By Ben Q. Li
This brief and concise primer takes the vantage aspect of theoretical physics and the harmony of physics. It units out to strip the burgeoning box of quantum info technology to its fundamentals by means of linking it to common thoughts in physics. an in depth lecture instead of a accomplished textbook, this quantity is predicated on classes brought over a number of years to complicated undergraduate and starting graduate scholars, yet primarily it addresses somebody with a operating wisdom of simple quantum physics. Readers will locate those lectures a so much enough access aspect for theoretical experiences during this box.
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Extra info for A Short Course in Quantum Information Theory: An Approach From Theoretical Physics
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. the spectral expansion) of a density matrix in function of the polarization vector s. 4. Magnetic rotation for |↑ −→ |↓ . Determine the (constant) magnetic field ω that rotates the electronic spin from state |↓ into state |↑ .
For two-state systems, equivalently, we supposed in Sect. 3 that the polarization unit-vector n is a perfectly random unit vector on the Bloch sphere. 3 Single state determination: no-cloning An unknown q-state can only be determined if we have access to a large number of systems in the same state. If we possess but a single system we would first try copying it, multiplying it. If multiplication were successful, we would produce any number of clones and using this ensemble we would determine the state.
The pure state |↑ polarized in the z-direction, can be prepared from an unknown state if we simply measure the polarization σ ˆz . If the raw state was a totally random pure state then in half of the cases the measurement outcome is +1 and the resulting state is the demanded |↑ . On average, in the other half of the cases the outcome is −1. 10) so that again we obtain the desired state |↑ . The pure states prepared in the above way on demand will serve for preparation of arbitrarily prescribed mixed states.
A Short Course in Quantum Information Theory: An Approach From Theoretical Physics by Ben Q. Li