1
$\begingroup$

Is there a particular name for a quantum state of the form (up to the normalization):

$$\sum_{i_1+\ldots+i_n = d-1} |i_1\rangle |i_2\rangle \ldots |i_n\rangle$$

or was it studied is some papers?

This state is a permutation symmetric state of $n$ qudits (i.e. $d$-level particles), and defined as a superposition (with equal amplitudes) of all compoments for which particle indices sum up to $d-1$.

For qudits ($d=2$) it is a well known W state (or here), i.e. a permutation symmetric sum of one $|1\rangle$ among $n-1$ $|0\rangle$s.

For example, for 3 qutrits ($d=3$) it is $$|002\rangle + |020\rangle + |200\rangle + |011\rangle + |101\rangle + |110\rangle$$ and for $n=3$, $d=4$: $$|003\rangle + |030\rangle + |300\rangle + |012\rangle + |021\rangle + |102\rangle + |120\rangle + |201\rangle + |210\rangle + |111\rangle.$$

(I am writing a paper using such state, and would like to reference it; or at least - not reinvent its name.

Yes, it looks like a state for $n$ harmonic oscillators energy summing up to a particular value; however, here this "equal amplitudes" part is crucial, summing to $d-1$ is also of a big importance (albeit less crucial, as one can cut qudits to qu($c<d$)its).)

$\endgroup$
1
$\begingroup$

So, out of lack an already established name, I called it excitation states in:

P. Migdał, J. Rodriguez-Laguna, M. Lewenstein,
Entanglement classes of permutation-symmetric qudit states: symmetric operations suffice, arXiv:1305.1506.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.