2,751 research outputs found

### Quantum Kaleidoscopes and Bell's theorem

A quantum kaleidoscope is defined as a set of observables, or states,
consisting of many different subsets that provide closely related proofs of the
Bell-Kochen-Specker (BKS) and Bell nonlocality theorems. The kaleidoscopes
prove the BKS theorem through a simple parity argument, which also doubles as a
proof of Bell's nonlocality theorem if use is made of the right sort of
entanglement. Three closely related kaleidoscopes are introduced and discussed
in this paper: a 15-observable kaleidoscope, a 24-state kaleidoscope and a
60-state kaleidoscope. The close relationship of these kaleidoscopes to a
configuration of 12 points and 16 lines known as Reye's configuration is
pointed out. The "rotations" needed to make each kaleidoscope yield all its
apparitions are laid out. The 60-state kaleidoscope, whose underlying
geometrical structure is that of ten interlinked Reye's configurations
(together with their duals), possesses a total of 1120 apparitions that provide
proofs of the two Bell theorems. Some applications of these kaleidoscopes to
problems in quantum tomography and quantum state estimation are discussed.Comment: Two new references (No. 21 and 22) to related work have been adde

### The generalized Kochen-Specker theorem

A proof of the generalized Kochen-Specker theorem in two dimensions due to
Cabello and Nakamura is extended to all higher dimensions. A set of 18 states
in four dimensions is used to give closely related proofs of the generalized
Kochen-Specker, Kochen-Specker and Bell theorems that shed some light on the
relationship between these three theorems.Comment: 5 pages, 1 Table. A new third paragraph and an additional reference
have been adde

### Entanglement Patterns in Mutually Unbiased Basis Sets for N Prime-state Particles

A few simply-stated rules govern the entanglement patterns that can occur in
mutually unbiased basis sets (MUBs), and constrain the combinations of such
patterns that can coexist (ie, the stoichiometry) in full complements of p^N+1
MUBs. We consider Hilbert spaces of prime power dimension (as realized by
systems of N prime-state particles, or qupits), where full complements are
known to exist, and we assume only that MUBs are eigenbases of generalized
Pauli operators, without using a particular construction. The general rules
include the following: 1) In any MUB, a particular qupit appears either in a
pure state, or totally entangled, and 2) in any full MUB complement, each qupit
is pure in p+1 bases (not necessarily the same ones), and totally entangled in
the remaining p^N-p. It follows that the maximum number of product bases is
p+1, and when this number is realized, all remaining p^N-p bases in the
complement are characterized by the total entanglement of every qupit. This
"standard distribution" is inescapable for two qupits (of any p), where only
product and generalized Bell bases are admissible MUB types. This and the
following results generalize previous results for qubits and qutrits. With
three qupits there are three MUB types, and a number of combinations (p+2) are
possible in full complements. With N=4, there are 6 MUB types for p=2, but new
MUB types become possible with larger p, and these are essential to the
realization of full complements. With this example, we argue that new MUB
types, showing new entanglement characteristics, should enter with every step
in N, and when N is a prime plus 1, also at critical p values, p=N-1. Such MUBs
should play critical roles in filling complements.Comment: 27 pages, one figure, to be submitted to Physical Revie

### Serrated polyps of the colon

Until recently, colonic polyps were traditionally classified as either hyperplastic or adenomatous, and only the latter were believed to have the potential to progress to carcinoma. However, it is now appreciated that a subset of serrated polyps also appear to have malignant potential. Serrated polyps are a heterogeneous group of colon polyps that include hyperplastic polyps, sessile serrated adenomas (SSAs), traditional serrated adenomas, and mixed polyps. Insights into these polyps were derived, in part, from studies of patients with the hyperplastic polyposis syndrome. SSAs show a predilection for the right colon, have a distinct histology, and their molecular genetic profile has recently been linked to a pathway for colon tumorigenesis that is characterized by microsatellite instability. Based upon available evidence, it is recommended that patients with serrated adenomas undergo colonoscopic follow-up at the same frequency as for conventional adenomas. It is important that physicians are aware of serrated polyps, particularly serrated adenomas and their relationship to colon cancer, and their proper clinical management

### New Examples of Kochen-Specker Type Configurations on Three Qubits

A new example of a saturated Kochen-Specker (KS) type configuration of 64
rays in 8-dimensional space (the Hilbert space of a triple of qubits) is
constructed. It is proven that this configuration has a tropical dimension 6
and that it contains a critical subconfiguration of 36 rays. A natural
multicolored generalisation of the Kochen-Specker theory is given based on a
concept of an entropy of a saturated configuration of rays.Comment: 24 page

### New Class of 4-Dim Kochen-Specker Sets

We find a new highly symmetrical and very numerous class (millions of
non-isomorphic sets) of 4-dim Kochen-Specker (KS) vector sets. Due to the
nature of their geometrical symmetries, they cannot be obtained from previously
known ones. We generate the sets from a single set of 60 orthogonal spin
vectors and 75 of their tetrads (which we obtained from the 600-cell) by means
of our newly developed "stripping technique." We also consider "critical KS
subsets" and analyze their geometry. The algorithms and programs for the
generation of our KS sets are presented.Comment: 7 pages, 3 figures; to appear in J. Math. Phys. Vol.52, No. 2 (2011

### Viable entanglement detection of unknown mixed states in low dimensions

We explore procedures to detect entanglement of unknown mixed states, which
can be experimentally viable. The heart of the method is a hierarchy of simple
feasibility problems, which provides sufficient conditions to entanglement. Our
numerical investigations indicate that the entanglement is detected with a cost
which is much lower than full state tomography. The procedure is applicable to
both free and bound entanglement, and involves only single copy measurements.Comment: 8 pages, 9 figures, 4 table

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