Distance-based degrees of polarization for a quantum field

Abstract

It is well established that unpolarized light is invariant with respect to any SU(2) polarization transformation. This requirement fully characterizes the set of density matrices representing unpolarized states. We introduce the degree of polarization of a quantum state as its distance to the set of unpolarized states. We use two different candidates of distance, namely the Hilbert-Schmidt and the Bures metric, showing that they induce fundamentally different degrees of polarization. We apply these notions to relevant field states and we demonstrate that they avoid some of the problems arising with the classical definition.

Multipolar hierarchy of efficient quantum polarization measures

“…Some results along these lines have already been reported, but either they use magnitudes difficult to determine in practice, such as distances [19], generalized visibilities [20][21][22][23], and central moments [24], or they go only up to second order [25,26], and the pertinent extensions are difficult to discern.…”

Measures of quantum state purity and classical degree of polarization

“…Our analysis adds to and clarifies much of the discussion on measures of higher dimensional polarization in the literature [13][14][15][16][17][18][19][20], classifying the measures and analyzing their relationship.…”

Multimode polarization degree of mixture optical states in integrated directional couplers

“…Propagation of multimode quantum states in linear and non-linear N Â N couplers have been widely analyzed [17][18][19], however, the study of the generalized quantum polarization presents certain difficulties, in fact the study of quantum standard polarization is not an entirely obvious question, such as can be seen from the more specialized literature [20][21][22][23]. However, we can also say that some types of quantum states, such as multimode single photon states (or also coherent states), present an extraordinary analogy with multimode classical states [24] and moreover are acquiring a high interest in modern quantum optical technology [25], therefore it is worth presenting the main results about multimode polarization for mixture multimode single photon states in N Â N couplers.…”

“…However, it must be stressed that the physical meanings of Q and D are very different although they reflect the analogy commented above between classical multimode states and multimode single photon states. In this case, as we will show, the multimode polarization degree can be understood as a parameter directly related to the purity degree of the quantum state and not exactly as a rigorous quantum polarization degree, as is defined, for example, in [12,[20][21][22][23]. Indeed, if we diagonalize the quantum density matrix Q then each eigenvaluep will be the probability of measuring the single photon super-eigenstate j1 i (analogous to a classical super-modeẽ ) and the purity of the state is Tr Q 2 .…”