Classical determinism is the notion that some action or another has a predictable and calculable outcome. For example: dropping a ball.
Thermodynamics and Newtonian physics has these bits covered pretty well. So where does quantum fit into this? Quantum mechanics studies small stuff, not the ball itself but the components of the atoms that the ball is made from. Here at the scale, things get very difficult to measure and predict. I get asked frequently to explain the problem, and more so to explain how classical determinism can be derived from apparent quantum randomness. To illustrate the point I have devised a simple experiment you can do at home (or in your head). So here goes....
Take a half glass of water, a condom and a tablespoon or two of bicarbonate of soda. Now, quickly add the bicarbonate of soda to the water and then stretch the condom over the top of the glass. Obviously as the bicarbonate of soda reacts with the water, gasses affect the condom that is trying to keep it all trapped inside?
OK, wash your hands and clean up.. what has this got to do with determinism you ask? On a classical level, a very predicable thing happened when the chemical reaction took place. The condom increased in size as it tried to contain the expanding gas. This reaction is "classically deterministic" and also a boolean truth. You can attribute some cast iron conclusions to the outcome. But what about the quantum like side of the puzzle?
At anything smaller than the macroscopic scale "i.e. the glass,the soda and the balloon" the stuff going on inside the experiment is theoretically impossible to predict. By this I mean, you cannot say anything concrete about where an individual gas molecule will end up in the whole system, let alone predict it. However we are able to use the macroscopic rules to do very useful things such as build computers and transmit radio waves.
This is what is happening in layman's terms in everything you touch and rely on. Your iPhone is made up of trillions of atomic structures that are like little "glass,water,soda" systems, all screaming about, but somehow remarkably staying contained into a predictable and useful object.
This is where it starts to get tricky.. The apparatus of our experiment - "a glass,water,soda and a balloon" all are subject to microscopic variations in the manufacture process, BUT, together they form a "model". Within that model, an almost impossible to track sequence of events is unfolding, but as a whole it is evolving in a fairly deterministic way subject to the degrees of difference of say the balloons physical manufacture and other factors such as the temperature of the experiment, the size and shape of the glass etc. Here is where the foundation of quantum determinism gets its ontological framework. The simple idea that billions of seemingly random events inside a model can give birth to largely similar but always totally individual end results - AKA "Free Will".
Once we accept that the environmental conditions around the apparatus have a role in determining the end result of the experiment, we fall unquestionably into the most esoteric and fascinating world of "quantum cosmology".
So to review the situation, we have 'a model of reality' in the apparatus. Inside this model, we have a representation of quantum mechanics that somehow gets its act together with enough coherence to create a seemingly deterministic outcome in the physical sense. Around this, the model sits in an environment (the neologistical quantum field, or quantum cosmos). This field affects the classical membrane and permeates it to affect the internal mechanics of the model also. But at a quantum level, the interior and exterior are both running on the same rules. This is where the theory of quantum consciousness lies in a pregnant ontological never-ending cyclic framework that connects all things.
Quantum determinism is an aspect of quantum information theory and is about the informational study of systems at this level, to try and learn more about how these systems can be harnessed and understood.