tag:blogger.com,1999:blog-5439168179960787195.post1499193004900515111..comments2024-03-28T17:13:01.117+10:00Comments on Condensed concepts: How much entanglement do you need?Ross H. McKenziehttp://www.blogger.com/profile/09950455939572097456noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-5439168179960787195.post-86574945598979953782011-09-01T15:25:58.326+10:002011-09-01T15:25:58.326+10:00Thanks for these extremely helpful comments. They ...Thanks for these extremely helpful comments. They have saved me a lot of time.Ross H. McKenziehttps://www.blogger.com/profile/09950455939572097456noreply@blogger.comtag:blogger.com,1999:blog-5439168179960787195.post-23113773024487458912011-08-26T10:57:24.478+10:002011-08-26T10:57:24.478+10:00If the arguments put forward recently by del Rio e...If the arguments put forward recently by del Rio et al.* are correct, than shouldn't the entanglement be related to some optimal degree of work extractable or required by a subsystem in order to set its state (i.e. to erase it)? <br /><br />*Rio, L. D., Åberg, J., Renner, R., Dahlsten, O., & Vedral, V. (2011). The thermodynamic meaning of negative entropy. Nature, 474(7349), 61–63. doi:10.1038/nature10123Seth Olsenhttps://www.blogger.com/profile/09304457461800104790noreply@blogger.comtag:blogger.com,1999:blog-5439168179960787195.post-48714859345403860672011-08-26T10:06:16.723+10:002011-08-26T10:06:16.723+10:00Hi Ross,
If your 2-qubit gate is unitary then it ...Hi Ross,<br /><br />If your 2-qubit gate is unitary then it turns out that any non-vanishing amount of entanglement is enough, see for example http://arxiv.org/abs/quant-ph/0207072 . Obviously if your gates are only weakly entangling you will typically need more applications of them in your computation.<br /><br />If the gate is non-unitary (as will always be the case in practice, due to experimental noise or interactions with the environment), it turns out that entanglement measures are not the most useful way of expressing the "imperfectness" of the gate. Instead the literature usually talks about an "error channel" (or a "CP map" to be more technical) e.g. we could model the gate as being a perfect unitary followed by an error channel that, say, flips both qubits with probability p_2 (although more complicated errors are usually expected). In that case, there has been a lot of theoretical work done to establish how small the error probability needs to be before a large scale quantum computer can be built using your gates. The current state-of-the-art is that the error probability (per gate) needs to be less than around 1 percent. (See http://iopscience.iop.org/1367-2630/9/6/199 and http://www.nature.com/nature/journal/v434/n7029/full/nature03350.html ).<br /><br />I guess one could convert these error-channel models into some entanglement measure, but the story is somewhat complicated by the fact that the amount of entanglement a gate yields actually depends on the input state used.Sean Barretthttps://www.blogger.com/profile/06411871490316449827noreply@blogger.com