My [text shows](http://www.cs.berkeley.edu/~vazirani/s07quantum/notes/lecture2.pdf) (sections 0.2 and 0.3) that the joint "state space" of a system composed of two subsystems with $k$ and $l$ "bits of information", respectively, requires $kl$ bits to fully describe it. A critical consequence of this is that the $k+l$ bits in each of the individual subsystems are not sufficient to "span" their joint space, so that there must be states that are "entangled" (formally, cannot be expressed by the tensor product of the states of the subsystems). That much I (*think*) I understand.

But the text then seems to argue that this is a property that is exclusive to quantum systems. Is that true? Certainly there are classical systems where the state of one subsystem depends on the state of another. Doesn't any joint system that requires conditional probabilities to describe need "extra bits" beyond those necessary to describe the individual subsystems?

Perhaps I'm missing some subtlety about what constitutes a "sub system" or some unstated assumption about how systems are broken into parts. Perhaps a classical system that is "entangled" by conditional probabilities isn't thought of as consisting of valid "subsystems" in the same way that quantum system is.

Is "entanglement" unique to quantum systems? Are conditional probabilities just a kind of "classical entanglement"?

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Please be pedagogical. This is not meant to be a deep or advanced mathematical question, just a simple conceptual and definitional one. Just imagine I'm having basic probability explained to me (without reference to quantum vs. classical, or even physics). If one struck out all occurrences of the word "quantum" from the linked [text](http://www.cs.berkeley.edu/~vazirani/s07quantum/notes/lecture2.pdf) (sections 0.2. and 0.3), wouldn't that be a perfectly valid part of such an explanation?