qit.invariant.state_inv

qit.invariant.state_inv(rho: State, k: int, perms: Sequence[Sequence[int]]) → complex

Local unitary polynomial invariants of quantum states.

Computes the permutation invariant $I_{k;{\pi }_1,{\pi }_2,\dots ,{\pi }_n}$ for the state $\rho$, defined as $\mathrm{Tr}({\rho }^{\otimes k}\mathrm{\Pi })$, where $\mathrm{\Pi }$ permutes all k copies of the i:th subsystem using ${\pi }_i$.

Parameters

• rho (State) – quantum state with n subsystems

• k (int) – order of the invariant, k >= 1

• perms (Sequence[Sequence[int]]) – Permutations. len(perms) == n, each element must be a full k-permutation (or an empty sequence denoting the identity permutation).

Returns

invariant

Return type

complex

Example: $I_{3;(123),(12)}(\rho )=$ state_inv(rho, 3, [(1, 2, 0), (1, 0, 2)])

This function can be very inefficient for some invariants, since it does no partial traces etc. which might simplify the calculation.

Uses the algorithm in [15].