Global Information Balance in Quantum Measurements

We perform an information-theoretical analysis of quantum measurement processes and obtain the global information balance in quantum measurements, in the form of a closed chain equation for quantum mutual entropies. Our balance provides a tight and general entropic information-disturbance trade-off, and explains the physical mechanism underlying it. Finally, the single-outcome case, that is, the case of measurements with postselection, is briefly discussed.

Figure 1

The action of a quantum measurement ${\mathcal{M}}^Q$ on the input state ${\rho }^Q$ (top), can always be extended as a tripartite indirect measurement (bottom), where the apparatus $A$, after having properly interacted with the input system through $U^{QA}$, undergoes the measurement ${\mathcal{M}}^{A^{\prime }}$. The conditional output pure states $\{{{\rm Y}}_m^{R{Q}^{\prime }{A}^{\prime \prime }}{\}}_m$ are such that ${\mathrm{Tr}}_{R{A}^{\prime \prime }}[{{\rm Y}}_m^{R{Q}^{\prime }{A}^{\prime \prime }}]={\rho }_m^{Q^{\prime }}$, $\forall m$. See Eqs. (1, 2) in the text.