By Lajos Diosi
This brief and concise primer takes the vantage aspect of theoretical physics and the team spirit of physics. It units out to strip the burgeoning box of quantum details technology to its fundamentals by means of linking it to common thoughts in physics. an in depth lecture instead of a entire textbook, this quantity relies on classes brought over numerous 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 sufficient access aspect 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
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. Similarly, if the outcome of the measurement of σ ˆx was −1 then Bob establishes that the given digit of the key is 1.
Two-state q-key protocol. 1. Universality of Hadamard and phase operations. Let us show that all 2 × 2 unitary matrices (upto a complex phase) can be constructed by the repeated applicaˆ and the phase-operation Tˆ(ϕ). Method: use Euler angles tion of the Hadamard- H of rigid body rotation kinematics. 2. Statistical error of qubit determination. Suppose Alice hands over N identically prepared qubits ρˆ to Bob but she does not tell Bob what the state ρˆ is. 2. 4 Applications of no-cloning and indistinguishability 51 the estimation errors ∆sx , ∆sy , ∆sz in function of s and the number of single state measurements.
Pure state fidelity from density matrices. 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.
A short course in quantum information theory an approach from theoretical physics by Lajos Diosi