Related papers: No-Existence Of Generalize Diffusion
We define infinitesimal contact transformations for ordinary difference schemes as transformations that depend on $K+1$ lattice points $(K \geq 1)$ and can be integrated to form a local or global Lie group. We then prove that such contact…
In a recent breakthrough paper [M. Braverman, A. Garg, D. Pankratov, and O. Weinstein, From information to exact communication, STOC'13] Braverman et al. developed a local characterization for the zero-error information complexity in the…
In \cite{Ca2016} and \cite{Ca2018}, we introduced a notion of effective reducibility between set-theoretical $\Pi_{2}$-statements; in \cite{Ca2025}, this was extended to statements of arbitrary (potentially even infinite) quantifier…
For $n \geq 2$ we construct a measurable subset of the unit ball in $\mathbb{R}^n$ that does not contain pairs of points at distance 1 and whose volume is greater than $(1/2)^n$ times the volume of the ball. This disproves a conjecture of…
We study the computational complexity of two Boolean nonlinearity measures: the nonlinearity and the multiplicative complexity. We show that if one-way functions exist, no algorithm can compute the multiplicative complexity in time…
Considered are operators that leave the set of non-invertible (in the sense of Ehrenpreis) distributions stable. They simultaneously generalise the operation of convolution by a distribution with compact support and the operation of…
From the Schmidt representation we have that, up to local gates, every 2-qubit state can be written as $[\phi\rangle=\lambda_1 [00\rangle+\lambda_2 [11\rangle$ with $\lambda_1$ and $\lambda_2$ real numbers. For 3-qubits states, it is known,…
We show that any classical two-way communication protocol with shared randomness that can approximately simulate the result of applying an arbitrary measurement (held by one party) to a quantum state of $n$ qubits (held by another), up to…
The notorious Wigner's friend thought experiment (and modifications thereof) has in recent years received renewed interest especially due to new arguments that force us to question some of the fundamental assumptions of quantum theory. In…
We consider an epidemic model with distributed-contacts. When the contact kernel concentrates, one formally reaches a very degenerate Fisher-KPP equation with a diffusion term that is not in divergence form. We make an exhaustive study of…
In this comment, we want to emphasize that when the state of the two qubit is $|0>_{B}|1>_{A}$ or $|1>_{A}|0>_{B}$, Bob's Bell basis measurement outcome can not be $|\phi ^{\pm}>$. Also, when the product state is $|0> |0>$ or $|1> |1>$,…
In this work, we reveal a new type of impossibility discovered in our recent research which forbids comparing the closeness of multiple unknown quantum states with any non-trivial threshold in a perfect or an unambiguous way. This…
The standard quantum states of $n$ complex Grassmann variables with a free-particle Lagrangian transform as a spinor of SO(2n). However, the same `free-fermion' model has a non-linearly realized $SU(n|1)$ symmetry; it can be viewed as the…
Given a real, expansive dilation matrix we prove that any bandlimited function $\psi \in L^2(\mathbb{R}^n)$, for which the dilations of its Fourier transform form a partition of unity, generates a wavelet frame for certain translation…
A unified form for real and complex wave functions is proposed for the stationary case, and the quantum Hamilton-Jacobi equation is derived in the three-dimensional space. The difficulties which appear in Bohm's theory like the vanishing…
Inofrmation-theoretical restrictions on information transferred in the measurement of object S by information system O are studied. It is shown that such constraints, induced by Heisenberg commutation relations, result in the loss of…
We study the sector of large charge operators $\phi^n$ ($\phi$ being the complexified scalar field) in the $O(2)$ Wilson-Fisher fixed point in $4-\epsilon$ dimensions that emerges when the coupling takes the critical value $g\sim \epsilon$.…
In this letter, we show the impossibility of the general operation introduced by Pati [3] using two different but consistent principles (i) no-signalling (ii) non increase of entanglement under LOCC.
The fast computation of the Gauss hypergeometric function 2F1 with all its parameters complex is a difficult task. Although the 2F1 function verifies numerous analytical properties involving power series expansions whose implementation is…
In this paper we provide a simple proof of the fact that for a system of two spin-1/2 particles, and for a choice of observables, there is a unique state which shows Hardy-type nonlocality. Moreover, an explicit expression for the…