By Lajos Diosi
This brief and concise primer takes the vantage element of theoretical physics and the harmony of physics. It units out to strip the burgeoning box of quantum info technological know-how to its fundamentals via linking it to common options in physics. an intensive lecture instead of a accomplished textbook, this quantity relies on classes added over a number of years to complicated undergraduate and starting graduate scholars, yet primarily it addresses someone with a operating wisdom of easy quantum physics. Readers will locate those lectures a so much sufficient access element for theoretical stories during this box.
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Extra resources for A short course in quantum information theory an approach from theoretical physics
The procedure as well as the state |ψbig are called purification of ρˆ. An alternative axiomatic construction of q-theory can therefore be started from pure states instead of mixed ones. One must avoid a certain terminological inexactitude. Purification of q-states is not a q-operation to be performed on the given q-ensemble. Rather it is a mathematical construction, a nonlinear map. 47): the density matrix must be a mixture of uncorrelated (tensor product) states. For pure composite states this is only possible if the state vector is of the tensor product form: |ψAB = |ψA ⊗ |ψB .
7) For physical reasons, we call the 3-dimensional real Bloch vector n the polarization vector of the pure state |n . As we shall see, the states |±n can be interpreted as the two eigenstates of the corresponding electronic spin-component matrix. As ˆ of the electron was introduced by Pauli. a q-physical quantity, the spin-vector σ/2 ˆ the vector of polarization. 2 Pauli representation σ ˆx = 01 0 −i 1 0 , σ ˆy = , σ ˆz = . 8) The generic component of the polarization along the direction n reads: ˆ.
Yet, in some important cases, the measurement outcomes are independent of the order of measurements. The corresponding condition is that the matrices of the two q-physical quantities commute: ˆ B ˆ = 0. 32) Q-physical quantities with commuting matrices are called compatible. On compatible q-physical quantities one can obtain simultaneous information. Two arbitrarily chosen q-physical quantities are, however, not compatible in general. 11) of a given q-physical quantity, will always commute, they are compatible, hence they can be measured simultaneously, cf.