Why can't all bits of an entanglement be read at once?

[Kenneth Adam Miller]

Suppose we have an entanglement state between many qubits. When we measure this state anywhere, the entanglement is destroyed. In quantum computing, we have two bits of parity for each qubit, and we have to re-setup the entanglement state for each qubit to read each piece of information individually.

Why? And what state are the other bits in upon the entanglement state being destroyed/measured?

 

[.Scott]

Suppose we have an entanglement state between many qubits. When we measure this state anywhere, the entanglement is destroyed. In quantum computing, we have two bits of parity for each qubit, and we have to re-setup the entanglement state for each qubit to read each piece of information individually.

Why? And what state are the other bits in upon the entanglement state being destroyed/measured?

The entanglement will only be destroyed to the extent that it needs to be given the information that was read.

So if A, B, and C are mutually entangled qubits, reading C may could still leave A and B entangled.

Others can check me on this, but once you have applied all the operators to your qubits, I don't believe it matters what order you read them out.