An apparatus (200, 200', 200"), comprising an input configured to receive a modulated optical data signal, the modulated optical data signal comprising components of a plurality of polarizations, the plurality of polarizations comprising at least a first polarization and a second polarization, a first optical detector (PD#1) coupled to the input to receive the modulated optical data signal, wherein the first optical detector (PD#1) is polarization-selective or polarization-sensitive to the first polarization and passes components of the modulated optical data signal having the second polarization, and wherein the first optical detector (PD#1) is configured to output a first electrical signal, a second optical detector (PD#2) coupled to the first optical detector (PD#1) to receive from the first optical detector (PD#1) the components of the modulated optical data signal having the second polarization, wherein the second optical detector (PD#2) is configured to output a second electrical signal, and a processor, the processor configured to • apply a Kramers-Kronig, KK, process (208a, 208b) to the first electrical signal and to the second electrical signal, and • output the data signal using the KK processed first and second electrical signals (210a, 210b), wherein a combiner, like an optical coupler, is connected between the input and the first optical detector (PD#1), the combiner configured to combine the modulated optical data signal with an unmodulated optical signal such that the unmodulated optical signal serves as a KK carrier for the first and second polarizations. an input configured to receive a modulated optical data signal, the modulated optical data signal comprising components of a plurality of polarizations, the plurality of polarizations comprising at least a first polarization and a second polarization, a first optical detector (PD#1) coupled to the input to receive the modulated optical data signal, wherein the first optical detector (PD#1) is polarization-selective or polarization-sensitive to the first polarization and passes components of the modulated optical data signal having the second polarization, and wherein the first optical detector (PD#1) is configured to output a first electrical signal, a second optical detector (PD#2) coupled to the first optical detector (PD#1) to receive from the first optical detector (PD#1) the components of the modulated optical data signal having the second polarization, wherein the second optical detector (PD#2) is configured to output a second electrical signal, and a processor, the processor configured to • apply a Kramers-Kronig, KK, process (208a, 208b) to the first electrical signal and to the second electrical signal, and • output the data signal using the KK processed first and second electrical signals (210a, 210b), • apply a Kramers-Kronig, KK, process (208a, 208b) to the first electrical signal and to the second electrical signal, and • output the data signal using the KK processed first and second electrical signals (210a, 210b), wherein a combiner, like an optical coupler, is connected between the input and the first optical detector (PD#1), the combiner configured to combine the modulated optical data signal with an unmodulated optical signal such that the unmodulated optical signal serves as a KK carrier for the first and second polarizations.