| Some Uncertainty Relation type inequalities for Composite Quantum Systems |
| کد مقاله : 1020-SHAA |
| نویسندگان |
|
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 |
| وضعیت: پذیرفته شده برای ارائه شفاهی |