Two-mode squeezed number states (TMSNS) are natural generalization of two-mode squeezed vacuum states. It has been known that every TMSNS is entangled whenever the squeezing parameter is non-zero. For a pair of entangled pure states Nielsens majoriza
tion theorem tells us whether one state can be transformed into the other state through local operation and classical communication based on the majorization property on their probability distributions of Schmidt bases. In this report we find two examples of majorization relations for a set of TMSNS.
We demonstrate unconditional quantum-noise suppression in a collective spin system via feedback control based on quantum non-demolition measurement (QNDM). We perform shot-noise limited collective spin measurements on an ensemble of $3.7times 10^5$ l
aser-cooled 171Yb atoms in their spin-1/2 ground states. Correlation between two sequential QNDMs indicates $-0.80^{+0.11}_{-0.12},mathrm{dB}$ quantum noise suppression in a conditional manner. Our feedback control successfully converts the conditional quantum-noise suppression into the unconditional one without significant loss of the noise
