♦ No particle can be entangled with more than one particle at a time. This is known as the “monogamy of entanglement“.
“If two systems are strongly entangled then each of them cannot be entangled very much with other systems” – reference
“Only knowing that the quantum correlations of A and B are very strong one can infer that A and B are not correlated with anything else.” – reference
♦ No cloning of a quantum mechanical state. We cannot create an identical copy of a quantum state.
You must read this article by William K. Wootters and Wojciech H. Zurek: “The No-Cloning Theorem
♦ No fermion particle can occupy the same state with another fermion particle. This is known as the “Pauli exclusion principle“.
“No two electrons in an atom can have identical quantum numbers. This is an example of a general principle which applies not only to electrons but also to other particles of half-integer spin (fermions). It does not apply to particles of integer spin (bosons). ” – reference
I’ll take this opportunity to mention Scott Aaronson’s “Introduction to Quantum Information Science” (University of Texas at Austin) where you can find more information about the principles mentioned above.
There is also the famous lecture notes by John Preskill.