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Li Yu

Publications and source records attributed to Li Yu.

At least 235 records · Page 13Linked to original sources
arXiv2011

Relative entropy derivation of the uncertainty principle with quantum side information

We give a simple proof of the uncertainty principle with quantum side information, as in [Berta et al. Nature Physics 6, 659 (2010)], invoking the monotonicity of the relative entropy. Our proof shows that the entropic uncertainty principle can be viewed as a data-processing inequality, a special case of the notion that information cannot increase due to evolution in time. This leads to a systematic method for finding the minimum uncertainty states of various entropic uncertainty relations; interestingly such states are intimately connected with the reversibility of time evolution.

quant-ph↗
arXiv2011

Average quantum dynamics of closed systems over stochastic Hamiltonians

We develop a master equation formalism to describe the evolution of the average density matrix of a closed quantum system driven by a stochastic Hamiltonian. The average over random processes generally results in decoherence effects in closed system dynamics, in addition to the usual unitary evolution. We then show that, for an important class of problems in which the Hamiltonian is proportional to a Gaussian random process, the 2nd-order master equation yields exact dynamics. The general formalism is applied to study the examples of a two-level system, two atoms in a stochastic magnetic field and the heating of a trapped ion.

quant-ph↗
arXiv2011

On Transition Functions of Topological Toric Manifolds

We show that any topological toric manifold can be covered by finitely many open charts so that all the transition functions between these charts are Laurent monomials of $z_j$'s and $\bar{z}_j$'s. In addition, we will describe toric manifolds and some special class of topological toric manifolds in terms of transition functions of charts up to (weakly) equivariant diffeomorphism.

math.AT↗
arXiv2011

Small Covers, infra-nilmanifolds and positive curvature

We show that all the small covers which are infra-nilmanifolds are exactly real Bott manifolds. This implies that any small cover which admits a flat Riemannian metric must be a real Bott manifold. In addition, we will study small covers which admit Riemannian metrics with positive or nonnegative Ricci curvature or sectional curvature. We will see that these geometric conditions put very strong restrictions on the topology of the small covers and the combinatorial structure of the underlying simple polytopes. Similar geometric problems are also studied for the real moment-angle complex of an arbitrary simple polytope.

math.GT↗
arXiv2011

Information theoretic treatment of tripartite systems and quantum channels

A Holevo measure is used to discuss how much information about a given POVM on system $a$ is present in another system $b$, and how this influences the presence or absence of information about a different POVM on $a$ in a third system $c$. The main goal is to extend information theorems for mutually unbiased bases or general bases to arbitrary POVMs, and especially to generalize "all-or-nothing" theorems about information located in tripartite systems to the case of \emph{partial information}, in the form of quantitative inequalities. Some of the inequalities can be viewed as entropic uncertainty relations that apply in the presence of quantum side information, as in recent work by Berta et al. [Nature Physics 6, 659 (2010)]. All of the results also apply to quantum channels: e.g., if $\EC$ accurately transmits certain POVMs, the complementary channel $\FC$ will necessarily be noisy for certain other POVMs. While the inequalities are valid for mixed states of tripartite systems, restricting to pure states leads to the basis-invariance of the difference between the information about $a$ contained in $b$ and $c$.

quant-ph↗
arXiv2011

Growth, Characterization and Fermi Surface of Heavy Fermion CeCoIn5 Superconductor

High quality single crystals of heavy Fermion CeCoIn5 superconductor have been grown by flux method with a typical size of (1~2)mm x (1~2)mm x ~0.1 mm. The single crystals are characterized by structural analysis from X-ray diffraction and Laue diffraction, as well as compositional analysis. Magnetic and electrical measurements on the single crystals show a sharp superconducting transition with a transition temperature at Tc(onset) ~ 2.3 K and a transition width of ~0.15 K. The resistivity of the CeCoIn5 crystal exhibits a hump at ~45 K which is typical of a heavy Fermion system. High resolution angle-resolved photoemission spectroscopy (ARPES) measurements of CeCoIn5 reveal clear Fermi surface sheets that are consistent with the band structure calculations when assuming itinerant Ce 4f electrons at low temperature. This work provides important information on the electronic structure of heavy Fermion CeCoIn5 superconductor. It also lays a foundation for further studies on the physical properties and superconducting mechanism of the heavy Fermion superconductors.

cond-mat.supr-con↗
arXiv2011

Extraction of Electron Self-Energy and Gap Function in the Superconducting State of Bi_2Sr_2CaCu_2O_8 Superconductor via Laser-Based Angle-Resolved Photoemission

Super-high resolution laser-based angle-resolved photoemission measurements have been performed on a high temperature superconductor Bi_2Sr_2CaCu_2O_8. The band back-bending characteristic of the Bogoliubov-like quasiparticle dispersion is clearly revealed at low temperature in the superconducting state. This makes it possible for the first time to experimentally extract the complex electron self-energy and the complex gap function in the superconducting state. The resultant electron self-energy and gap function exhibit features at ~54 meV and ~40 meV, in addition to the superconducting gap-induced structure at lower binding energy and a broad featureless structure at higher binding energy. These information will provide key insight and constraints on the origin of electron pairing in high temperature superconductors.

cond-mat.supr-con↗
arXiv2011

Common Fermi Surface Topology and Nodeless Superconducting Gap in K0.68Fe1.79Se2 and (Tl0.45K0.34)Fe1.84Se2 Superconductors Revealed from Angle-Resolved Photoemission Spectroscopy

We carried out high resolution angle-resolved photoemission measurements on the electronic structure and superconducting gap of K_0.68Fe_1.79Se_2 (T_c=32 K) and (Tl_0.45K_0.34)Fe_1.84Se_2 (T_c=28 K) superconductors. In addition to the electron-like Fermi surface near M(π,π), two electron-like Fermi pockets are revealed around the zone center Γ(0,0) in K0.68Fe1.79Se_2. This observation makes the Fermi surface topology of K_0.68Fe_1.79Se_2 consistent with that of (Tl,Rb)_xFe_{2-y}Se_2 and (Tl,K)_xFe_{2-y}Se_2 compounds. A nearly isotropic superconducting gap (Δ) is observed along the electron-like Fermi pocket near the M point in K_0.68Fe_1.79Se_2 (Δ\sim 9 meV) and (Tl_0.45K_0.34)Fe_1.84Se_2 (Δ\sim 8 meV). The establishment of a universal picture on the Fermi surface topology and superconducting gap in the A_xFe_2-ySe_2 (A=K, Tl, Cs, Rb and etc.) superconductors will provide important information in understanding the superconductivity mechanism of the iron-based superconductors.

cond-mat.supr-con↗
arXiv2011

Cubes and Generalized Real Bott Manifolds

We define a notion of facets-pairing structure and its seal space on a nice manifold with corners. We will study facets-pairing structures on any cube in detail and investigate when the seal space of a facets-pairing structure on a cube is a closed manifold. In particular, for any binary square matrix $A$ with zero diagonal in dimension n, there is a canonical facets-pairing structure $F_A$ on the n-dimensional cube. We will show that all the closed manifolds that we can obtain from the seal spaces of such $F_A$'s are neither more nor less than all the generalized real Bott manifolds --- a special class of real toric manifolds introduced by Choi, Masuda and Suh.

math.AT↗
arXiv2011

Distinct Fermi Surface Topology and Nodeless Superconducting Gap in (Tl0.58Rb0.42)Fe1.72Se2 Superconductor

High resolution angle-resolved photoemission measurements have been carried out to study the electronic structure and superconducting gap of the (Tl$_{0.58}$Rb$_{0.42}$)Fe$_{1.72}$Se$_2$ superconductor with a T$_c$=32 K. The Fermi surface topology consists of two electron-like Fermi surface sheets around $Γ$ point which is distinct from that in all other iron-based compounds reported so far. The Fermi surface around the M point shows a nearly isotropic superconducting gap of $\sim$12 meV. The large Fermi surface near the $Γ$ point also shows a nearly isotropic superconducting gap of $\sim$15 meV while no superconducting gap opening is clearly observed for the inner tiny Fermi surface. Our observed new Fermi surface topology and its associated superconducting gap will provide key insights and constraints in understanding superconductivity mechanism in the iron-based superconductors.

cond-mat.supr-con↗
arXiv2010

Comment on arXiv:1012.1484v1 Structural origin of apparent Fermi surface pockets in angle-resolved photoemission of Bi_2Sr_{2-x}La_xCuO_{6+δ} by King et al

In our Nature paper, we reported observation of Fermi pocket in Bi_2(Sr_{2-x}La_x)CuO_{6+δ} (La-Bi2201) by angle-resolved photoemission (ARPES) measurements. King et al. tried to assign the Fermi pocket we observed as due to an additional q2 superstructure. In the process, it creates a number of serious inconsistencies and flaws in their interpretation. Any one of these inconsistencies goes strongly against King et al.'s proposal, making their proposed structural origin highly unlikely as the cause of the observed Fermi pocket. In our Nature paper, we already pointed out that this structural origin is unlikely based on the absence of additional q2-induced first-order superstructure bands of the main band MB. This conclusion remains valid and gains even stronger support by considering King et al's data.

cond-mat.str-el↗
arXiv2010

Small Cover and Halperin-Carlsson Conjecture -II

For a small cover Q^n and any principal (Z_2)^m-bundle M^n over Q^n, it was shown in a previous work of the author that the total sum of Z_2-Betti numbers of M^n is at least 2^m. In this paper, we prove that when M^n is connected, the total sum of Z_2-Betti numbers of such an M^n exactly equals 2^m if and only if M^n is homeomorphic to a product of spheres, and Q^n in this case must be a generalized real Bott manifold (or equivalent, Q^n is a small cover over a product of simplices).

math.AT↗
arXiv2010

Local cloning of entangled states

We investigate the conditions under which a set $\SC$ of pure bipartite quantum states on a $D\times D$ system can be locally cloned deterministically by separable operations, when at least one of the states is full Schmidt rank. We allow for the possibility of cloning using a resource state that is less than maximally entangled. Our results include that: (i) all states in $\SC$ must be full Schmidt rank and equally entangled under the $G$-concurrence measure, and (ii) the set $\SC$ can be extended to a larger clonable set generated by a finite group $G$ of order $|G|=N$, the number of states in the larger set. It is then shown that any local cloning apparatus is capable of cloning a number of states that divides $D$ exactly. We provide a complete solution for two central problems in local cloning, giving necessary and sufficient conditions for (i) when a set of maximally entangled states can be locally cloned, valid for all $D$; and (ii) local cloning of entangled qubit states with non-vanishing entanglement. In both of these cases, a maximally entangled resource is necessary and sufficient, and the states must be related to each other by local unitary "shift" operations. These shifts are determined by the group structure, so need not be simple cyclic permutations. Assuming this shifted form and partially entangled states, then in D=3 we show that a maximally entangled resource is again necessary and sufficient, while for higher dimensional systems, we find that the resource state must be strictly more entangled than the states in $\SC$. All of our necessary conditions for separable operations are also necessary conditions for LOCC, since the latter is a proper subset of the former. In fact, all our results hold for LOCC, as our sufficient conditions are demonstrated for LOCC, directly.

quant-ph↗
arXiv2010

Efficient implementation of bipartite nonlocal unitary gates using prior entanglement and classical communication

Any bipartite nonlocal unitary operation can be carried out by teleporting a quantum state from one party to the other, performing the unitary gate locally, and teleporting a state back again. This paper investigates unitaries which can be carried out using less prior entanglement and classical communication than are needed for teleportation. Large families of such unitaries are constructed using (projective) representations of finite groups. Among the tools employed are: a diagrammatic approach for representing entangled states, a theorem on the necessary absence of information at certain times and locations, and a representation of bipartite unitaries based on a group Fourier transform.

quant-ph↗
arXiv2010

Small Cover and Halperin-Carlsson Conjecture

We prove that the Halperin-Carlsson conjecture holds for any free (Z_2)^m action on a compact manifold whose orbit space is a small cover. In addition, we show that if the total space of a principal (Z_2)^m bundle over a small cover is connected, it must be equivalent to a partial quotient of the corresponding real moment-angle manifold with some canonical Z_2-torus action.

math.AT↗
arXiv2010

On the constructions of free and locally standard Z_2-torus actions on Manifolds

We introduce an elementary way of constructing principal (Z_2)^m-bundles over compact smooth manifolds. In addition, we will define a general notion of locally standard (Z_2)^m-actions on closed manifolds for all m>0, and then give a general way to construct all such (Z_2)^m-actions from the orbit space. Some related topology problems are also studied.

math.AT↗
arXiv2009

Topological types of 3-dimensional small covers

In this paper we study the (equivariant) topological types of a class of 3-dimensional closed manifolds (i.e., 3-dimensional small covers), each of which admits a locally standard $(\mathbb{Z}_2)^3$-action such that its orbit space is a simple convex 3-polytope. We introduce six equivariant operations on 3-dimensional small covers. These six operations are interesting because of their combinatorial natures. Then we show that each 3-dimensional small cover can be obtained from $\mathbb{R}P^3$ and $S^1\times\mathbb{R}P^2$ with certain $(\mathbb{Z}_2)^3$-actions under these six operations. As an application, we classify all 3-dimensional small covers up to $({\Bbb Z}_2)^3$-equivariant unoriented cobordism.

math.GT↗