Constructing positive maps from block matrices

Positive maps are useful for detecting entanglement in quantum information theory. Any entangled state can be detected by some positive map. In this paper, the relation between positive block matrices and completely positive trace-preserving maps is characterized. Consequently, a new method for constructing decomposable maps from positive block matrices is derived. In addition, a method for constructing positive but not completely positive maps from Hermitian block matrices is also obtained.Comment: 13 page

Quantum Metrological Bounds for Vector Parameter

Precise measurement is crucial to science and technology. However, the rule of nature imposes various restrictions on the precision that can be achieved depending on specific methods of measurement. In particular, quantum mechanics poses the ultimate limit on precision which can only be approached but never be violated. Depending on analytic techniques, these bounds may not be unique. Here, in view of prior information, we investigate systematically the precision bounds of the total mean-square error of vector parameter estimation which contains $d$ independent parameters. From quantum Ziv-Zakai error bounds, we derive two kinds of quantum metrological bounds for vector parameter estimation, both of which should be satisfied. By these bounds, we show that a constant advantage can be expected via simultaneous estimation strategy over the optimal individual estimation strategy, which solves a long-standing problem. A general framework for obtaining the lower bounds in a noisy system is also proposed.Comment: 8 pages, 4 figure

A quantum model of dark energy

We propose a quantum model of dark energy. The proposed candidate for dark energy is gluon field, as is well-known, gluons are the elementary particles. We assume that gluons may not be completely massless but have tiny masses, thus the gluon field can provide a non-zero energy-momentum tensor. This model corresponds to Einstein's cosmological constant which is one of the generally accepted models for dark energy. Besides the gluon field, we also discuss the properties of electroweak boson field and compare our results with previous known results.Comment: 4 page

Quantum gravity and mass of gauge field: a four-dimensional unified quantum theory

We present in detail a four-dimensional unified quantum theory. In this theory, we identify three class of parameters, coordinate-momentum, spin and gauge, as all and as the only fundamental parameters to describe quantum fields. The coordinate-momentum is formulated by the general relativity in four-dimensional space-time. This theory satisfies the general covariance condition and the general covariance derivative operator is given. In an unified and combined description, the matter fields, gravity field and gauge fields satisfy Dirac equation, Einstein equation and Yang-Mills equation in operator form. In the framework of our theory, we mainly realize the following aims: (1) The gravity field is described by a quantum theory, the graviton is massless, it is spin-2; (2) The mass problem of gauge theory is solved. Mass arises naturally from the gauge space and thus Higgs mechanism is not necessary; (3) Color confinement of quarks is explained; (4) Parity violation for weak interactions is obtained; (5) Gravity will cause CPT violation; (6) A dark energy solution of quantum theory is presented. It corresponds to Einstein's cosmological constant. We propose that the candidate for dark energy should be gluon which is one of the elementary particles.Comment: 86 pages, v2 typos correcte

The Anatomy of Gauge/String Duality in Lunin-Maldacena Background

We consider the correspondence between the spinning string solutions in Lunin-Maldacena background and the single trace operators in the Leigh-Strassler deformation of N=4 SYM. By imposing an appropriate rotating string ans\"atz on the Landau-Lifshitz reduced sigma model in the deformed SU(2) sector, we find two types of `elliptic' solutions with two spins, which turn out to be the solutions associated with the Neumann-Rosochatius system. We then calculate the string energies as functions of spins, and obtain their explicit forms in terms of a set of moduli parameters. On the deformed spin-chain side, we explicitly compute the one-loop anomalous dimensions of the gauge theory operators dual to each of the two types of spinning string solutions, extending and complementing the results of hep-th/0511164. Moreover, we propose explicit ans\"atze on how the locations of the Bethe strings are affected due to the deformation, with several supports from the string side.Comment: 1+31 pages, 3 figures, references added, typos corrected, discussion on constraints and free parameters in spin-chain analysis added and correcte

Direct Measure of Quantum Correlation

The quantumness of the correlation known as quantum correlation is usually measured by quantum discord. So far various quantum discords can be roughly understood as indirect measure by some special discrepancy of two quantities. We present a direct measure of quantum correlation by revealing the difference between the structures of classically and quantum correlated states. Our measure explicitly includes the contributions of the inseparability and local non-orthogonality of the eigenvectors of a density. Besides its relatively easy computability, our measure can provide a unified understanding of quantum correlation of all the present versions

Instantons and Emergent AdS_3 x S^3 Geometry

Two dimensional N=(4,4) gauge theories flow to interacting superconformal field theories on their Higgs branch. We examine worldsheet instantons in these theories through the eyes of a D-brane construction. The effective instanton partition function is shown to reveal an emergent background AdS_3 x S^3 geometry.Comment: 16 pages, 1 figure. v2 typos correcte

Zeno dynamics in quantum open systems

Quantum Zeno effect shows that frequent observations can slow down or even stop the unitary time evolution of an unstable quantum system. This effect can also be regarded as a physical consequence of the the statistical indistinguishability of neighboring quantum states. The accessibility of quantum Zeno dynamics under unitary time evolution can be quantitatively estimated by quantum Zeno time in terms of Fisher information. In this work, we investigate the accessibility of quantum Zeno dynamics in quantum open systems by calculating noisy Fisher information, in which a trace preserving and completely positive map is assumed. We firstly study the consequences of non-Markovian noise on quantum Zeno effect and give the exact forms of the dissipative Fisher information and the quantum Zeno time. Then, for the operator-sum representation, an achievable upper bound of the quantum Zeno time is given with the help of the results in noisy quantum metrology. It is of significance that the noise affecting the accuracy in the entanglement-enhanced parameter estimation can conversely be favorable for the accessibility of quantum Zeno dynamics of entangled states.Comment: 6 pages, 2 figure

On Higgs Branch Localization of Seiberg-Witten Theories on Ellipsoid

In this note, we consider so-called "Higgs Branch Localization" for four dimensional N=2 field theories on 4d ellipsoid. We find a new set of saddle point equations arising from additional Higgs branch deformation term, whose solutions include both Higgs branch and BPS instanton-vortex mixed configurations. By evaluating the contour integral, we also demonstrate the ellipsoid partition almost factorizes into purely b and 1/b dependent parts, using SQCD as an explicit example. We identify various factorized parts with the ellipsoid partition function of two dimensional N=(2,2) SQCDA, which is precisely the vortex world volume theory. We also give physical interpretation for the non-factorizable parts and discuss future directions.Comment: 30 pages, 2 Figures. Instanton calculation corrected and various other clarifications and comments added, reference list Improve

Disorder-protected topological entropy after a quantum quench

Topological phases of matter are considered the bedrock of novel quantum materials as well as ideal candidates for quantum computers that possess robustness at the physical level. The robustness of the topological phase at finite temperature or away from equilibrium is therefore a very desirable feature. Disorder can improve the lifetime of the encoded topological qubits. Here we tackle the problem of the survival of the topological phase as detected by topological entropy, after a sudden quantum quench. We introduce a method to study analytically the time evolution of the system after a quantum quench and show that disorder in the couplings of the Hamiltonian of the toric code and the resulting Anderson localization can make the topological entropy resilient.Comment: typos fixed; 5.5 pages + 1.5 supplemental material; 4 figure