Odd properly colored cycles in edge-colored graphs

It is well-known that an undirected graph has no odd cycle if and only if it is bipartite. A less obvious, but similar result holds for directed graphs: a strongly connected digraph has no odd cycle if and only if it is bipartite. Can this result be further generalized to more general graphs such as edge-colored graphs? In this paper, we study this problem and show how to decide if there exists an odd properly colored cycle in a given edge-colored graph. As a by-product, we show how to detect if there is a perfect matching in a graph with even (or odd) number of edges in a given edge set

On the communication cost of entanglement transformations

We study the amount of communication needed for two parties to transform some given joint pure state into another one, either exactly or with some fidelity. Specifically, we present a method to lower bound this communication cost even when the amount of entanglement does not increase. Moreover, the bound applies even if the initial state is supplemented with unlimited entanglement in the form of EPR pairs, and the communication is allowed to be quantum mechanical. We then apply the method to the determination of the communication cost of asymptotic entanglement concentration and dilution. While concentration is known to require no communication whatsoever, the best known protocol for dilution, discovered by Lo and Popescu [Phys. Rev. Lett. 83(7):1459--1462, 1999], requires a number of bits to be exchanged which is of the order of the square root of the number of EPR pairs. Here we prove a matching lower bound of the same asymptotic order, demonstrating the optimality of the Lo-Popescu protocol up to a constant factor and establishing the existence of a fundamental asymmetry between the concentration and dilution tasks. We also discuss states for which the minimal communication cost is proportional to their entanglement, such as the states recently introduced in the context of ``embezzling entanglement'' [W. van Dam and P. Hayden, quant-ph/0201041].Comment: 9 pages, 1 figure. Added a reference and some further explanations. In v3 some arguments are given in more detai

Protocols for entanglement transformations of bipartite pure states

We present a general theoretical framework for both deterministic and probabilistic entanglement transformations of bipartite pure states achieved via local operations and classical communication. This framework unifies and greatly simplifies previous works. A necessary condition for ``pure contraction'' transformations is given. Finally, constructive protocols to achieve both probabilistic and deterministic entanglement transformations are presented.Comment: 7 pages, no figures. Version slightly modified on Physical Review A reques

Faithful remote state preparation using finite classical bits and a non-maximally entangled state

We present many ensembles of states that can be remotely prepared by using minimum classical bits from Alice to Bob and their previously shared entangled state and prove that we have found all the ensembles in two-dimensional case. Furthermore we show that any pure quantum state can be remotely and faithfully prepared by using finite classical bits from Alice to Bob and their previously shared nonmaximally entangled state though no faithful quantum teleportation protocols can be achieved by using a nonmaximally entangled state.Comment: 6 page

Acyclicity in edge-colored graphs

A walk $W$ in edge-colored graphs is called properly colored (PC) if every pair of consecutive edges in $W$ is of different color. We introduce and study five types of PC acyclicity in edge-colored graphs such that graphs of PC acyclicity of type $i$ is a proper superset of graphs of acyclicity of type $i+1$, $i=1,2,3,4.$ The first three types are equivalent to the absence of PC cycles, PC trails, and PC walks, respectively. While graphs of types 1, 2 and 3 can be recognized in polynomial time, the problem of recognizing graphs of type 4 is, somewhat surprisingly, NP-hard even for 2-edge-colored graphs (i.e., when only two colors are used). The same problem with respect to type 5 is polynomial-time solvable for all edge-colored graphs. Using the five types, we investigate the border between intractability and tractability for the problems of finding the maximum number of internally vertex disjoint PC paths between two vertices and the minimum number of vertices to meet all PC paths between two vertices

Impact of neoadjuvant treatment on total mesorectal excision for ultra-low rectal cancers

<p>Abstract</p> <p>Background</p> <p>This study reviewed the impact of pre-operative chemoradiotherapy or post-operative chemotherapy and/or radiotherapy on total mesorectal excision (TME) for ultralow rectal cancers that required either low anterior resection with peranal coloanal anastomosis or abdomino-perineal resection (APR). We examined surgical complications, local recurrence and survival.</p> <p>Methods</p> <p>Of the 1270 patients who underwent radical resection for rectal cancer from 1994 till 2007, 180 with tumors within 4 cm with either peranal coloanal anastomosis or APR were analyzed. Patients were compared in groups that had surgery only (Group A), pre-operative chemoradiotherapy (Group B), and post-operative therapy (Group C).</p> <p>Results</p> <p>There were 115 males and the mean age was 65.43 years (range 30-89). APR was performed in 134 patients while 46 had a sphincter-preserving resection with peranal coloanal anastomosis. The mean follow-up period was 52.98 months (range: 0.57 to 178.9). There were 69, 58 and 53 patients in Groups A, B, and C, respectively. Nine patients in Group B could go on to have sphincter-saving rectal resection. The overall peri-operative complication rate was 43.4% in Group A vs. 29.3% in Group B vs. 39.6% in Group C, respectively. The local recurrence rate was significantly lower in Group B (8.6.9% vs. 21.7% in Group A vs. 33.9% in Group C) <it>p < 0.05</it>. The 5-year cancer-specific survival rates for Group A was 49.3%, Group B was 69.9% and Group C was 38.8% (<it>p </it>= 0.14).</p> <p>Conclusion</p> <p>Pre-operative chemoradiation in low rectal cancer is not associated with a higher incidence of peri-operative complications and its benefits may include reduction local recurrence.</p

Higher-order squeezing for the codirectional Kerr nonlinear coupler

In this Letter we study the evolution of the higher-order squeezing, namely, $n$th-order single-mode squeezing, sum- and difference-squeezing for the codirectional Kerr nonlinear coupler. We show that the amount of squeezing decreases when $n$, i.e. the squeezing order, increases. For specific values of the interaction parameters squeezing factors exhibit a series of revival-collapse phenomena, which become more pronounced when the value of $n$ increases. Sum-squeezing can provide amounts of squeezing greater than those produced by the $n$th higher-order ($n\geq 2$) squeezing for the same values of interaction parameters and can map onto amplitude-squared squeezing. Further, we prove that the difference-squeezing is not relevant measure for obtaining information about squeezing from this device.Comment: 13 pages, 3 figure