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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Some improved Caffarelli-Kohn-Nirenberg inequalities and uncertainty principles
Caffarelli Kohn-Nierberg不等式 不确定性原理
2023/11/13
In this talk we introduce some improved Caffarelli-Kohn-Nirenberg inequalities and uncertainty principle for complex- and vector-valued functions on ?n, which is a further study of the results given i...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Quantum Inequalities and Their Extremisers
量子不等式 极端值 量子对称性
2023/4/14
In this talk, we shall present a series of inequalities for quantum symmetries such as Hausdorff-Young inequalities, Young's inequalities, uncertainty principles, sumset estimation and entropic inequa...
EPR argument and Bell inequalities for Bose-Einstein spin condensates
Condensate spin state quantum mechanical particles
2014/12/19
We discuss the properties of two Bose-Einstein condensates in different spin states, represented quantum mechanically by a double Fock state. Individual measurements of the spins of the particles are ...
On generalized Cramér-Rao inequalities, generalized Fisher informations and characterizations of generalized q-Gaussian distributions
generalized Cramer-Rao inequalities generalized Fisher informations characterizations of generalized q-Gaussian distributions Mathematical Physics
2012/6/19
This paper deals with Cram\'er-Rao inequalities in the context of nonextensive statistics and in estimation theory. It gives characterizations of generalized q-Gaussian distributions, and introduces g...
A complete set of multidimensional Bell inequalities
multidimensional Bell inequalities Quantum Physics
2011/9/30
Abstract: We give a multidimensional generalisation of the complete set of Bell-correlation inequalities given by Werner and Wolf for the two-dimensional case. Our construction applies for the n parti...
Induced Metric And Matrix Inequalities On Unitary Matrices
eigenvalues, metric, singular values, quantum information science, quantum mechanics, unitary matrices
2011/8/25
Abstract: We show that any symmetric norm on $\bR^n$ induces a metric on U(n), the group of all $n\times n$ unitary matrices. Using the same technique, we prove an inequality concerning the eigenvalue...
Infinitely many constrained inequalities for the von Neumann entropy
von Neumann entropy Quantum Physics
2011/9/29
Abstract: We exhibit infinitely many new, constrained inequalities for the von Neumann entropy, and show that they are independent of each other and the known inequalities obeyed by the von Neumann en...
Extension of Berezin-Lieb Inequalities
Berezin-Lieb Inequalities partition function phase space Quantum Physics
2011/7/29
Abstract: The Berezin-Lieb inequalities provide upper and lower bounds for a partition function based on phase space integrals that involve the Glauber-Sudarshan and Husimi representations, respective...
Photon Antibunching, Sub-Poisson Statistics and Cauchy-Bunyakovsky and Bell's Inequalities
Photon Antibunching Sub-Poisson Statistics Cauchy-Bunyakovsky Quantum Physics
2011/7/27
Abstract: We discuss some mathematical aspects of photon antibunching and sub-Poisson photon statistics. It is known that Bell's inequalities for entangled states can be reduced to the Cauchy-Bunyakov...
Quantum Bell Inequalities from Macroscopic Locality
Macroscopic Locality Bell Inequalities Quantum Physics
2010/11/8
We propose a method to generate analytical quantum Bell inequalities based on the principle of Macroscopic Locality. By imposing locality over binary processings of virtual macroscopic intensities, we...
Probabilistic Inequalities and Upper Probabilities in Quantum Mechanical Entanglement
Probabilistic Inequalities Upper Probabilities Quantum Mechanical Entanglement
2010/11/5
In this paper we analyze the existence of joint probabilities for the Bell-type and GHZ entangled states. We then propose the usage of nonmonotonic upper probabilities as a tool to derive consistent j...
Fano type quantum inequalities in terms of $q$-entropies
Fano inequality Tsallis q-entropy relative q-entropy entanglement fidelity
2010/11/4
Generalizations of the quantum Fano inequality are considered. The notion of $q$-entropy exchange is introduced. This quantity is concave in each of its two arguments. For $q\geq0$, the inequality of ...
Non-adaptive Measurement-based Quantum Computation and Multi-party Bell Inequalities
Non-adaptive Measurement-based Quantum Computation Multi-party Bell Inequalities
2010/10/21
Quantum correlations exhibit behaviour that cannot be resolved with a local hidden variable picture of the world. In quantum information, they are also used as resources for information processing tas...
Entropic Inequalities for a Class of Quantum Secret Sharing States
entropic inequalities monotone span programs quantum secret sharing stabilizer states von Neumann entropy
2010/10/18
It is well-known that von Neumann entropy is nonmonotonic unlike Shannon entropy (which is
monotonically nondecreasing). Consequently, it is difficult to relate the entropies of the subsystems of a g...
Squeezing Inequalities and Entanglement for Identical Particles
Squeezing Inequalities Entanglement Identical Particles
2010/10/18
By identifying non-local effects in systems of identical Bosonic qubits through correlations of their commuting observables, we show that entanglement is not necessary to violate certain squeezing ine...