scholarly journals Strongly nonlocal unextendible product bases do exist

Quantum ◽  
2022 ◽  
Vol 6 ◽  
pp. 619
Author(s):  
Fei Shi ◽  
Mao-Sheng Li ◽  
Mengyao Hu ◽  
Lin Chen ◽  
Man-Hong Yung ◽  
...  
Keyword(s):  
Quantum Nonlocality ◽  
Local Measurement ◽  
Minimum Dimension ◽  
Local Measurements ◽  
Orthogonal Product ◽  
Open Question

A set of multipartite orthogonal product states is locally irreducible, if it is not possible to eliminate one or more states from the set by orthogonality-preserving local measurements. An effective way to prove that a set is locally irreducible is to show that only trivial orthogonality-preserving local measurement can be performed to this set. In general, it is difficult to show that such an orthogonality-preserving local measurement must be trivial. In this work, we develop two basic techniques to deal with this problem. Using these techniques, we successfully show the existence of unextendible product bases (UPBs) that are locally irreducible in every bipartition in d⊗d⊗d for any d≥3, and 3⊗3⊗3 achieves the minimum dimension for the existence of such UPBs. These UPBs exhibit the phenomenon of strong quantum nonlocality without entanglement. Our result solves an open question given by Halder et al. [Phys. Rev. Lett. 122, 040403 (2019)] and Yuan et al. [Phys. Rev. A 102, 042228 (2020)]. It also sheds new light on the connections between UPBs and strong quantum nonlocality.

Constructing the three-qudit unextendible product bases with strong nonlocality

2022 ◽  
Author(s):  
Bichen Che ◽  
Zhao Dou ◽  
Xiubo Chen ◽  
Yu Yang ◽  
Li Jian ◽  
...  
Keyword(s):  
Positive Answer ◽  
Quantum Nonlocality ◽  
Rubik's Cube ◽  
The Family ◽  
Rubik’S Cube ◽  
Orthogonal Product ◽  
Open Question ◽  
General Method

Abstract The unextendible product bases (UPB) are interesting members of the family of orthogonal product bases. In this paper, we investigate the construction of 3-qudit UPB with strong nonlocality. First, a UPB set in ${{C}^{3}}\otimes {{C}^{3}}\otimes {{C}^{3}}$ of size 19 is presented based on the Shifts UPB. By mapping the system to a Rubik's Cube, we provide a general method of constructing UPB in ${{C}^{d}}\otimes {{C}^{d}}\otimes {{C}^{d}}$ of size ${{\left(d-1 \right)}^{3}}+2d+5$, whose corresponding Rubik's Cube is composed of four parts. Second, for the more general case where the dimensions of parties are different, we extend the classical tile structure to the 3-qudit system and propose the Tri-tile structure. By means of this structure, a ${{C}^{4}}\otimes {{C}^{4}}\otimes {{C}^{5}}$ system of size 38 is obtained based on a ${{C}^{3}}\otimes {{C}^{3}}\otimes {{C}^{4}}$ system of size 19. Then, we generalize this approach to ${{C}^{{{d}_{1}}}}\otimes {{C}^{{{d}_{2}}}}\otimes {{C}^{{{d}_{3}}}}$ system which also consists of four parts. Our research provides a positive answer to the open question raised in [Halder, et al., PRL, 122, 040403 (2019)], indicating that there do exist UPB that can exhibit strong quantum nonlocality without entanglement.

scholarly journals Strong quantum nonlocality for unextendible product bases in heterogeneous systems

2021 ◽  
Author(s):  
Fei Shi ◽  
Mao-Sheng Li ◽  
Lin Chen ◽  
Xiande Zhang
Keyword(s):  
Heterogeneous Systems ◽  
Quantum Nonlocality ◽  
Minimum Size ◽  
Orthogonal Product ◽  
Open Question

Abstract A set of multipartite orthogonal product states is strongly nonlocal if it is locally irreducible in every bipartition, which shows the phenomenon of strong quantum nonlocality without entanglement. It is known that unextendible product bases (UPBs) can show the phenomenon of quantum nonlocality without entanglement. Thus it is interesting to investigate the strong quantum nonlocality for UPBs. Most of the UPBs with the minimum size cannot demonstrate strong quantum nonlocality. In this paper, we construct a series of UPBs with different large sizes in dAXdBxdC and dAxdBxdCxdD for dA, dB, dC, dD ≧3, and we also show that these UPBs have strong quantum nonlocality, which answers an open question given by Halder et al. [Phys. Rev. Lett. 122, 040403 (2019)] and Yuan et al. [Phys. Rev. A 102, 042228 (2020)] for any possible three and four-partite systems. Furthermore, we propose an entanglement-assisted protocol to locally discriminate the UPB in 3x3x4, and it consumes less entanglement resource than the teleportation-based protocol. Our results build the connection between strong quantum nonlocality and UPBs.

scholarly journals Distant foreground and the Planck-derived Hubble constant

2020 ◽  
Vol 492 (4) ◽  
pp. 5052-5056 ◽  
Author(s):  
V N Yershov ◽  
A A Raikov ◽  
N Yu Lovyagin ◽  
N P M Kuin ◽  
E A Popova
Keyword(s):  
Hubble Constant ◽  
Temperature Fluctuations ◽  
Coarse Grain ◽  
Model Parameters ◽  
Local Measurement ◽  
Microwave Background ◽  
Random Samples ◽  
Local Measurements ◽  
Grain Dust ◽  
Cmb Temperature

ABSTRACT It is possible to reduce the discrepancy between the local measurement of the cosmological parameter H0 and the value derived from the Planck measurements of the cosmic microwave background (CMB) by considering contamination of the CMB by emission from some medium around distant extragalactic sources, such as extremely cold coarse-grain dust. Though being distant, such a medium would still be in the foreground with respect to the CMB, and, as any other foreground, it would alter the CMB power spectrum. This could contribute to the dispersion of CMB temperature fluctuations. By generating a few random samples of CMB with different dispersions, we have checked that the increased dispersion leads to a smaller estimated value of H0, the rest of the cosmological model parameters remaining fixed. This might explain the reduced value of the Planck-derived parameter H0 with respect to the local measurements. The signature of the distant foreground in the CMB traced by supernovae (SNe) was previously reported by the authors of this paper – we found a correlation between the SN redshifts, zSN, and CMB temperature fluctuations at the SNe locations, TSN. Here we have used the slopes of the regression lines $T_{\rm SN}\, /\, z_{\rm SN}$ corresponding to different Planck wavebands in order to estimate the possible temperature of the distant extragalactic medium, which turns out to be very low, about 5 K. The most likely ingredient of this medium is coarse-grain (grey) dust, which is known to be almost undetectable, except for the effect of dimming remote extragalactic sources.

scholarly journals A COMPLETELY ENTANGLED SUBSPACE OF MAXIMAL DIMENSION

2006 ◽  
Vol 04 (02) ◽  
pp. 325-330 ◽  
Author(s):  
B. V. RAJARAMA BHAT
Keyword(s):  
Tensor Product ◽  
Hilbert Spaces ◽  
Product Formula ◽  
Maximal Dimension ◽  
Maximum Dimension ◽  
Dimension Formula ◽  
Finite Dimensional ◽  
Minimum Dimension ◽  
Orthogonal Product ◽  
Product Vector

Consider a tensor product [Formula: see text] of finite-dimensional Hilbert spaces with dimension [Formula: see text], 1 ≤ i ≤ k. Then the maximum dimension possible for a subspace of [Formula: see text] with no non-zero product vector is known to be d1 d2…dk - (d1 + d2 + … + dk + k - 1. We obtain an explicit example of a subspace of this kind. We determine the set of product vectors in its orthogonal complement and show that it has the minimum dimension possible for an unextendible product basis of not necessarily orthogonal product vectors.

Quantum nonlocality of multipartite orthogonal product states

2016 ◽  
Vol 93 (3) ◽  
Author(s):  
Guang-Bao Xu ◽  
Qiao-Yan Wen ◽  
Su-Juan Qin ◽  
Ying-Hui Yang ◽  
Fei Gao
Keyword(s):  
Quantum Nonlocality ◽  
Orthogonal Product

Mars: was There an Ancient Eden?

1997 ◽  
Vol 161 ◽  
pp. 203-218 ◽  
Author(s):  
Tobias C. Owen
Keyword(s):  
Positive Answer ◽  
Biogenic Elements ◽  
Habitable Zones ◽  
The Face ◽  
The Origin Of Life ◽  
Early Mars ◽  
Favorable Conditions ◽  
Open Question ◽  
Rocky Planets ◽  
Impact Erosion

AbstractThe clear evidence of water erosion on the surface of Mars suggests an early climate much more clement than the present one. Using a model for the origin of inner planet atmospheres by icy planetesimal impact, it is possible to reconstruct the original volatile inventory on Mars, starting from the thin atmosphere we observe today. Evidence for cometary impact can be found in the present abundances and isotope ratios of gases in the atmosphere and in SNC meteorites. If we invoke impact erosion to account for the present excess of129Xe, we predict an early inventory equivalent to at least 7.5 bars of CO2. This reservoir of volatiles is adequate to produce a substantial greenhouse effect, provided there is some small addition of SO2(volcanoes) or reduced gases (cometary impact). Thus it seems likely that conditions on early Mars were suitable for the origin of life – biogenic elements and liquid water were present at favorable conditions of pressure and temperature. Whether life began on Mars remains an open question, receiving hints of a positive answer from recent work on one of the Martian meteorites. The implications for habitable zones around other stars include the need to have rocky planets with sufficient mass to preserve atmospheres in the face of intensive early bombardment.

On the Semantic Content of Grammatical Gender and Its Impact on the Representation of Human Referents

2010 ◽  
Vol 57 (5) ◽  
pp. 367-375 ◽  
Author(s):  
Lisa Irmen ◽  
Julia Kurovskaja
Keyword(s):  
Semantic Content ◽  
Grammatical Gender ◽  
Differential Effects ◽  
Gender Information ◽  
Masculine Role ◽  
Feminine Role ◽  
And Gender ◽  
Gender Categories ◽  
Open Question

Grammatical gender has been shown to provide natural gender information about human referents. However, due to formal and conceptual differences between masculine and feminine forms, it remains an open question whether these gender categories influence the processing of person information to the same degree. Experiment 1 compared the semantic content of masculine and feminine grammatical gender by combining masculine and feminine role names with either gender congruent or incongruent referents (e.g., Dieser Lehrer [masc.]/Diese Lehrerin [fem.] ist mein Mann/meine Frau; This teacher is my husband/my wife). Participants rated sentences in terms of correctness and customariness. In Experiment 2, in addition to ratings reading times were recorded to assess processing more directly. Both experiments were run in German. Sentences with grammatically feminine role names and gender incongruent referents were rated as less correct and less customary than those with masculine forms and incongruent referents. Combining a masculine role name with an incongruent referent slowed down reading to a greater extent than combining a feminine role name with an incongruent referent. Results thus specify the differential effects of masculine and feminine grammatical gender in denoting human referents.

Die Europäische Union: eine neue Supermacht mit imperialen Ambitionen?

2005 ◽  
Vol 35 (139) ◽  
pp. 247-266 ◽  
Author(s):  
Hans-Jürgen Bieling
Keyword(s):  
World War Ii ◽  
Economic Crisis ◽  
Europäische Union ◽  
World War ◽  
Political Sovereignty ◽  
Military Conflicts ◽  
Imperial Power ◽  
International Role ◽  
Open Question ◽  
The Eu

Recent theoretical conceptions of imperialism may be useful correctives against idealising and harmonising views of international interdependency and co-operation. Analytically, however, they are not necessarily helpful. In terms of the EU, they do not really comprehend its particular international role. Despite improved financial and military capacities, the EU represents not yet an imperial power. Instead, it still pursues a rather hegemonic foreign policy approach due to internal economic restrictions, fragmented political sovereignty and the historical experiences of beneficial economic and political co-operation after World War II. Eventually, however, it remains an open question, whether the multilateralist, law-based and co-operative posture of the EU will prevail even under conditions of economic crisis and further military conflicts in the adjacent neighbourhood.

Tax competition and the activity of the regional tax policy

2020 ◽  
pp. 5-27
Author(s):  
S. M. Drobyshevsky ◽  
N. S. Kostrykina ◽  
A. V. Korytin
Keyword(s):  
Tax Competition ◽  
Tax Policy ◽  
Fiscal Federalism ◽  
Policy Instruments ◽  
Tax Incentives ◽  
Fiscal Autonomy ◽  
Tax Legislation ◽  
Tax Exemptions ◽  
Open Question ◽  
Regional Budgets

The problem of efficiency of regional tax expenditures is an actual issue of the fiscal policy and fiscal federalism in Russia. A large fiscal autonomy allows federal subjects to realize a more active tax policy to attract new investments. One cannot claim current fiscal powers of the Russian regions to be wide. However, not all the regions use even existing tax policy instruments. Moreover, out of the regions that use them only few provide incentives to stimulate investment decisions. Others use regional tax measures to support businesses that already have strong positions in the region. And it is an open question whether such tax incentives are efficient. On the other hand, an aggressive tax competition for investors can also be wasteful for regional budgets. In this paper, we calculate indicators that characterize the depth and scope of tax exemptions provided at the regional level. The calculations are based on the open tax statistics. Through the analysis of the tax legislation as well as the economic structure of selected regions, we reveal the inducements of their higher activity: federal regional tax policy, tax competition or benefits for budget-forming companies of the region.

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