I have built a machine that I have connected to an ordinary desktop computer, which is in turn connected to the internet.
When turned on, the machine isolates a pair of quantum-entangled particles; one of the pair is manipulated in such a way that time severely dilates - the particle "ages" only one second for every hour that passes for everything else (including the particle's entangled partner). After operating like this for, let's say, 24 hours, the machine is set to its data transfer mode. This mode change stops the time dilation, so now one particle is effectively offset in time by just shy of 24 hours from its entangled partner. In this mode, a quantum state of one of the particles can be flipped in accordance with an input signal, and the corresponding quantum state of its entangled partner can be read to recover the original input signal. By this means a message can be sent back in time according to the offset created between the entangled particles.
A lottery holds weekly draws; tickets are sold up to an hour before each draw. After each draw, the winning number is published on a website.
My computer checks the website after each draw; it creates a message consisting of the current date and time and the winning lottery number and feeds that message into the machine. The computer listens to the machine for any messages and displays them on the screen.
Some 60 hours before the current week's lottery draw, I turn the machine on. 24 hours later (some 36 hours before the draw), I set the machine to its data transfer mode. A few hours before the draw (while there is still time to buy a ticket for it), I return to the computer to look for a message bearing a time stamp representing the upcoming draw and the winning number. Seeing the number, I go out and buy a ticket bearing that number.
I am pretty sure quantum entanglement does not/cannot work as I have depicted, but if it did (if this was the only conceit), is my scenario plausible? Are there any paradoxes, causality violations, or other time travel "gotchas"?