# What was the meaning of Lossless Quantum compression?

I was reading few questions regarding lossless quantum compression on stack exchange, then out of curiosity, I started reading this article. After reading I end up being confused about what does quantum compression really means? For example take$$|\psi\rangle=(|00\rangle+|10\rangle)/\sqrt{2}$$ article was saying compression means making $$|00\rangle$$ to $$|0\rangle$$ and $$|10\rangle$$ to $$|1\rangle$$, then storing the length and append zeros to decompress. Why can't they measure the quantum state and store the information, instead of compressing the quantum state? What was the use of the density matrix in this entire article is it just to measure the information?

• If you remind me 24 hours before the bounty expires, I can take a look at the paper. I don't think it's a very popular article (it's been cited 39 times in 20 years), so not many people will have read it before. May 4 '21 at 1:56
• Ok.Thank you for responding. I will do that. May 4 '21 at 4:36
• Hope you get the answer.@ user1271772 May 5 '21 at 22:05
• Hi @ user1271772 can you take a look at this article? May 6 '21 at 21:49
• I haven't read the full paper, but in the introduction they say Now we ask: Is it possible to compress quantum messages without any loss of information?. So if the question is "why do they compress the state?", the answers seems to be "to show that it is possible to do so". I suppose an advantage of compressing directly the state would be when you are insterested in sending quantum states, rather than classical messages, through whatever communication channel you are considering
– glS
May 18 '21 at 10:05