Some Uncertainty Relation type inequalities for Composite Quantum‎ ‎Systems
کد مقاله : 1020-SHAA
علی دادخواه *1، آقای دکتر محسن کیان2
1گروه محض
2دانشگاه بجنورد
چکیده مقاله:
‎Due to the postulates of Quantum Mechanics‎, ‎if the Hilbert spaces $mathscr{H}_1‎, ‎ldots‎, ‎mathscr{H}_k$ are the state spaces‎, ‎then the composite system is described by the tensor product Hilbert space $bigotimes_{i=1}^kmathscr{H}_i$‎. ‎Hence‎, ‎if $A_i in mathbb{B}(mathscr{H}_i)$ ($1leq i leq k$) are observables‎, ‎then $tilde{textbf{A}}=A_1otimes cdots otimes A_k in bigotimes_{i=1}^kmathbb{B}(mathscr{H}_i)$ is an observable in the composite system‎. ‎If $tilde{textbf{A}}$ and $tilde{textbf{B}}$ commute‎, ‎in particular‎, ‎if we consider‎
‎$ tilde{textbf{A}}=(I_1otimes cdotsotimes I_{i-1}otimes Aotimes I_{i+1}otimes cdotsotimes I_k) text{ and } tilde{textbf{B}}=(I_1otimes cdotsotimes I_{j-1}otimes Botimes I_{j+1}otimes cdotsotimes I_k)quad (ineq j)$‎, ‎then the classical Heisenberg uncertainty relation is trivial and therefore does not provide sufficient information‎
‎about the uncertainty of observables such $tilde{textbf{A}}$ and $tilde{textbf{B}}$‎. ‎In this paper‎, ‎based on the components of composite systems‎, ‎we define a variance and a covariance and present some uncertainty type inequalities that are not trivial for such $tilde{textbf{A}}$ and $tilde{textbf{B}}$ in composite systems‎.
کلیدواژه ها:
positive map‎, ‎quantum information‎, ‎tracial map‎, ‎uncertainty relation
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