187,328 research outputs found
The LU-LC conjecture is false
The LU-LC conjecture is an important open problem concerning the structure of
entanglement of states described in the stabilizer formalism. It states that
two local unitary equivalent stabilizer states are also local Clifford
equivalent. If this conjecture were true, the local equivalence of stabilizer
states would be extremely easy to characterize. Unfortunately, however, based
on the recent progress made by Gross and Van den Nest, we find that the
conjecture is false.Comment: Added a new part explaining how the counterexamples are foun
The LU-LC conjecture is false
The LU-LC conjecture is an important open problem concerning the structure of entanglement of states described in the stabilizer formalism. It states that two local unitary equivalent stabilizer states are also local Clifford equivalent. If this conjecture were true, the local equivalence of stabilizer states would be extremely easy to characterize. Unfortunately, however, based on the recent progress made by Gross and Van den Nest, we find that the conjecture is false. © Rinton Press
The noncommutative Choquet boundary
Let S be an operator system -- a self-adjoint linear subspace of a unital
C*-algebra A such that contains 1 and A=C*(S) is generated by S. A boundary
representation for S is an irreducible representation \pi of C*(S) on a Hilbert
space with the property that has a unique completely
positive extension to C*(S). The set of all (unitary equivalence
classes of) boundary representations is the noncommutative counterpart of the
Choquet boundary of a function system that separates points
of X.
It is known that the closure of the Choquet boundary of a function system S
is the Silov boundary of X relative to S. The corresponding noncommutative
problem of whether every operator system has "sufficiently many" boundary
representations was formulated in 1969, but has remained unsolved despite
progress on related issues. In particular, it was unknown if is
nonempty for generic S. In this paper we show that every separable operator
system has sufficiently many boundary representations. Our methods use
separability in an essential way.Comment: 22 pages. A significant revision, including a new section and many
clarifications. No change in the basic mathematic
Alternatives to Dark Matter and Dark Energy
We review the underpinnings of the standard Newton-Einstein theory of
gravity, and identify where it could possibly go wrong. In particular, we
discuss the logical independence from each other of the general covariance
principle, the equivalence principle and the Einstein equations, and discuss
how to constrain the matter energy-momentum tensor which serves as the source
of gravity. We identify the a priori assumption of the validity of standard
gravity on all distance scales as the root cause of the dark matter and dark
energy problems, and discuss how the freedom currently present in gravitational
theory can enable us to construct candidate alternatives to the standard theory
in which the dark matter and dark energy problems could then be resolved. We
identify three generic aspects of these alternate approaches: that it is a
universal acceleration scale which determines when a luminous Newtonian
expectation is to fail to fit data, that there is a global cosmological effect
on local galactic motions which can replace galactic dark matter, and that to
solve the cosmological constant problem it is not necessary to quench the
cosmological constant itself, but only the amount by which it gravitates.Comment: LaTeX, 87 pages, 3 figures. To appear in Progress in Particle and
Nuclear Physics, 2005. Final version, contains expanded references and
footnote
On the Existence and Uniqueness of Static, Spherically Symmetric Stellar Models in General Relativity
The Fluid Ball Conjecture states that a static stellar model is spherically symmetric. This conjecture has been the motivation of much work since first mentioned by Kunzle and Savage in 1980. There have been many partial results( ul-Alam, Lindblom, Beig and Simon,etc) which rely heavily on arguments using the positive mass theorem and the equivalence of conformal flatness and spherical symmetry. The purpose of this paper is to outline the general problem, analyze and compare the key differences in several of the partial results, and give existence and uniqueness proofs for a particular class of equations of state which represents the most recent progress towards a fully generalized solution
One-Way Functions and a Conditional Variant of MKTP
One-way functions (OWFs) are central objects of study in cryptography and computational complexity theory. In a seminal work, Liu and Pass (FOCS 2020) proved that the average-case hardness of computing time-bounded Kolmogorov complexity is equivalent to the existence of OWFs. It remained an open problem to establish such an equivalence for the average-case hardness of some natural NP-complete problem. In this paper, we make progress on this question by studying a conditional variant of the Minimum KT-complexity Problem (MKTP), which we call McKTP, as follows.
1) First, we prove that if McKTP is average-case hard on a polynomial fraction of its instances, then there exist OWFs.
2) Then, we observe that McKTP is NP-complete under polynomial-time randomized reductions.
3) Finally, we prove that the existence of OWFs implies the nontrivial average-case hardness of McKTP. Thus the existence of OWFs is inextricably linked to the average-case hardness of this NP-complete problem. In fact, building on recently-announced results of Ren and Santhanam [Rahul Ilango et al., 2021], we show that McKTP is hard-on-average if and only if there are logspace-computable OWFs
Why does preferential diffusion strongly affect premixed turbulent combustion?
Combustion of premixed reactants in a turbulent flow is a classical but unresolved problem. The key problem is to explain the following data: the maximal turbulent and laminar burning velocities u(sub t) and u(sub L) occur at different equivalence ratios Phi. It is known that the equivalence ratio varies along a curved flame if molecular diffusivity D(sub fuel) does not equal D(sub oxygen). However, the mean flame radius of curvature is much larger than the laminar flame thickness delta-L. Therefore, significant influence of preferential diffusion should occur only if the flame propagation speed varies with flame curvature. This conclusion agrees with Zel'dovich's long-standing idea about the important role of leading points of a flame. The main objective of this paper is to prove Zel'dovich's hypothesis. An equation for the mean flame surface area density (MFSAD) is employed for this purpose. The second objective of this paper is to suggest a different approach to the derivation of the equation for MFSAD. It is based on the pdf equation for the reaction progress variable C and the relation between the pdf and MFSAD. This treatment suggests an entirely different closure assumption
- …