Pascal’s triangle and quantum entanglement

In an experiment involving multiple independent trials of a simple two-outcome random process, such as tossing a coin, it is well-known that the cumulative result is described by the binomial probability distribution. In a quantum mechanical version, in which the coins are replaced by identical independent qubits, the same distribution will describe the cumulative outcomes, and it is intuitive that quantum entanglement is not present, otherwise the outcomes of measurements on different qubits will be correlated, and the trials will no longer be independent. Here, we examine whether such assumptions are valid, and find that maximally entangled qubit states, symmetric under interchange of any pair of qubits (specifically, they are eigenvectors of the SWAP operator with eigenvalue + 1 ), can also give a binomially distributed outcome.