Masking quantum information in multipartite scenario

Recently, Kavan Modi \emph{et al.} found that masking quantum information is impossible in bipartite scenario in [Phys. Rev. Lett. \textbf{120}, 230501 (2018)]. This adds another item of the no-go theorems. In this paper, we present some new schemes different from error correction codes, which show that quantum states can be masked when more participants are allowed in the masking process. Moreover, using a pair of mutually orthogonal Latin squares of dimension $d$, we show that all the $d$ level quantum states can be masked into tripartite quantum systems whose local dimensions are $d$ or $d+1$. This highlight some difference between the no-masking theorem and the classical no-cloning theorem or no-deleting theorem.Comment: 6 pages, 0 figur

Nodal-knot semimetals

Topological nodal-line semimetals are characterized by one-dimensional lines of band crossing in the Brillouin zone. In contrast to nodal points, nodal lines can be in topologically nontrivial configurations. In this paper, we study the simplest topologically nontrivial forms of nodal line, namely, a single nodal line taking the shape of a knot in the Brillouin zone. We introduce a generic construction for various "nodal-knot semimetals", which yields the simplest trefoil nodal knot and other more complicated nodal knots in the Brillouin zone. The knotted-unknotted transitions by nodal-line reconnections are also studied. Our work brings the knot theory to the subject of topological semimetals.Comment: 7 pages, 5 figures. Figure quality improved

Unextendible maximally entangled bases in dxd

We investigate the unextendible maximally entangled bases in $\mathbb{C}^{d}\bigotimes\mathbb{C}^{d}$ and present a $30$-number UMEB construction in $\mathbb{C}^{6}\bigotimes\mathbb{C}^{6}$. For higher dimensional case, we show that for a given $N$-number UMEB in $\mathbb{C}^{d}\bigotimes\mathbb{C}^{d}$, there is a $\widetilde{N}$-number, $\widetilde{N}=(qd)^2-(d^2-N)$, UMEB in $\mathbb{C}^{qd}\bigotimes\mathbb{C}^{qd}$ for any $q\in\mathbb{N}$. As an example, for $\mathbb{C}^{12n}\bigotimes\mathbb{C}^{12n}$ systems, we show that there are at least two sets of UMEBs which are not equivalent.Comment: Errors correcte

On small set of one-way LOCC indistinguishability of maximally entangled states

In this paper, we study the one-way local operations and classical communication (LOCC) problem. In $\mathbb{C}^d\otimes\mathbb{C}^d$ with $d\geq4$, we construct a set of $3\lceil\sqrt{d}\rceil-1$ one-way LOCC indistinguishable maximally entangled states which are generalized Bell states. Moreover, we show that there are four maximally entangled states which cannot be perfectly distinguished by one-way LOCC measurements for any dimension $d\geq 4$.Comment: 10 pages.Very recently, we became aware of related work \cite{Zhang2} in which the same $\lceil\frac{d}{2}\rceil+2$ states in $\mathbb{C}^d\otimes\mathbb{C}^d$ is proved to be one-way LOCC indistinguishable. arXiv admin note: text overlap with arXiv:1310.4220 by other autho

Chemical Property of Colliding Sources in 124,136Xe and 112,124Sn Induced Collisions in Isobaric Ratio Difference and Isoscaling Methods

The isoscaling and isobaric ratio difference (IBD) methods are used to study the $\Delta\mu/T$ ($\Delta\mu$ being the difference between the chemical potentials of neutron and proton, and $T$ being the temperature) in the measured 1$A$ GeV $^{124}$Sn + $^{124}$Sn, $^{112}$Sn + $^{112}$Sn, $^{136}$Xe + Pb and $^{124}$Xe + Pb reactions. The isoscaling phenomena in the $^{124}$Sn/$^{112}$Sn and the $^{136}$Xe/$^{124}$Xe reactions pairs are investigated, and the isoscaling parameter $\alpha$ and $\beta$ are obtained. The $\Delta\mu/T$ determined by the isoscaling method (IS--$\Delta\mu/T$) and IBD method (IB--$\Delta\mu/T$) in the measured Sn and Xe reactions are compared. It is shown that in most of fragments, the IS-- and IB-- $\Delta\mu/T$ are consistent in the Xe reactions, while the IS-- and IB-- $\Delta\mu/T$ are only similar in the less neutron-rich fragments in the Sn reactions. The shell effects in IB--$\Delta\mu/T$ are also discussed.Comment: 5 figures, submitted to J. Phys. G: Nucl. Part. Phy

Isobaric Yield Ratio Difference in Heavy-ion Collisions, and Comparison to Isoscaling

An isobaric yield ratio difference (IBD) method is proposed to study the ratio of the difference between the chemical potential of neutron and proton to temperature ($\Delta\mu/T$) in heavy-ion collisions. The $\Delta\mu/T$ determined by the IBD method (IB-$\Delta\mu/T$) is compared to the results of the isoscaling method (IS-$\Delta\mu/T$), which uses the isotopic or the isotonic yield ratio. Similar distributions of the IB- and IS-$\Delta\mu/T$ are found in the measured 140$A$ MeV $^{40,48}$Ca + $^{9}$Be and the $^{58,64}$Ni + $^{9}$Be reactions. The IB- and IS-$\Delta\mu/T$ both have a distribution with a plateau in the small mass fragments plus an increasing part in the fragments of relatively larger mass. The IB- and IS-$\Delta\mu/T$ plateaus show dependence on the $n/p$ ratio of the projectile. It is suggested that the height of the plateau is decided by the difference between the neutron density ($\rho_n$) and the proton density ($\rho_p$) distributions of the projectiles, and the width shows the overlapping volume of the projectiles in which $\rho_n$ and $\rho_p$ change very little. The difference between the IB- and IS-$\Delta\mu/T$ is explained by the isoscaling parameters being constrained by the many isotopes and isotones, while the IBD method only uses the yields of two isobars. It is suggested that the IB-$\Delta\mu/T$ is more reasonable than the IS-$\Delta\mu/T$, especially when the isotopic or isotonic ratio disobeys the isoscaling. As to the question whether the $\Delta\mu/T$ depends on the density or the temperature, the density dependence is preferred since the low density can result in low temperature in the peripheral reactions.Comment: 6 pages, 6 figures, mistake of reference correcte

Residue Coulomb interaction among isobars and its influence in symmetry energy of neutron-rich fragment

The residue Coulomb interaction (RCI), which affects the results of symmetry energy of neutron-rich nucleus in isobaric yield ratio (IYR) methods, is difficult to be determined. Four RCI approximations are investigated: (1) the M1--RCI adopting the $a_{c}/T$ (the ratio of Coulomb energy coefficient to temperature) determined from the IYR of mirror-nuclei fragment; (2) the M2--RCI by fitting the difference between IYRs; (3) the M3--RCI by adopting the standard Coulomb energy at a temperature $T=2$MeV; and (4) neglecting the RCI among the three isobars. The M1--, M2-- and M3--RCI is found to no larger than 0.4. In particular, the M2--RCI is very close to zero. The effects of RCI in the $a_{sym}/T$ of fragment are also studied. The M1-- and M4--$a_{sym}/T$ are found to be the lower and upper limitations of $a_{sym}/T$, respectively. The M2--$a_{sym}/T$ overlaps the M4--$a_{sym}/T$, which indicates that the M2--RCI is negligible, at the same time the RCI among the three isobars can be neglected. A relative consistent low values of M3--$a_{sym}/T$ ($7.5\pm2.5$) are found in very neutron-rich isobars.Comment: 7pages, 7 figure

Experimental discovery of nodal chains

Three-dimensional (3D) topological nodal points, such as Weyl and Dirac nodes have attracted wide-spread interest across multiple disciplines and diverse material systems. Unlike nodal points that contain little structural variations, nodal lines can have numerous topological configurations in the momentum space, forming nodal rings, nodal chains and potentially nodal links and nodal knots. However, nodal lines have much less development for the lack of ideal material platforms. In condensed matter for example, nodal lines are often fragile to spin-orbit-coupling, locating off the Fermi level, coexisting with energy-degenerate trivial bands and dispersing strongly in energy of the line degeneracy. Here, overcoming all above difficulties, we theoretically predict and experimentally observe nodal chains in a metallic-mesh photonic crystal having frequency-isolated linear bandtouching rings chained across the entire Brillouin zone (BZ). These nodal chains are protected by mirror symmetries and have a frequency variation less than 1%. We used angle-resolved transmission (ART) to probe the projected bulk dispersions and performed Fourier-transformed field scan (FTFS) to map out the surface dispersions, which is a quadratic touching between two drumhead surface bands. Our results established an ideal nodal-line material for further studies of topological line-degeneracies with nontrivial connectivities, as well as the consequent wave dynamics richer than 2D Dirac and 3D Weyl materials.Comment: 5 pages, 4 figure

Constructing unextendible product bases from the old ones

We studied the construction problem of the unextendible product basis (UPB). We mainly give a method to construct a UPB of a quantum system through the UPBs of its subsystem. Using this method and the UPBs which are known for us, we construct different kinds of UPBs in general bipartite quantum system. Then we use these UPBs to construct a family of UPBs in multipartite quantum system. The UPBs can be used to construct the bound entangled states with different ranks.Comment: 6 pages, 1 figure

dd locally indistinguishable maximally entangled states in Cd⊗Cd\mathbb{C}^d\otimes\mathbb{C}^d

We give a explicit construction of $d$ locally indistinguishable orthogonal maximally entangled states in $\mathbb{C}^d\otimes\mathbb{C}^d$ for any $d\geq 4$. This gives an answer to the conjecture proposed by S. Bandyopadhyay in 2009. Thus it reflects the nonlocality of the fundamental feature of quantum mechanics.Comment: The paper is rewrited, especally the introduction. 5 pages, no figure