156 research outputs found
Tsirelson's problem and Kirchberg's conjecture
Tsirelson's problem asks whether the set of nonlocal quantum correlations
with a tensor product structure for the Hilbert space coincides with the one
where only commutativity between observables located at different sites is
assumed. Here it is shown that Kirchberg's QWEP conjecture on tensor products
of C*-algebras would imply a positive answer to this question for all bipartite
scenarios. This remains true also if one considers not only spatial
correlations, but also spatiotemporal correlations, where each party is allowed
to apply their measurements in temporal succession; we provide an example of a
state together with observables such that ordinary spatial correlations are
local, while the spatiotemporal correlations reveal nonlocality. Moreover, we
find an extended version of Tsirelson's problem which, for each nontrivial Bell
scenario, is equivalent to the QWEP conjecture. This extended version can be
conveniently formulated in terms of steering the system of a third party.
Finally, a comprehensive mathematical appendix offers background material on
complete positivity, tensor products of C*-algebras, group C*-algebras, and
some simple reformulations of the QWEP conjecture.Comment: 57 pages, to appear in Rev. Math. Phy
Connes' embedding problem and Tsirelson's problem
We show that Tsirelson's problem concerning the set of quantum correlations
and Connes' embedding problem on finite approximations in von Neumann algebras
(known to be equivalent to Kirchberg's QWEP conjecture) are essentially
equivalent. Specifically, Tsirelson's problem asks whether the set of bipartite
quantum correlations generated between tensor product separated systems is the
same as the set of correlations between commuting C*-algebras. Connes'
embedding problem asks whether any separable II factor is a subfactor of
the ultrapower of the hyperfinite II factor. We show that an affirmative
answer to Connes' question implies a positive answer to Tsirelson's.
Conversely, a positve answer to a matrix valued version of Tsirelson's problem
implies a positive one to Connes' problem
Entanglement and non-locality are different resources
Bell's theorem states that, to simulate the correlations created by
measurement on pure entangled quantum states, shared randomness is not enough:
some "non-local" resources are required. It has been demonstrated recently that
all projective measurements on the maximally entangled state of two qubits can
be simulated with a single use of a "non-local machine". We prove that a
strictly larger amount of this non-local resource is required for the
simulation of pure non-maximally entangled states of two qubits
with
.Comment: 8 pages, 3 figure
Non-locality of non-Abelian anyons
Topological systems, such as fractional quantum Hall liquids, promise to
successfully combat environmental decoherence while performing quantum
computation. These highly correlated systems can support non-Abelian anyonic
quasiparticles that can encode exotic entangled states. To reveal the non-local
character of these encoded states we demonstrate the violation of suitable Bell
inequalities. We provide an explicit recipe for the preparation, manipulation
and measurement of the desired correlations for a large class of topological
models. This proposal gives an operational measure of non-locality for anyonic
states and it opens up the possibility to violate the Bell inequalities in
quantum Hall liquids or spin lattices.Comment: 7 pages, 3 figure
Topological analysis of chemical bonding in the layered FePSe3 upon pressure-induced phase transitions
The authors acknowledge the assistance of the University Computer Center of Saint-Petersburg State University in the accomplishment of high-performance computations. A.K. is grateful to the Latvian Council of Science project no. lzp-2018/2-0353 for financial support. Institute of Solid State Physics, University of Latvia as the Center of Excellence has received funding from the European Union’s Horizon 2020 Framework Programme H2020-WIDESPREAD-01-2016-2017-TeamingPhase2 under grant agreement No. 739508, project CAMART2.Two pressure-induced phase transitions have been theoretically studied in the layered iron phosphorus triselenide (FePSe3 ). Topological analysis of chemical bonding in FePSe3 has been performed based on the results of first-principles calculations within the periodic linear combination of atomic orbitals (LCAO) method with hybrid Hartree-Fock-DFT B3LYP functional. The first transition at about 6 GPa is accompanied by the symmetry change from R 3 ¯ to C2/m, whereas the semiconductor-to-metal transition (SMT) occurs at about 13 GPa leading to the symmetry change from C2/m to P 3 ¯ 1 m . We found that the collapse of the band gap at about 13 GPa occurs due to changes in the electronic structure of FePSe3 induced by relative displacements of phosphorus or selenium atoms along the c-axis direction under pressure. The results of the topological analysis of the electron density and its Laplacian demonstrate that the pressure changes not only the interatomic distances but also the bond nature between the intralayer and interlayer phosphorus atoms. The interlayer P-P interactions are absent in two non-metallic FePSe3 phases while after SMT the intralayer P-P interactions weaken and the interlayer P-P interactions appear.Latvian Council of Science project no. lzp-2018/2-0353; Institute of Solid State Physics, University of Latvia as the Center of Excellence has received funding from the European Union’s Horizon 2020 Framework Programme H2020-WIDESPREAD-01-2016-2017-TeamingPhase2 under grant agreement No. 739508, project CAMART2
Device-independent quantum key distribution secure against collective attacks
Device-independent quantum key distribution (DIQKD) represents a relaxation
of the security assumptions made in usual quantum key distribution (QKD). As in
usual QKD, the security of DIQKD follows from the laws of quantum physics, but
contrary to usual QKD, it does not rely on any assumptions about the internal
working of the quantum devices used in the protocol. We present here in detail
the security proof for a DIQKD protocol introduced in [Phys. Rev. Lett. 98,
230501 (2008)]. This proof exploits the full structure of quantum theory (as
opposed to other proofs that exploit the no-signalling principle only), but
only holds again collective attacks, where the eavesdropper is assumed to act
on the quantum systems of the honest parties independently and identically at
each round of the protocol (although she can act coherently on her systems at
any time). The security of any DIQKD protocol necessarily relies on the
violation of a Bell inequality. We discuss the issue of loopholes in Bell
experiments in this context.Comment: 25 pages, 3 figure
Zeros of the i.i.d. Gaussian power series: a conformally invariant determinantal process
Consider the zero set of the random power series f(z)=sum a_n z^n with i.i.d.
complex Gaussian coefficients a_n. We show that these zeros form a
determinantal process: more precisely, their joint intensity can be written as
a minor of the Bergman kernel. We show that the number of zeros of f in a disk
of radius r about the origin has the same distribution as the sum of
independent {0,1}-valued random variables X_k, where P(X_k=1)=r^{2k}. Moreover,
the set of absolute values of the zeros of f has the same distribution as the
set {U_k^{1/2k}} where the U_k are i.i.d. random variables uniform in [0,1].
The repulsion between zeros can be studied via a dynamic version where the
coefficients perform Brownian motion; we show that this dynamics is conformally
invariant.Comment: 37 pages, 2 figures, updated proof
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