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 details technology to its fundamentals via linking it to common ideas in physics. an intensive lecture instead of a complete textbook, this quantity relies on classes added over a number of years to complicated undergraduate and starting graduate scholars, yet basically it addresses an individual with a operating wisdom of simple quantum physics. Readers will locate those lectures a such a lot enough access element for theoretical stories during this box.
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Additional info for A Short Course in Quantum Information Theory: An Approach From Theoretical Physics
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. 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 |↑ .
49) ˆ ABint is zero then the tensor product initial state remains tensor product state, If H the dynamics does not create correlation between the q-subsystems. Non-vanishing ˆ ABint does usually create correlation. The motion of the whole q-system is reH versible (unitary), of course. But that of the subsystems is not. In case of tensor 8 This definition of q-separability was introduced by Werner . 6 Collective system 29 product initial state ρˆA (0) ⊗ ρˆB (0), for instance, the reduced q-dynamics of the subsystem A will represent the time-dependent irreversible q-operation MA (t) which we can formally write as: ˆAB (t)ˆ ˆ † (t) ≡ MA (t)ˆ ρA (0) ⊗ ρˆB (0)U ρA (0) .
Method: determine the mean statistical fluctuation of the counts N↑x , N↑y , N↑z . 3. Fidelity of qubit determination. Suppose Alice sends Bob a random qubit |n . Bob knows this but he does not know the state itself. Bob measures a polarization σ ˆm chosen along a random direction m. Let us determine the best expected fidelity of Bob’s state estimate. 4. Post-measurement depolarization. Alice prepares for Bob a state of polarization s which is unknown to Bob but he wishes to learn it. On the received state, Bob would measure the polarization along a random direction, for lack of a better idea.
A Short Course in Quantum Information Theory: An Approach From Theoretical Physics by Lajos Diosi