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State-of-the-art methods for 3D reconstruction of faces from a single image require 2D-3D pairs of ground-truth data for supervision. Such data is costly to acquire, and most datasets available in the literature are restricted to pairs for which the input 2D images depict faces in a near fronto-parallel pose. Therefore, many data-driven methods for single-image 3D facial reconstruction perform poorly on profile and near-profile faces. We propose a method to improve the performance of single-image 3D facial reconstruction networks by utilizing the network to synthesize its own training data for fine-tuning, comprising: (i) single-image 3D reconstruction of faces in near-frontal images without ground-truth 3D shape; (ii) application of a rigid-body transformation to the reconstructed face model; (iii) rendering of the face model from new viewpoints; and (iv) use of the rendered image and corresponding 3D reconstruction as additional data for supervised fine-tuning. The new 2D-3D pairs thus produced have the same high-quality observed for near fronto-parallel reconstructions, thereby nudging the network towards more uniform performance as a function of the viewing angle of input faces. Application of the proposed technique to the fine-tuning of a state-of-the-art single-image 3D-reconstruction network for faces demonstrates the usefulness of the method, with particularly significant gains for profile or near-profile views.

Applications of quantum technology often require fidelities to quantify performance. These provide a fundamental yardstick for the comparison of two quantum states. While this is straightforward in the case of pure states, it is much more subtle for the more general case of mixed quantum states often found in practice. A large number of different proposals exist. In this review, we summarize the required properties of a quantum fidelity measure, and compare them, to determine which properties each of the different measures has. We show that there are large classes of measures that satisfy all the required properties of a fidelity measure, just as there are many norms of Hilbert space operators, and many measures of entropy. We compare these fidelities, with detailed proofs of their properties. We also summarize briefly the applications of these measures in teleportation, quantum memories, quantum computers, quantum communications, and quantum phase-space simulations., Comment: 22 + 6 + 3.5 pages, 7 figures, 6 tables, several proofs

We consider the problems of maximizing the entanglement negativity of X-form qubit-qutrit density matrices with (i) a fixed spectrum and (ii) a fixed purity. In the first case, the problem is solved in full generality whereas, in the latter, partial solutions are obtained by imposing extra spectral constraints such as rank-deficiency and degeneracy, which enable a semidefinite programming treatment for the optimization problem at hand. Despite the technically-motivated assumptions, we provide strong numerical evidence that three-fold degenerate X states of purity $P$ reach the highest entanglement negativity accessible to arbitrary qubit-qutrit density matrices of the same purity, hence characterizing a sparse family of likely qubit-qutrit maximally entangled mixed states., Comment: 19 pages, 6 figures

For every possible spectrum of $2^N$-dimensional density operators, we construct an $N$-qubit X-state of same spectrum and maximal genuine multipartite (GM-) concurrence, hence characterizing a global unitary transformation that --- constrained to output X-states --- maximizes the GM-concurrence of an arbitrary input mixed state of $N$ qubits. We also apply semidefinite programming methods to obtain $N$-qubit X-states with maximal GM-concurrence for a given purity and to provide an alternative proof of optimality of a recently proposed set of density matrices for the role, the so-called X-MEMS. Furthermore, we introduce a numerical strategy to tailor a quantum operation that converts between any two given density matrices using a relatively small number of Kraus operators. We apply our strategy to design short operator-sum representations for the transformation between any given $N$-qubit mixed state and a corresponding X-MEMS of same purity., Comment: 22 pages, 2 figures. v2 (published version): connection with "biseparability from spectrum" dropped from the concluding remarks since, in the last paragraph os Sec. 3, an argument was included to demonstrate that N-qubit X-MEMS are generally not N-qubit MEMS

For every N-qubit density matrix written in the computational basis, an associated "X-density matrix" can be obtained by vanishing all entries out of the main- and anti-diagonals. It is very simple to compute the genuine multipartite (GM) concurrence of this associated N-qubit X-state, which, moreover, lower bounds the GM-concurrence of the original (non-X) state. In this paper, we rely on these facts to introduce and benchmark a heuristic for estimating the GM-concurrence of an arbitrary multiqubit mixed state. By explicitly considering two classes of mixed states, we illustrate that our estimates are usually very close to the standard lower bound on the GM-concurrence, being significantly easier to compute. In addition, while evaluating the performance of our proposed heuristic, we provide the first characterization of GM-entanglement in the steady states of the driven Dicke model at zero temperature., Comment: 19 pages, 5 figures

We demonstrate that for every two-qubit state there is a X-counterpart, i.e., a corresponding two-qubit X-state of same spectrum and entanglement, as measured by concurrence, negativity or relative entropy of entanglement. By parametrizing the set of two-qubit X-states and a family of unitary transformations that preserve the sparse structure of a two-qubit X-state density matrix, we obtain the parametric form of a unitary transformation that converts arbitrary two-qubit states into their X-counterparts. Moreover, we provide a semi-analytic prescription on how to set the parameters of this unitary transformation in order to preserve concurrence or negativity. We also explicitly construct a set of X-state density matrices, parametrized by their purity and concurrence, whose elements are in one-to-one correspondence with the points of the concurrence versus purity (CP) diagram for generic two-qubit states., Comment: 24 pages, 6 figures. v2 includes new references and minor changes (accepted version)

We introduce a self-consistent theoretical framework associated with the Schwinger unitary operators whose basic mathematical rules embrace a new uncertainty principle that generalizes and strengthens the Massar-Spindel inequality. Among other remarkable virtues, this quantum-algebraic approach exhibits a sound connection with the Wiener-Kinchin theorem for signal processing, which permits us to determine an effective tighter bound that not only imposes a new subtle set of restrictions upon the selective process of signals and wavelets bases, but also represents an important complement for property testing of unitary operators. Moreover, we establish a hierarchy of tighter bounds, which interpolates between the tightest bound and the Massar-Spindel inequality, as well as its respective link with the discrete Weyl function and tomographic reconstructions of finite quantum states. We also show how the Harper Hamiltonian and discrete Fourier operators can be combined to construct finite ground states which yield the tightest bound of a given finite-dimensional state vector space. Such results touch on some fundamental questions inherent to quantum mechanics and their implications in quantum information theory., Comment: 31 pages, 3 figures, comments welcome

This thesis addresses the problem of developing a quantum counter-part of the well established classical theory of control. We dwell on the fundamental fact that quantum states are generally not perfectly distinguishable, and quantum measurements typically introduce noise in the system being measured. Because of these, it is generally not clear whether the central concept of the classical control theory -- that of observing the system and then applying feedback -- is always useful in the quantum setting. We center our investigations around the problem of transforming the state of a quantum system into a given target state, when the system can be prepared in different ways, and the target state depends on the choice of preparation. We call this the "quantum tracking problem" and show how it can be formulated as an optimization problem that can be approached both numerically and analytically. This problem provides a simple route to the characterization of the quantum trade-off between information gain and disturbance, and is seen to have several applications in quantum information., Comment: PhD Thesis, The University of Queensland, 196 pages, 29 figures

We propose an alternative fidelity measure (namely, a measure of the degree of similarity) between quantum states and benchmark it against a number of properties of the standard Uhlmann-Jozsa fidelity. This measure is a simple function of the linear entropy and the Hilbert-Schmidt inner product between the given states and is thus, in comparison, not as computationally demanding. It also features several remarkable properties such as being jointly concave and satisfying all of "Jozsa's axioms". The trade-off, however, is that it is supermultiplicative and does not behave monotonically under quantum operations. In addition, new metrics for the space of density matrices are identified and the joint concavity of the Uhlmann-Jozsa fidelity for qubit states is established., Comment: 12 pages, 3 figures. v2 includes minor changes, new references and new numerical results (Sec. IV)

In classical control theory, tracking refers to the ability to perform measurements and feedback on a classical system in order to enforce some desired dynamics. In this paper we investigate a simple version of quantum tracking, namely, we look at how to optimally transform the state of a single qubit into a given target state, when the system can be prepared in two different ways, and the target state depends on the choice of preparation. We propose a tracking strategy that is proved to be optimal for any input and target states. Applications in the context of state discrimination, state purification, state stabilization and state-dependent quantum cloning are presented, where existing optimality results are recovered and extended., Comment: 15 pages, 8 figures. Extensive revision of text, optimality results extended, other physical applications included

An expression for the joint probability distribution of the principal curvatures at an arbitrary point in the ensemble of isosurfaces defined on isotropic Gaussian random fields on Rn is derived. The result is obtained by deriving symmetry properties of the ensemble of second derivative matrices of isotropic Gaussian random fields akin to those of the Gaussian orthogonal ensemble., Comment: 10 pages, six references. Fuller version with correct proof of important theorem

Measurements in quantum mechanics cannot perfectly distinguish all states and necessarily disturb the measured system. We present and analyse a proposal to demonstrate fundamental limits on quantum control of a single qubit arising from these properties of quantum measurements. We consider a qubit prepared in one of two non-orthogonal states and subsequently subjected to dephasing noise. The task is to use measurement and feedback control to attempt to correct the state of the qubit. We demonstrate that projective measurements are not optimal for this task, and that there exists a non-projective measurement with an optimum measurement strength which achieves the best trade-off between gaining information about the system and disturbing it through measurement back-action. We study the performance of a quantum control scheme that makes use of this weak measurement followed by feedback control, and demonstrate that it realises the optimal recovery from noise for this system. We contrast this approach with various classically inspired control schemes., Comment: 12 pages, 7 figures, v2 includes new references and minor changes

We consider a universal set of quantum gates encoded within a perturbed decoherence-free subspace of four physical qubits. Using second-order perturbation theory and a measuring device modeled by an infinite set of harmonic oscillators, simply coupled to the system, we show that continuous observation of the coupling agent induces inhibition of the decoherence due to spurious perturbations. We thus advance the idea of protecting or even creating a decoherence-free subspace for processing quantum information., Comment: 7 pages, 1 figure. To be published in Journal of Physics A: Mathematical and General