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By Lajos Diosi

This brief and concise primer takes the vantage element of theoretical physics and the team spirit of physics. It units out to strip the burgeoning box of quantum info technological know-how to its fundamentals by means of linking it to common suggestions in physics. an in depth lecture instead of a complete textbook, this quantity is predicated on classes brought over a number of years to complex undergraduate and starting graduate scholars, yet primarily it addresses a person with a operating wisdom of simple quantum physics. Readers will locate those lectures a so much sufficient access element for theoretical reviews during this box.

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Example text

E. the qubit, is an abstract two-state q-system. This Chapter is technical: you learn standard mathematics of a single abstract qubit. 1). The notion of qubit is best realized in the computational basis. We introduce the computational basis vectors |0 and |1 : |x x| = Iˆ , {|x ; x = 0, 1} , x |x = δx x . 1) x=0,1 Also the primitive binary q-physical quantity x ˆ is defined in the computational basis: x |x x| = |1 1| . 2) x=0,1 This is the (singular) 2 × 2 hermitian matrix of the qubit, as q-physical quantity.

10) λ If E = 0 then all wλ vanish except for a single one which is unity; the composite state vector becomes a tensor product which is, indeed, not entangled. 11) λ and this state we consider maximally entangled. 6). 10) between entropy and entanglement can be verified later, in the possession of the rudiments of information theory in Sects. 7. 1 of an arbitrary q-state: S(ˆ ρ) = − tr (ˆ ρ log ρˆ) ; 0 ≤ S ≤ log d . 12) The von Neumann entropy is zero for pure states and may serve as a measure of the mixedness of the state.

0 , |1 , |1 . 31) Alice and the bank log the otherwise public serial number together with the encoded N -digit binary “q-serial-number”. The latter as well as the logs are kept private. At the same time, both states |0 , |1 can be published. If they were orthogonal to each other, Bob would make any number of perfect forges even without destroying the original banknotes. g. 32) then Bob can never profit from forgery. Even doing his best, Bob is not able to produce a sufficient number of high fidelity copies.

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