Time travel in quantum computing

[Philip Thrift]

https://newatlas.com/physics/quantum-time-travel-simulator-butterfly-effect/

Recovery of Damaged Information and the Out-of-Time-Ordered Correlators

https://arxiv.org/abs/2003.07267

@philipthrift

[Lawrence Crowell]

This looks interesting. There are relative time machines in QM, where one system may by virtue of its energy move faster or slower in time.

For a two-state system the string of binary outputs has Kolmogorov complexity 2^N. However, the quantum complexity is exp(2^N). for N = 4 the K-complexity is 15, but the quantum complexity is 8886110.52. This pertains to the possible phase structure that can exist. As a result much of the “butterfly effect” in QM or quantum chaos is in the phasor structure. 

With a black hole Alice can transform a set of states with an apparatus, so her EPR pair is transformed into a state to be transmitted. She sends these quantum states into her black hole and transmits this information to Bob who is facing a black hole entangled with Alice’s.  Bob then performs the operations according to Alice’s transmission and the states Alice sent in will appear in the quantum radiation of the BH. This is a form of teleportation via black hole. There is no reason why Alice might decide to transmit this information to Bob and wait a long time and send her EPR pairs into the BH long after Bob has received these instructions. Bob then quickly performs these operations and reconstructs Alice’s transmitted states long before, on his Hubble frame, before Alice transmitted them. Teleportation back in time is in principle possible with BHs.

The difference between the transmitted and received states are with the quantum phase, where the quantum complexity of Alice’s states are not constructible by Bob. The black hole as an Einstein-Rosen bridge is not traversable. A traversable black hole, which violates the Hawking-Penrose energy conditions, would allow for the duplication of a state. A traversable wormhole with one opening boosted to a near light speed frame and then back will have its clocks behind the first opening. Then transmitting a quantum state into the wormhole, means at an earlier time that state appears in the second opening so the experimenter for a time has a copy of the state. This is a process that is not unitary. This sort of problem does not happen with entangled black holes or ER bridges.

LC