proofsmallestThe Kochen–Specker theorem states that noncontextual hidden variable theories are incompatible with quantum mechanics.We provide a state-independent proof of the Kochen–Specker theorem using the smallest number of projectors,i.e.,thirty rank-2 projectors,associated with the Mermin pentagram...
Taylor’s theorem approximates the output of a function f ( x ) around a given point, such as x = a , by providing a k-times differentiable function and a polynomial of degree k, which is known as the kth-order Taylor polynomial. In other words, the first-order Taylor polynomial prov...
Ionizing radiation refers to charged (𝛼α and 𝛽β particles, and protons) and uncharged (neutrons) particles or electromagnetic radiation (X-rays and 𝛾γ-rays) that have enough energy to ionize atoms or molecules by detaching electrons from them. Cosmic rays are also ionizing radiation....
Theorem: Let │ψAB∈HA ⊗ HB. Then ∃ orthonormal |kA〉∈ HA and |kB〉∈ HB such that │ψAB=∑kλk|kA〉|kB〉, where ∑kλk2=1 and ∀k, λk≥0.λk are known as the Schmidt coefficients for |ψA B〉. Proof: In terms of basis ...
The famous, yet unsolved, Fermi-Hubbard model for strongly-correlated electronic systems is a prominent target for quantum computers. However, accurately representing the Fermi-Hubbard ground state for large instances may be beyond the reach of near-term
Theorem 1.1 Assume that [Math Processing Error](V) holds. Then equation (1.1) admits a ground state solution and infinitely many pairs of geometrically distinct solutions.2 Proof of theorem Throughout this paper, we denote by [Math Processing Error]‖⋅‖s the usual norm of the space [Math...
butter to quantum information theorists; moreover the language of functional analysis was not foreign to me either and so I believed I ought to have more than it should take to make the explanations clear; in my mind I had a clear theorem, together with an airtight proof, to communicate. ...
If the combination of parameters Ω0/ω and Ω1/ω gives rise to unstable solutions of the Mathieu equation, the quasienergy spectrum of the parametrically driven oscillator becomes absolutely continuous37 so that the system can absorb an infinite amount of energy from the drive; this case is ...
In this work, we provide a heuristic derivation of AMP and its state evolution, based on the idea of "first-order cancellation," that provides insights missing from the LBP derivation while being much shorter than the rigorous SE proof. 展开 ...
This note revisits the proof of the Steady-State Growth Theorem,first given by Uzawa in1961.We provide a clear statement of the theorem,discuss intuition for why it holds,and present a new,elegant proof due to Schlicht(2006).Key Words:Steady state,balanced growth,labor-augmenting technical ...