Time-reversal of an unknown quantum state

[allisrelative]

A very interesting paper was recently released that's a follow up to the paper that talked about Time Reversal to a known state. If you remember a lot of papers talked about how they reversed time. Here's more from the new article.

Abstract

For decades, researchers have sought to understand how the irreversibility of the surrounding world emerges from the seemingly time-symmetric, fundamental laws of physics. Quantum mechanics conjectured a clue that final irreversibility is set by the measurement procedure and that the time-reversal requires complex conjugation of the wave function, which is overly complex to spontaneously appear in nature. Building on this Landau-Wigner conjecture, it became possible to demonstrate that time-reversal is exponentially improbable in a virgin nature and to design an algorithm artificially reversing a time arrow for a given quantum state on the IBM quantum computer. However, the implemented arrow-of-time reversal embraced only the known states initially disentangled from the thermodynamic reservoir. Here we develop a procedure for reversing the temporal evolution of an arbitrary unknown quantum state. This opens the route for general universal algorithms sending temporal evolution of an arbitrary system backward in time.

Basically, Schrodinger's equation is reversable and there's no reason why a quantum system can't spontaneously return to it's original state like billiard balls re-racking themselves. This would be an extremely rare event but it can happen. They had around an 85% success rate with 2 qubits but when they added another qubit it dropped to 50%. That was the older study, here's more from the recent one.

An origin of the arrow of time, the concept coined for expressing one-way direction of time, is inextricably associated with the Second Law of Thermodynamics1, which declares that entropy growth stems from the system’s energy dissipation to the environment2,3,4,5,6. Thermodynamic considerations7,8,9,10,11,12,13,14,15,16,17, combined with the quantum mechanical hypothesis that irreversibility of the evolution of the physical system is related to measurement procedure18,19, and to the necessity of the anti-unitary complex conjugation of the wave function of the system for time reversal20, led to understanding that the energy dissipation can be treated in terms of the system’s entanglement with the environment1,21,22,23,24. The quantum mechanical approach to the origin of the entropy growth problem was crowned by finding that in a quantum system initially not correlated with an environment, the local violation of the second law can occur25. Extending then the solely quantum viewpoint on the arrow of time and elaborating on the implications of the Landau–Neumann–Wigner hypothesis18,19,20, enabled to quantify the complexity of reversing the evolution of the known quantum state and realize the reversal of the arrow of time on the IBM quantum computer26.

In all these past studies, a thermodynamic reservoir at finite temperatures has been appearing as a high-entropy stochastic bath thermalizing a given quantum system and increasing thus its thermal disorder, hence entropy. We find that most unexpectedly, it is exactly the presence of the reservoir that makes it possible to prepare the high-temperature thermal states of an auxiliary quantum system governed by the same Hamiltonian H^H^ as the Hamiltonian of a given system. This enables us to devise the operator of the backward-time evolution U^=exp(iH^t)U^=exp⁡(iH^t) reversing the temporal dynamics of the given quantum system. The necessary requirement is that the dynamics of the both, auxiliary and given, systems were governed by the same Hamiltonian H^H^. The time-reversal protocol comprises the cyclic sequential process of quantum computation on the combined auxiliary and the given systems and the thermalization process of the auxiliary system. A universal time-reversal procedure of an unknown quantum state defined through the density matrix ρ^(t)ρ^(t) of a quantum system SS will be described as a reversal of the temporal system evolution ρ^(t)→ρ^(0)=exp(iH^t/ℏ)ρ^(t)exp(−iH^t/ℏ)ρ^(t)→ρ^(0)=exp⁡(iH^t/ℏ)ρ^(t)exp⁡(−iH^t/ℏ) returning it to system’s original state ρ^(0)ρ^(0). Importantly, we need not know the quantum state of this system in order to implement the arrow of time reversal. A dramatic qualitative advance of the new protocol is that it eliminates the need of keeping an exponentially huge record of classical information about the values of the state amplitudes. Moreover, the crucial step compared with the protocol of time reversal of the known quantum state26 is that we now lift the requirement that initially the evolving quantum system must be a pure uncorrelated state. Here, we develop a procedure where the initial state can be a mixed state and, therefore, include correlations due to system’s past interaction with the environment.

https://www.nature.com/articles/s42005-020-00396-0

This is pretty amazing. They still need to find a quantum computer that supports thermalization to carry out the experiment.

Here's the 4 steps:

Step 1: Thermalization.

Step 2: Separation.

Step 3: Manipulation. Run a noncomplete quantum SWAP operation.

Step 4: Reiteration. Repeat steps 1 through 3 a number of times.

With 2 qubits it's 16 cycles. With 3 qubits, 64 and it grows as the number increases. You could re-create the past with this.

 

[mfb]

You could re-create the past with this.

The past of a low-qubit quantum state in a well-known environment, yes.