Toric codes and quantum doubles from two-body Hamiltonians

We present here a procedure to obtain the Hamiltonians of the toric code and Kitaev quantum double models as the low-energy limits of entirely two-body Hamiltonians. Our construction makes use of a new type of perturbation gadget based on error-detecting subsystem codes. The procedure is motivated by a projected entangled pair states (PEPS) description of the target models, and reproduces the target models' behavior using only couplings that are natural in terms of the original Hamiltonians. This allows our construction to capture the symmetries of the target models

Thermalization, Error-Correction, and Memory Lifetime for Ising Anyon Systems

We consider two-dimensional lattice models that support Ising anyonic excitations and are coupled to a thermal bath. We propose a phenomenological model for the resulting short-time dynamics that includes pair-creation, hopping, braiding, and fusion of anyons. By explicitly constructing topological quantum error-correcting codes for this class of system, we use our thermalization model to estimate the lifetime of the quantum information stored in the encoded spaces. To decode and correct errors in these codes, we adapt several existing topological decoders to the non-Abelian setting. We perform large-scale numerical simulations of these two-dimensional Ising anyon systems and find that the thresholds of these models range between 13% to 25%. To our knowledge, these are the first numerical threshold estimates for quantum codes without explicit additive structure.Comment: 34 pages, 9 figures; v2 matches the journal version and corrects a misstatement about the detailed balance condition of our Metropolis simulations. All conclusions from v1 are unaffected by this correctio

SIC~POVMs and Clifford groups in prime dimensions

We show that in prime dimensions not equal to three, each group covariant symmetric informationally complete positive operator valued measure (SIC~POVM) is covariant with respect to a unique Heisenberg--Weyl (HW) group. Moreover, the symmetry group of the SIC~POVM is a subgroup of the Clifford group. Hence, two SIC~POVMs covariant with respect to the HW group are unitarily or antiunitarily equivalent if and only if they are on the same orbit of the extended Clifford group. In dimension three, each group covariant SIC~POVM may be covariant with respect to three or nine HW groups, and the symmetry group of the SIC~POVM is a subgroup of at least one of the Clifford groups of these HW groups respectively. There may exist two or three orbits of equivalent SIC~POVMs for each group covariant SIC~POVM, depending on the order of its symmetry group. We then establish a complete equivalence relation among group covariant SIC~POVMs in dimension three, and classify inequivalent ones according to the geometric phases associated with fiducial vectors. Finally, we uncover additional SIC~POVMs by regrouping of the fiducial vectors from different SIC~POVMs which may or may not be on the same orbit of the extended Clifford group.Comment: 30 pages, 1 figure, section 4 revised and extended, published in J. Phys. A: Math. Theor. 43, 305305 (2010

Constrained bounds on measures of entanglement

Entanglement measures constructed from two positive, but not completely positive maps on density operators are used as constraints in placing bounds on the entanglement of formation, the tangle, and the concurrence of 4 x N mixed states. The maps are the partial transpose map and the $\Phi$-map introduced by Breuer [H.-P. Breuer, Phys. Rev. Lett. 97, 080501 (2006)]. The norm-based entanglement measures constructed from these two maps, called negativity and $\Phi$-negativity, respectively, lead to two sets of bounds on the entanglement of formation, the tangle, and the concurrence. We compare these bounds and identify the sets of 4 x N density operators for which the bounds from one constraint are better than the bounds from the other. In the process, we present a new derivation of the already known bound on the concurrence based on the negativity. We compute new bounds on the three measures of entanglement using both the constraints simultaneously. We demonstrate how such doubly constrained bounds can be constructed. We discuss extensions of our results to bipartite states of higher dimensions and with more than two constraints.Comment: 28 pages, 12 figures. v2 simplified and generalized derivation of main results; errors correcte

Gastrointestinal neuroendocrine neoplasms (GI-NENs): hot topics in morphological, functional, and prognostic imaging

Neuroendocrine neoplasms (NENs) are heterogeneous tumours with a common phenotype descended from the diffuse endocrine system. NENs are found nearly anywhere in the body but the most frequent location is the gastrointestinal tract. Gastrointestinal neuroendocrine neoplasms (GI-NENs) are rather uncommon, representing around 2% of all gastrointestinal tumours and 20–30% of all primary neoplasms of the small bowel. GI-NENs have various clinical manifestations due to the different substances they can produce; some of these tumours appear to be associated with familial syndromes, such as multiple endocrine neoplasm and neurofibromatosis type 1. The current WHO classification (2019) divides NENs into three major categories: well-differentiated NENs, poorly differentiated NENs, and mixed neuroendocrine-non-neuroendocrine neoplasms. The diagnosis, localization, and staging of GI-NENs include morphology and functional imaging, above all contrast-enhanced computed tomography (CECT), and in the field of nuclear medicine imaging, a key role is played by (68)Ga-labelled-somatostatin analogues ((68)Ga-DOTA-peptides) positron emission tomography/computed tomography (PET/TC). In this review of recent literature, we described the objectives of morphological/functional imaging and potential future possibilities of prognostic imaging in the assessment of GI-NENs

Sequential measurements of conjugate observables

We present a unified treatment of sequential measurements of two conjugate observables. Our approach is to derive a mathematical structure theorem for all the relevant covariant instruments. As a consequence of this result, we show that every Weyl-Heisenberg covariant observable can be implemented as a sequential measurement of two conjugate observables. This method is applicable both in finite and infinite dimensional Hilbert spaces, therefore covering sequential spin component measurements as well as position-momentum sequential measurements.Comment: 25 page

The Lie Algebraic Significance of Symmetric Informationally Complete Measurements

Examples of symmetric informationally complete positive operator valued measures (SIC-POVMs) have been constructed in every dimension less than or equal to 67. However, it remains an open question whether they exist in all finite dimensions. A SIC-POVM is usually thought of as a highly symmetric structure in quantum state space. However, its elements can equally well be regarded as a basis for the Lie algebra gl(d,C). In this paper we examine the resulting structure constants, which are calculated from the traces of the triple products of the SIC-POVM elements and which, it turns out, characterize the SIC-POVM up to unitary equivalence. We show that the structure constants have numerous remarkable properties. In particular we show that the existence of a SIC-POVM in dimension d is equivalent to the existence of a certain structure in the adjoint representation of gl(d,C). We hope that transforming the problem in this way, from a question about quantum state space to a question about Lie algebras, may help to make the existence problem tractable.Comment: 56 page

On SIC-POVMs in Prime Dimensions

The generalized Pauli group and its normalizer, the Clifford group, have a rich mathematical structure which is relevant to the problem of constructing symmetric informationally complete POVMs (SIC-POVMs). To date, almost every known SIC-POVM fiducial vector is an eigenstate of a "canonical" unitary in the Clifford group. I show that every canonical unitary in prime dimensions p > 3 lies in the same conjugacy class of the Clifford group and give a class representative for all such dimensions. It follows that if even one such SIC-POVM fiducial vector is an eigenvector of such a unitary, then all of them are (for a given such dimension). I also conjecture that in all dimensions d, the number of conjugacy classes is bounded above by 3 and depends only on d mod 9, and I support this claim with computer computations in all dimensions < 48.Comment: 6 pages, no figures. v3 Refs added, improved discussion of previous work. Ref to a proof of the main conjecture also adde

Reelin expression in human prostate cancer: a marker of tumor aggressiveness based on correlation with grade.

Reelin is a glycoprotein that plays a critical role in the regulation of neuronal migration during brain development and, since reelin has a role in the control of cell migration, it might represents an important factor in cancer pathology. In this study, 66 surgical specimens of prostate cancer were analyzed for reelin expression by immunohistochemical method. The reelin expression was correlated with Gleason score and individual Gleason patterns. Reelin expression was found in 39% prostate cancers. Stromal tissues, normal epithelial cells and prostate intraepithelial neoplasia (PIN) of any grade around and distant from cancer were always negative for reelin. Reelin was found in malignant prostatic epithelial glands of 50% cases Gleason score 10, 52% Gleason score 9, 56% Gleason score 8, 18% Gleason score 7, while no sample of prostate cancers with Gleason score 6 showed reelin expression (P=0,005). As reelin staining is frequently found in high Gleason score prostate cancers, we explored whether reelin expression is influenced by single Gleason patterns

Zoledronic acid induces a significant decrease of circulating endothelial cells and circulating endothelial precursor cells in the early prostate cancer neoadjuvant setting

Purpose: Published data demonstrated that zoledronic acid (ZOL) exhibits antiangiogenetic effects. A promising tool for monitoring antiangiogenic therapies is the measurement of circulating endothelial cells (CECs) and circulating endothelial precursor cells (CEPs) in the peripheral blood of patients. Our aim was to investigate the effects of ZOL on levels of CECs and CEPs in localized prostate cancer. Methods: Ten consecutive patients with a histologic diagnosis of low-risk prostate adenocarcinoma were enrolled and received an intravenous infusion of ZOL at baseline (T0), 28 days (T28) and 56 days (T56). Blood samples were collected at the following times: T0 (before the first infusion of ZOL), T3 (72 h after the first dose), T28, T56 (both just before the ZOL infusion) and T84 (28 days after the last infusion of ZOL) and CEC/CEP levels were directly quantified by flow cytometry at all these time points. Results: Our analyses highlighted a significant reduction of mean percentage of CECs and CEPs after initiation of ZOL treatment [p = 0.014 (at day 3) and p = 0.012 (at day 84), respectively]. Conclusion: These preliminary results demonstrate that ZOL could exert an antiangiogenic effect in early prostate cancer through CEP and CEC modulation