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According to Wigner theorem, transformations of quantum states which preserve the probabilities are either unitary or antiunitary. This short communication presents an elementary proof of this theorem that significantly departs from the numerous ones already existing in the literature. The main line of the argument remains valid even in quantum field theory where Hilbert spaces are non-separable.
Mapping is one of the essential steps by which fermionic systems can be solved by quantum computers. In this letter, we give a unified framework of transformations mapping fermionic systems to qubit systems. Many existed transformations, such as Jord
A sequence of random variables is called exchangeable if the joint distribution of the sequence is unchanged by any permutation of the indices. De Finettis theorem characterizes all ${0,1}$-valued exchangeable sequences as a mixture of sequences of i
We give an elementary proof of Grothendiecks non-vanishing Theorem: For a finitely generated non-zero module $M$ over a Noetherian local ring $A$ with maximal ideal $m$, the local cohomology module $H^{dim M}_{m}(M)$ is non-zero.
Even the most sophisticated artificial neural networks are built by aggregating substantially identical units called neurons. A neuron receives multiple signals, internally combines them, and applies a non-linear function to the resulting weighted su
Hanners theorem is a classical theorem in the theory of retracts and extensors in topological spaces, which states that a local ANE is an ANE. While Hanners original proof of the theorem is quite simple for separable spaces, it is rather involved for