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In this paper we present a modified version of the proof given Jing-Yang-Zhao's paper titled "Local Unitary Equivalence of Quantum States and Simultaneous Orthogonal Equivalence," which established the correspondance between local unitary equivalence and simultaneous orthogonal equivalence of $2$-qubits. Our modified proof utilizes a hypermatrix algebra framework, and through this framework we are able to generalize this correspondence to $3$-qubits. Finally, we apply a generalization of Specht's criterion (first proved in "Specht's Criterion for Systems of Linear Mappings" by V. Futorney, R. A. Horn, and V. V. Sergeichuk) to reduce the problem of local unitary equivalence of $3$-qubits to checking trace identities and a few other easy-to-check properties. We also note that all of these results can be extended to $2$ and $3$ qudits if we relax the notion of LU equivalence to quasi-LU equivalence, as defined in the aforementioned paper by Jing et. al.

In this paper, we represent $n$-qubits as hypermatrices and consider various applications to quantum entanglement. In particular, we use the higher-order singular value decomposition of hypermatrices to prove that the $\pi$-transpose is an LU invariant. Additionally, through our construction we show that the matrix representation of the combinatorial hyperdeterminant of $2n$-qubits can be expressed as a product of the second Pauli matrix, allowing us to derive a formula for the combinatorial hyperdeterminant of $2n$-qubits in terms of the $n$-tangle., Comment: 11 pages; New title and revised version

Person re-identification is a standard and established problem in the computer vision community. In recent years, vehicle re-identification is also getting more attention. In this paper, we focus on both these tasks and propose a method for aggregation of features in temporal domain as it is common to have multiple observations of the same object. The aggregation is based on weighting different elements of the feature vectors by different weights and it is trained in an end-to-end manner by a Siamese network. The experimental results show that our method outperforms other existing methods for feature aggregation in temporal domain on both vehicle and person re-identification tasks. Furthermore, to push research in vehicle re-identification further, we introduce a novel dataset CarsReId74k. The dataset is not limited to frontal/rear viewpoints. It contains 17,681 unique vehicles, 73,976 observed tracks, and 277,236 positive pairs. The dataset was captured by 66 cameras from various angles., Comment: Under consideration at Computer Vision and Image Understanding

First order quantum phase transition (QPT) between spherical and axially deformed nuclei shows coexisting, but well-separated regions of regular and chaotic dynamics. We employ a Hamiltonian of the Arima-Iachello Interacting Boson Model (IBM) with an arbitrarily high potential barrier separating the phases. Classical and quantum analyses reveal markedly distinct behavior of the two phases: Deformed phase is completely regular, while the spherical phase shows highly chaotic dynamics, similar to the H\'enon-Heiles system. Rotational bands with quasi-SU(3) characteristics built upon the regular vibrational spectrum of beta- and gamma-vibrations are observed in the deformed phase up to very high excitation energies., Comment: 3 pages, 2 figures, to appear in AIP Conference Proceedings, SYMMETRIES AND ORDER: ALGEBRAIC METHODS IN MANY BODY SYSTEMS, In honor of Professor Francesco Iachello on the occasion of his retirement, October 5-6, 2018 at Yale University (v3, minor misprints corrected)

The core issue for the implementation of the diamond NV centre qubits technology is the sensitive readout of NV spin state. We have recently demonstrated the photoelectric detection of NV magnetic resonances (PDMR), anticipated to be faster and more sensitive than optical detection (ODMR). Here we report on a PDMR contrast of 9 % - three times enhanced compared to previous work - on shallow N-implanted diamond. Based on ab-initio modelling, we demonstrate a novel one-photon ionization dual-beam PDMR protocol. We predict that this scheme is significantly less vulnerable to the influence of defects such as substitutional nitrogen., Comment: 12 pages, 3 figures

We investigate the relationship between ground-state (zero-temperature) quantum phase transitions in systems with variable Hamiltonian parameters and classical (temperature-driven) phase transitions in standard thermodynamics. An analogy is found between (i) phase-transitional distributions of the ground-state related branch points of quantum Hamiltonians in the complex parameter plane and (ii) distributions of zeros of classical partition functions in complex temperatures. Our approach properly describes the first- and second-order quantum phase transitions in the interacting boson model and can be generalized to finite temperatures., Comment: to be published by AIP in Proc. of the Workshop "Nuclei and Mesoscopic Physics" (Michigan State Univ., Oct 2004); 10 pages, 3 figures

Reduced probabilities B(E2) of \gamma transitions between states of positive parity in the ^160Dy nucleus are calculated within the framework of the interacting boson model (IBM-1). The results are compared with the experimental data., Comment: 3 pages of text ScientificWorkPlace file, 8 ps files with tables

Positive-parity levels and 16 rotational bands are theoretically analyzed on the basis of phenomenological models of the atomic nucleus with the use of new experimental data on excited states in the ^{160}Dy nucleus recently gained in the investigation of the decay ^{160}Er → ^{160m,g}Ho → ^{160}Dy., Comment: 14 pages Scientific WorkPlace text, 8 eps files with 18 tables

We propose a relationship between thermodynamic phase transitions and ground-state quantum phase transitions in systems with variable Hamiltonian parameters. It is based on a link between zeros of the canonical partition function at complex temperatures and exceptional points of a quantum Hamiltonian in the complex-extended parameter space. This approach is applied in the interacting boson model, where it is shown to properly distinguish the first- and second-order phase transitions., Comment: 14 pages, 5 figures

The SU(4) algebraic model of high-temperature superconductivity is studied employing the boson mapping techniques. The bosonization of the model enables us to get exact numerical solution of the model. The order parameters are discussed. The situation close to the SO(5) dynamical symmetry limit is interpreted as a modelling case for the behaviour of $D$-wave superconducting and antiferromagnetic phases in cuprates., Comment: 3 pages, Latex, 1 Postscript figure, uses epsf.sty

Neutron-proton pairing correlations are studied within the context of two solvable models, one based on the algebra SO(5) and the other on the algebra SO(8). Boson-mapping techniques are applied to these models and shown to provide a convenient methodological tool both for solving such problems and for gaining useful insight into general features of pairing. We first focus on the SO(5) model, which involves generalized T=1 pairing. Neither boson mean-field methods nor fermion-pair approximations are able to describe in detail neutron-proton pairing in this model. The analysis suggests, however, that the boson Hamiltonian obtained from a mapping of the fermion Hamiltonian contains a pairing force between bosons, pointing to the importance of boson-boson (or equivalently four-fermion) correlations with isospin T=0 and spin S=0. These correlations are investigated by carrying out a second boson mapping. Closed forms for the fermion wave functions are given in terms of the fermion-pair operators. Similar techniques are applied -- albeit in less detail -- to the SO(8) model, involving a competition between T=1 and T=0 pairing. Conclusions similar to those of the SO(5) analysis are reached regarding the importance of four-particle correlations in systems involving neutron-proton pairing., Comment: 31 pages, Latex, 3 Postscript figures, uses epsf.sty, submitted to Physical Review C

Within the context of the isovector-pairing SO(5) model, three methods measuring numbers of different kinds of nucleon pairs are discussed. Though methods do not give the same results, the odd-even staggering in pair numbers in even-even and odd-odd N=Z nuclei and the reduction of the np pair number with increasing T_z is observed in all three procedures., Comment: 9 pages, Latex, 3 Postscript figures, uses epsf.sty, submitted to Physics Letters B

It is shown how the boson mapping formalism may be applied as a useful many-body tool to solve a fermion problem. This is done in the context of generalized Ginocchio models for which we introduce S-, D-, and G-pairs of fermions and subsequently construct the sdg-boson realizations of the generalized Dyson type. The constructed SO(12) and Sp(10) fermion models are solved beyond the explicit symmetry limits. Phase transitions to rotational structures are obtained, also in situations where there is no underlying SU(3) symmetry., Comment: 25 LaTeX pages, 4 uuencoded postscript figures included, Preprint IFT/8/94 & STPHY-TH/94-4