I'm having trouble understanding the physical information one might extract from partial traces, by interpreting the partial trace of a qubit as if the qubit was averaged out of the system.

For example, imagine I have three qubits in a GHZ state $$ |GHZ> = {1 \over \sqrt{2}}(|000>_{abc}+|111>_{abc}), $$ and I give qubit $a$ to Alice, $b$ to Bob and $c$ to Charlie. If I partial trace qubit $c$, I end up with a separable mixed state. From what I understand, this means that if Alice and Bob completely ignore Charlie's qubit and any information Charlie might give, they will not be able to successfully execute a protocol that needs their qubits to be entangled, because the subsystem Alice-Bob is not entangled when the qubit $c$ is ignored.

The situation would be the opposite if the W state $$ |W> = {1 \over \sqrt{2}}(|100>_{abc}+|010>_{abc}+|001>_{abc}) $$ was considered, because the partial trace of qubit $c$ gives an entangled mixed state, pointing that the subsystem Alice-Bob is entangled.

Is this reasoning correct or not? Thank you very much for any help!


closed as unclear what you're asking by Norbert Schuch, sammy gerbil, Martin, Cosmas Zachos, Daniel Griscom Mar 6 '18 at 2:21

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

  • $\begingroup$ not sure what you are asking. Yes your reasoning is correct, the $W$ state has a more "stable" kind of entanglement in this sense, while for the GHZ the entanglement cannot be used without access to all three parties, as you correctly noted. $\endgroup$ – glS Feb 25 '18 at 1:11