A Short Course in Quantum Information Theory: An Approach by Lajos Diosi

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By Lajos Diosi

This brief and concise primer takes the vantage element of theoretical physics and the cohesion 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 thoughts in physics. an in depth lecture instead of a entire textbook, this quantity is predicated on classes introduced over a number of years to complicated undergraduate and starting graduate scholars, yet primarily it addresses someone with a operating wisdom of uncomplicated quantum physics. Readers will locate those lectures a so much 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.

4. Magnetic rotation for |↑ −→ |↓ . Determine the (constant) magnetic field ω that rotates the electronic spin from state |↓ into state |↑ . How long time must the field be switched on? 5. Interrelated q-bit physical quantities. Write down all pairwise relationships for the matrices σ ˆn , Pˆn , Pˆ−n . 6. Mixing non-orthogonal polarizations. Suppose we mix the pure states |↑ z and |↑ x together at rate 1/3 : 2/3. Write down the polarization vector s of the resulting mixed state. , on a single qubit.

The latter is this. Each banknote contains a sequence of N independent two-state q-systems (qubits). Each qubit is either |0 or |1 at random4 . : 4 Despite identical notations, one should not confuse |0 , |1 in this Section with the computational basis in the rest of the volume. 48 6 One-qubit manipulations |1 , |0 , |0 , . . , |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.

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