured one [Phys. Rev. A 84, 052110 (2011)].We also show that, redefining the geometric discord with the trace norm, better bounds can be obtained. We illustrate our results numerically.

Entanglement of indistinguishable particles as a probe for quantum phase transitions in the extended Hubbard model

We investigate the quantum phase transitions of the extended Hubbard model at half-filling with periodic boundary conditions employing the entanglement of particles, as opposed to the more traditional entanglement of modes. Our results show that the entanglement has either discontinuities or local minima at the critical points. We associate the discontinuities to first order transitions, and the minima to second order ones. Thus we show that the entanglement of particles can be used to derive the phase diagram, except for the subtle transitions between the phases SDW-BOW, and the superconductor phases TS-SS.

Quantum State Tomography with incomplete data: Maximum Entropy and Variational Quantum Tomography

Whenever we do not have an informationally complete set of measurements, the estimate of a quantum state can not be uniquely determined. In this case, among the density matrices compatible with the available data, it is commonly preferred that one which is the most uncommitted with the missing information. This is the purpose of the Maximum Entropy estimation (MaxEnt) and the Variational Quantum Tomography (VQT). Here, we propose a variant of Variational Quantum Tomography and show its relationship with Maximum Entropy methods in quantum tomographies with incomplete set of measurements. We prove their equivalence in case of eigenbasis measurements, and through numerical simulations we stress their similar behavior. Hence, in the modified VQT formulation we have an estimate of a quantum state as unbiased as in MaxEnt and with the benefit that VQT can be more efficiently solved by means of linear semidefinite programs.

Most incompatible measurements for robust steering tests

From a fundamental point of view, deciding whether a given entangled state is able to demonstrate Einstein-Podolsky-Rosen steering under arbitrary measurement conditions is an important problem to which some effort has been dedicated. However, from a practical point of view, a crucial problem is to characterize the steerability of quantum states under restrictive measurement scenarios. Here we address the problem of determining whether a quantum state can demonstrate steering when subjected to

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Experimental implementation of a NMR entanglement witness

measurements of

Variational Quantum Tomography With Incomplete Information By Means Of Semidefinite Programs

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Quantifying quantum correlations in fermionic systems using witness operators

outcomes. We consider cases where the steering party is able to perform either general POVMs or specific kinds of measurements (e.g. projective or symmetric). We propose general methods to calculate lower and upper bounds for the white noise robustness of a quantum state under different measurement scenarios. Our techniques are also applicable to the study of the noise robustness of the incompatibility of

Viable entanglement detection of unknown mixed states in low dimensions

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Error regions in quantum state tomography: computational complexity caused by geometry of quantum states

arbitrary unknown qudit measurements. We show that some mutually unbiased bases, symmetric informationally complete measurements, and other symmetric choices of measurements are not the most incompatible ones nor are they optimal for steering the isotropic states. Finally, we give numerical evidence that non-projective POVMs do not improve over projective ones for this task.