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 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.

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.

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.

Examining perceptions of stress, wellbeing and fear among Hungarian adolescents and their parents under lockdown during the COVID-19 pandemic

2020 ◽  
Author(s):  
Gabor Csikos ◽  
Krisztina Dr Törő ◽  
Judit Mokos ◽  
Sandor Rozsa ◽  
Hadházi Éva ◽  
...  
Keyword(s):  
Family Relationships ◽  
Parental Stress ◽  
Significant Negative Correlation ◽  
Post Traumatic Stress ◽  
Natural Catastrophes ◽  
Parents And Children ◽  
Wellbeing Index ◽  
The Family ◽  
Post Traumatic ◽  
Open Question

Intensified anxiety responses and even symptoms of post-traumatic stress are commonly observed under quarantine conditions. In this study, the effects on fear, anxiety and wellbeing of the recent pandemic caused by SARS-CoV-2 were investigated in a sample of otherwise healthy Hungarians. Taking the family as a microsystem, differences in gender, age, family relationships and time spent in isolation were the main focus of this investigation. 346 parent-child dyads were examined; the children were 11-17 years of age. Standard psychological questionnaires (Perceived Stress Scale, WHO Wellbeing Index), and an open question test (the Metamorphosis test) were used, and the results analysed with the aid of basic statistical methods. Stress levels and wellbeing displayed a significant negative correlation with each other in both parents and children. Parental stress and levels of wellbeing had a weak but significant impact on the wellbeing of their children. Among the demographic variables examined, none of them was found to explain the wellbeing or stress level of parents. Natural catastrophes, such as pandemics, create a stressful social environment for parents, and therefore directly impact the psychological wellbeing of all family members.

scholarly journals Algebraic conditions and the sparsity of spectrally arbitrary patterns

2021 ◽  
Vol 9 (1) ◽  
pp. 257-274
Author(s):  
Louis Deaett ◽  
Colin Garnett
Keyword(s):  
Major Goal ◽  
Algebraic Condition ◽  
Open Question ◽  
Algebraic Tool ◽  
General Method ◽  
Square Matrix ◽  
Spectrally Arbitrary

Abstract Given a square matrix A, replacing each of its nonzero entries with the symbol * gives its zero-nonzero pattern. Such a pattern is said to be spectrally arbitrary when it carries essentially no information about the eigenvalues of A. A longstanding open question concerns the smallest possible number of nonzero entries in an n × n spectrally arbitrary pattern. The Generalized 2n Conjecture states that, for a pattern that meets an appropriate irreducibility condition, this number is 2n. An example of Shitov shows that this irreducibility is essential; following his technique, we construct a smaller such example. We then develop an appropriate algebraic condition and apply it computationally to show that, for n ≤ 7, the conjecture does hold for ℝ, and that there are essentially only two possible counterexamples over ℂ. Examining these two patterns, we highlight the problem of determining whether or not either is in fact spectrally arbitrary over ℂ. A general method for making this determination for a pattern remains a major goal; we introduce an algebraic tool that may be helpful.

Hardy spaces on ZN

2002 ◽  
Vol 132 (1) ◽  
pp. 25-43 ◽  
Author(s):  
Santiago Boza ◽  
María J. Carro
Keyword(s):  
Maximal Function ◽  
Hardy Spaces ◽  
Atomic Decomposition ◽  
Classical Case ◽  
Positive Answer ◽  
Riesz Transforms ◽  
Homogeneous Type ◽  
Spaces Of Homogeneous Type ◽  
Definition Of ◽  
Open Question

The work of Coifman and Weiss concerning Hardy spaces on spaces of homogeneous type gives, as a particular case, a definition of Hp(ZN) in terms of an atomic decomposition.Other characterizations of these spaces have been studied by other authors, but it was an open question to see if they can be defined, as it happens in the classical case, in terms of a maximal function or via the discrete Riesz transforms.In this paper, we give a positive answer to this question.

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