The Sony Xperia Z1 will not receive Android 6.0 Marhsmallow, despite being a smartphone with technical characteristics of a sufficient level to run the new version of the operating system. However, you can already have this new version on your Sony Xperia Z1, thanks to this ROM based on AOSP.
Android 6.0 Marshmallow
The Sony Xperia Z1 will not officially update to the new version of the operating system. At least, that is what has been officially confirmed so far, since there has also been talk of the possibility that the official update does reach the smartphone, after the Sony Xperia whose official update is confirmed have been updated. However, it is a smartphone that has sufficient technical characteristics to be able to run Android 6.0 Marhsmallow, so it was clear that in a very short time some ROM with Android 6.0 Marsmallow would arrive for the Sony Xperia Z1. Now this ROM is already available, it is based on AOSP, so we will find the basic Android interface, very similar to the one present in Nexus smartphones. But the most relevant thing is that it is based on the latest version of the operating system, and can already have Android 6.0 Marshmallow in the Sony Xperia Z1.
Of course, since it is a ROM that has just been released, it has errors, some of them quite relevant. For example, the camera does not work, nor does the NFC connectivity, as well as the GPS. Also, there are errors related to the internal memory (not the main memory, but the additional internal memory).
Thus, all those users who already want to install Andorid 6.0 Marshmallow, you can find all the information about this ROM in the XDA Developers. Although it is true that it is currently an update that could be somewhat useless for users who want to have a smartphone without errors, it may be interesting to follow the progress of the ROM until it already has these errors.
More information - XDA Developers