# Generalization of n-th level entangled system

I have seen qubits, qutrits & entangled bits (e-bits) a decent amount. I have also seen qunits/qudits for n-th level qubits. What I am trying to wrap my head around is the differences between n-th level e-bits vs n-th level qunits. What are the similarities? Differences?

What generalizations exist about n-th level e-bits / qunits?

• Whenever you mention such non-standard terms (by "non-standard" I mean terms which aren't normally seen on common references like Wikipedia), you should mention the source where you saw them. – Blue Jun 21 at 6:35
• Noted! Will keep in mind for the future. – meowzz Jun 21 at 7:29

Disclaimer: Since you haven't stated the source from where you got those terms, I will mention the most obvious definitions for those, which occur to me - simply looking at the names.

"Qunit" refers to any quantum system whose state lies in a complex vector space whose dimension is any natural number $n$. Example of qunits are qubits, for which $n=2$ and qutrits for which $n=3$. Also check this for other less commonly used terms: Do any specific types of qudits other than qubits and qutrits have a name?

Next, remember that a system of two qubits will lie in a $2\times 2$-dimensional vector space i.e. $\Bbb C^2\times \Bbb C^2$. A system of three qubits will lie in a $2\times 2 \times 2$-dimensional vector space $\Bbb C^2\times \Bbb C^2\times \Bbb C^2$ and so on. By "$n$-dimensional" e-bits they're referring to the dimension of the vector space again. As for the "e-bit" part, that's simple. That is, the state of the system of qubits is basically not separable into individual qubit states lying in $\Bbb C^2$ each (i.e. the qubits are entangled). Check out the answers in: How do I show that a two-qubit state is an entangled state?

• Any good references for n-th level systems (besides 3 papers linked to in 1st link)? Also, thoughts on showing an n-level system is entangled (just found out about entanglement witness)? – meowzz Jun 21 at 7:28
• @meowzz "thoughts on showing an n-level system is entangled" - please ask that as a new question! It's a bit too broad to cover here, and apart from that, I forgot the general (non-brute-force) method for it. It would be helpful for me as well! :) – Blue Jun 21 at 7:35