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 info technology to its fundamentals by way of linking it to common innovations in physics. an intensive lecture instead of a accomplished textbook, this quantity is predicated on classes introduced over numerous years to complex undergraduate and starting graduate scholars, yet basically it addresses someone with a operating wisdom of easy quantum physics. Readers will locate those lectures a such a lot sufficient access element for theoretical experiences during this box.
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Additional info for A Short Course in Quantum Information Theory: An Approach From Theoretical Physics
For lack of a better idea, he alternates randomly between the measurement of the two physical quantities: ˆx ≡ 2 |1 1| − Iˆ . 33) The potential outcomes of the measurements are always ±1. The average frequency of the −1 is 25%, and in all these cases Bob obtains exact information about the qubit received from Alice. When, for instance, the measurement of σ ˆz yields −1 then the received state only can have been the |↑ x , never the |↑ z . Hence Bob can safely establish that Alice’s raw-key contains the 0 in the given binary digit.
7) for the inner product m|n of pure states can be derived in a single step starting from the corresponding two density matrices. Method: let us express | m|n |2 . 2. Unitary rotation for |↑ −→ |↓ . What can be the rotation vector α that rotates the state |↑ into the orthogonal state |↓ ? Let us make a simple choice for the rotation ˆ (α) and verify the axis! Calculate the matrix of the corresponding unitary rotation U result. 3. Density matrix eigenvalues and -states in terms of polarization. e.
This way the above q-state can be parametrized by that unit vector itself: |n = cos θ θ |↑ + eiϕ sin |↓ . 6) All pure states of a 2-dimensional q-system have thus been brought to a one-toone correspondence with the surface points of the 3-dimensional unit-sphere called the Bloch sphere. The two basis q-states |↑ , |↓ correspond to the north and south poles, respectively, on the Bloch sphere. Diametric points of the surface will always correspond to a pair of orthogonal q-states: −n| n = 0. Hence |±n form a basis.
A Short Course in Quantum Information Theory: An Approach From Theoretical Physics by Lajos Diosi