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We look for local unitary operators $W_1 \otimes W_2$ which would rotate allequally entangled two-qubit pure states by the same but arbitrary amount. It isshown that all two-qubit maximally entangled states can be rotated through thesame but arbitrary amount by local unitary operators. But there is no localunitary operator which can rotate all equally entangled non-maximally entangledstates by the same amount, unless it is unity. We have found the optimal setsof equally entangled non-maximally entangled states which can be rotated by thesame but arbitrary amount via local unitary operators $W_1 \otimes W_2$, whereat most one these two operators can be identity. In particular, when $W_1 = W_2= (i/\sqrt{2})({\sigma}_x + {\sigma}_y)$, we get the local quantum NOToperation. Interestingly, when we apply the one-sided local depolarizing map,we can rotate all equally entangled two-qubit pure states through the sameamount. We extend our result for the case of three-qubit maximally entangledstate.

Constant rotation of two-qubit equally entangled pure states by local quantum operations