Off-diagonal geometric phase for mixed states

We extend the off-diagonal geometric phase [Phys. Rev. Lett. {\bf 85}, 3067 (2000)] to mixed quantal states. The nodal structure of this phase in the qubit (two-level) case is compared with that of the diagonal mixed state geometric phase [Phys. Rev. Lett. {\bf 85}, 2845 (2000)]. Extension to higher dimensional Hilbert spaces is delineated. A physical scenario for the off-diagonal mixed state geometric phase in polarization-entangled two-photon interferometry is proposed.Comment: small corrections; journal reference adde

Generating random density matrices

We study various methods to generate ensembles of random density matrices of a fixed size N, obtained by partial trace of pure states on composite systems. Structured ensembles of random pure states, invariant with respect to local unitary transformations are introduced. To analyze statistical properties of quantum entanglement in bi-partite systems we analyze the distribution of Schmidt coefficients of random pure states. Such a distribution is derived in the case of a superposition of k random maximally entangled states. For another ensemble, obtained by performing selective measurements in a maximally entangled basis on a multi--partite system, we show that this distribution is given by the Fuss-Catalan law and find the average entanglement entropy. A more general class of structured ensembles proposed, containing also the case of Bures, forms an extension of the standard ensemble of structureless random pure states, described asymptotically, as N \to \infty, by the Marchenko-Pastur distribution.Comment: 13 pages in latex with 8 figures include

Integrability of Lie systems and some of its applications in physics

The geometric theory of Lie systems will be used to establish integrability conditions for several systems of differential equations, in particular Riccati equations and Ermakov systems. Many different integrability criteria in the literature will be analyzed from this new perspective and some applications in physics will be given.Comment: 16 page

Fidelity approach to quantum phase transitions

We review briefly the quantum fidelity approach to quantum phase transitions in a pedagogical manner. We try to relate all established but scattered results on the leading term of the fidelity into a systematic theoretical framework, which might provide an alternative paradigm for understanding quantum critical phenomena. The definition of the fidelity and the scaling behavior of its leading term, as well as their explicit applications to the one-dimensional transverse-field Ising model and the Lipkin-Meshkov-Glick model, are introduced at the graduate-student level. In addition, we survey also other types of fidelity approach, such as the fidelity per site, reduced fidelity, thermal-state fidelity, operator fidelity, etc; as well as relevant works on the fidelity approach to quantum phase transitions occurring in various many-body systems.Comment: 41 pages, 31 figures. We apologize if we omit acknowledging your relevant works. Do tell. An updated version with clearer figures can be found at: http://www.phy.cuhk.edu.hk/~sjgu/fidelitynote.pd

Optimal manipulations with qubits: Universal quantum entanglers

We analyze various scenarios for entangling two initially unentangled qubits. In particular, we propose an optimal universal entangler which entangles a qubit in unknown state $|\Psi>$ with a qubit in a reference (known) state $|0>$. That is, our entangler generates the output state which is as close as possible to the pure (symmetrized) state $(|\Psi>|0> +|0>|\Psi>)$. The most attractive feature of this entangling machine, is that the fidelity of its performance (i.e. the distance between the output and the ideally entangled -- symmetrized state) does not depend on the input and takes the constant value $F= (9+3\sqrt{2})/14\simeq 0.946$. We also analyze how to optimally generate from a single qubit initially prepared in an unknown state |\Psi\r a two qubit entangled system which is as close as possible to a Bell state $(|\Psi\r|\Psi^\perp\r+|\Psi^\perp\r|\Psi\r)$, where \l\Psi|\Psi^\perp\r =0.Comment: 11 pages, 3 eps figures, accepted for publication in Phys. Rev.

Hubungan Kelelahan Kerja dan Stress Kerja dengan Kecelakaan Kerja Tertusuk Jarum Jahit pada Pekerja Bagian Garmen di PT. Danliris Sukoharjo

Latar Belakang : Meningkatnya penggunaan teknologi di berbagai sektor usaha dapat pula mengakibatkan semakin tinggi resiko terjadinya kecelakaan kerja dan penyakit akibat kerja atau penyakit yang berhubungan dengan pekerjaan yang mengancam keselamatan, kesehatan dan kesejahteraan tenaga kerja. Dalam tiga tahun terakhir di PT. Danliris Sukoharjo, terjadi 38 kasus kecelakaan kerja tertusuk jarum jahit. Tujuan penelitian ini untuk mengetahui apakah kelelahan kerja dan stress kerja mempunyai hubungan dengan terjadinya kecelakaan kerja tertusuk jarum jahit. Metode : Penelitian ini menggunakan metode observasional analitik dengan rancangan cross sectional. Sampel diambil dengan metode simple random sampling sebanyak 200 pekerja bagian garmen. Pengumpulan data dilakukan dengan pengisian kuesioner kelelahan kerja dan stress kerja serta kecelakaan kerja tertusuk jarum jahit dilakukan dengan observasional. Pengolahan dan analisa data menggunakan uji statistik chi square dengan uji alterrnatif fisher. Hasil : Hasil penelitian ini menunjukkan tidak ada hubungan antara kelelahan kerja dengan terjadinya kecelakaan kerja tertusuk jarum jahit (p value 0.619) dan tidak ada hubungan antara stress kerja dengan kecelakaan kerja tertusuk jarum jahit (p value 0.137). Kesimpulan : Kelelahan kerja dan stress kerja tidak mempunyai hubungan dengan terjadinya kecelakaan kerja tertusuk jarum jahit. Kata Kunci : Kelelahan Kerja, Stress Kerja, Kecelakaan Kerj

Entanglement of a Pair of Quantum Bits

The ``entanglement of formation'' of a mixed state of a bipartite quantum system can be defined in terms of the number of pure singlets needed to create the state with no further transfer of quantum information. We find an exact formula for the entanglement of formation for all mixed states of two qubits having no more than two non-zero eigenvalues, and we report evidence suggesting that the formula is valid for all states of this system.Comment: 10 page

INDICATORS OF CLASSICALITY/QUANTUMNESS OF FINITE- DIMENSIONAL SYSTEMS

We discuss measures of classicality/quantumness of states of finite-dimensional quantum systems, which are based on a deviation of quasiprobability distributions from true statistical distributions