Families of pure PEPS with efficiently simulatable local hidden variable models for most measurements

An important problem in quantum information theory is to understand what makes entangled quantum systems non-local or hard to simulate efficiently. In this work we consider situations in which various parties have access to a restricted set of measurements on their particles, and construct entangled quantum states that are essentially classical for those measurements. In particular, given any set of local measurements on a large enough Hilbert space whose dual strictly contains (i.e. contains an open neighborhood of) a pure state, we use the PEPS formalism and ideas from generalized probabilistic theories to construct pure multiparty entangled states that have (a) local hidden variable models, and (b) can be efficiently simulated classically. We believe that the examples we construct cannot be efficiently classically simulated using previous techniques. Without the restriction on the measurements, the states that we construct are non-local, and in some proof-of-principle cases are universal for measurement based quantum computation.This work was supported by EPSRC grant EP/K022512/1.This work was supported by EPSRC grant EP/K022512/1

A new class of entanglement measures

We introduce new entanglement measures on the set of density operators on tensor product Hilbert spaces. These measures are based on the greatest cross norm on the tensor product of the sets of trace class operators on Hilbert space. We show that they satisfy the basic requirements on entanglement measures discussed in the literature, including convexity, invariance under local unitary operations and non-increase under local quantum operations and classical communication.Comment: Revised version accepted by J Math Phys, 12 pages, LaTeX, contains Sections 1-5 & 7 of the previous version. The previous Section 6 is now in quant-ph/0105104 and the previous Section 8 is superseded by quant-ph/010501

Verifying continuous-variable entanglement in finite spaces

Starting from arbitrary Hilbert spaces, we reduce the problem to verify entanglement of any bipartite quantum state to finite dimensional subspaces. Hence, entanglement is a finite dimensional property. A generalization for multipartite quantum states is also given.Comment: 4 page

Characterizing entanglement with geometric entanglement witnesses

We show how to detect entangled, bound entangled, and separable bipartite quantum states of arbitrary dimension and mixedness using geometric entanglement witnesses. These witnesses are constructed using properties of the Hilbert-Schmidt geometry and can be shifted along parameterized lines. The involved conditions are simplified using Bloch decompositions of operators and states. As an example we determine the three different types of states for a family of two-qutrit states that is part of the "magic simplex", i.e. the set of Bell-state mixtures of arbitrary dimension.Comment: 19 pages, 4 figures, some typos and notational errors corrected. To be published in J. Phys. A: Math. Theo

Nonlinear entanglement witnesses, covariance matrices and the geometry of separable states

Entanglement witnesses provide a standard tool for the analysis of entanglement in experiments. We investigate possible nonlinear entanglement witnesses from several perspectives. First, we demonstrate that they can be used to show that the set of separable states has no facets. Second, we give a new derivation of nonlinear witnesses based on covariance matrices. Finally, we investigate extensions to the multipartite case.Comment: 12 pages, 2 figures, for the proceedings of DICE2006 in Piombino (Italy

A separability criterion for density operators

We give a necessary and sufficient condition for a mixed quantum mechanical state to be separable. The criterion is formulated as a boundedness condition in terms of the greatest cross norm on the tensor product of trace class operators.Comment: REVTeX, 5 page

Low-Dose Continuous 5-Fluorouracil Combined with Leucovorin, nab-Paclitaxel, Oxaliplatin, and Bevacizumab for Patients with Advanced Pancreatic Cancer: A Retrospective Analysis.

BackgroundContinuous-infusion 5-fluorouracil (5FU) and calcium leucovorin plus nab-paclitaxel and oxaliplatin have been shown to be active in patients with pancreatic cancer. As a protracted low-dose infusion, 5FU is antiangiogenic, and has synergy with bevacizumab. As shown in the treatment of breast cancer, bevacizumab and nab-paclitaxel are also synergetic.ObjectiveIn this paper we retrospectively analyze the survival of 65 patients with advanced pancreatic cancer who were treated with low-dose continuous (metronomic) chemotherapy given in conjunction with conventional anti-VEGF therapy.Patients and methodsSince July of 2008, we have treated 65 patients with 5FU (180 mg/m2/day × 14 days) via an ambulatory pump. Calcium leucovorin (20 mg/m2 IV), nab-paclitaxel (60 mg/m2) IV as a 30-min infusion, and oxaliplatin (50 mg/m2) IV as a 60-min infusion were given on days 1, 8, and 15. Bevacizumab (5 mg/kg) IV over 30 min was administered on days 1 and 15. Cycles were repeated every 28-35 days. There were 42 women and 23 men, and the median age was 59 years. Forty-six patients had stage IV disease.ResultsThe median survival was 19 months, with 82% of patients surviving 12 months or longer. The overall response rate was 49%. There were 28 patients who had received prior treatment, 15 of whom responded to therapy. Fifty-two patients had elevated CA 19-9 prior to treatment. Of these, 21 patients had 90% or greater reduction in CA 19-9 levels. This cohort had an objective response rate of 71% and a median survival of 27 months. Thirty patients stopped treatment due to disease progression, and an additional 22 stopped because of toxicity. One patient died while on therapy.ConclusionsThis non-gemcitabine-based regimen resulted in higher response rates and better survival than what is commonly observed with therapy given at conventional dosing schedules. Low-dose continuous (metronomic therapy) cytotoxic chemotherapy combined with antiangiogenic therapy is safe and effective

Some Properties of the Computable Cross Norm Criterion for Separability

The computable cross norm (CCN) criterion is a new powerful analytical and computable separability criterion for bipartite quantum states, that is also known to systematically detect bound entanglement. In certain aspects this criterion complements the well-known Peres positive partial transpose (PPT) criterion. In the present paper we study important analytical properties of the CCN criterion. We show that in contrast to the PPT criterion it is not sufficient in dimension 2 x 2. In higher dimensions we prove theorems connecting the fidelity of a quantum state with the CCN criterion. We also analyze the behaviour of the CCN criterion under local operations and identify the operations that leave it invariant. It turns out that the CCN criterion is in general not invariant under local operations.Comment: 7 pages; accepted by Physical Review A; error in Appendix B correcte