## A Short Course In Quantum Information Theory An Approach by Lajos Diosi

By Lajos Diosi

This brief and concise primer takes the vantage aspect of theoretical physics and the solidarity of physics. It units out to strip the burgeoning box of quantum details technological know-how to its fundamentals via linking it to common options in physics. an intensive lecture instead of a complete textbook, this quantity relies on classes introduced over a number of years to complex undergraduate and starting graduate scholars, yet basically it addresses someone with a operating wisdom of simple quantum physics. Readers will locate those lectures a such a lot enough access element for theoretical reviews during this box.

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We could try to duplicate the unknown pure state |ψ , cf. Sect. 3, of our q-system by cloning it to replace the prepared state |ψ0 of another q-system with the same dimension of Hilbert space. Let us prove that the map |ψ ⊗ |ψ0 → |ψ ⊗ |ψ can not be unitary. Method: let us test whether the above transformation preserves the value of inner products. 5 Two-state q-system: qubit representations Obviously the simplest q-systems are the two-state systems. Typical realization are an atom with its ground state and one of its excited states, a photon with its two polarization states, or an electronic spin with its “up” and “down” states.

We can suppose more knowledge and less ignorance. To make the definitions more operational, it is common to personalize the one who knows the state and the other one who does not. 32) between which she has decided upon her tossing a coin. That is all that also Bob knows but he does not know which of the two states he has actually received. We say that Bob has an unknown qubit it this sense. If interested, he must perform a q-measurement. 2 can be transformed into each other by the conventional mapping of the corresponding bases: |0 = |↑ = 1 0 , |1 = |↓ = .

5 Approximate state determination and cloning Let us calculate the average fidelity between an unknown qubit |n and its faint copy |m . Suppose Alice passes a state |n = |↑ to Bob. Bob needs a copy. 21) and he prepares his copy |m after the resulting state |↑ z or |↓ z according to the measurement outcome ±1. The average fidelity of the copy is: p↑ | ↑|↑ z |2 + p↓ | ↑|↓ z |2 . 22) Since Bob could only choose the direction z at random, the expected fidelity of the copy will be the isotropic average over all directions, that is 2/3.