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Scrambling of quantum information validated by quantum teleportation

The delocalization of information in interacting quantum systems seems to play a key part in their evolution. A method has been developed that could enable the dynamics of this process to be directly probed in experiments.
Jonathan Home is at the Institute for Quantum Electronics, Department of Physics, ETH Zürich, 8093 Zürich, Switzerland.
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Quantum correlations that spread between parts of a many-body system are intrinsically linked to the system’s evolution towards thermal equilibrium, in a process called thermalization. Measuring these correlations is challenging, because of the need to filter relevant information from the huge amount that is present, without the measurement being mimicked or corrupted by the presence of noise. In a paper in Nature, Landsman et al.1 demonstrate that quantum teleportation of a single quantum bit (qubit) can provide direct evidence of dynamics that lead to correlations between all the components of a three-body system. This approach could be a powerful tool for characterizing future many-body quantum simulators — controllable quantum systems that can be used to model other quantum systems.

When physical systems interact, information is distributed between them. In general, this process leads to correlations between the systems. In the case of quantum-mechanical interactions, the correlated systems are said to be entangled; the information cannot subsequently be retrieved from any single system, but is shared across the whole composite array. As a result, if we were to look at only a local region (such as a single system), we would conclude that the interactions have caused any initial information to be lost. This effect is connected to the progression of the interacting systems towards thermal equilibrium — a highly disordered state. Delocalization of information in this manner has become known as information scrambling, and its consequences for thermalization make it a useful feature to understand and measure in interacting quantum systems.

An established method for studying scrambling involves looking at measurements, taken at different times, of different parts of a many-body system. When interactions have had enough time to spread correlations between two spatially separated systems, A and B, a measurement of A will influence a subsequent measurement of B. This effect can be tested by comparing whether the sequence of measuring A, allowing the systems to evolve over time, and measuring B produces the same results as the sequence of measuring B, evolving the systems in reverse and measuring A. These measurements are then used to compute mathematical functions called out-of-time-ordered correlation functions2.

Under ideal conditions, when this method is applied to all pairs of systems, it provides evidence of information scrambling. However, scrambling is indicated by a failure to obtain the same result every time the measurements are repeated. This type of signal is often inconclusive, because it is mimicked by the effects of noise or other imperfections, which cause similar reductions in repeatability. Therefore, it is important to devise techniques that verify that a correct measurement of information scrambling was carried out.

The approach used by Landsman and co-workers accomplishes just such a verification, based on a previous proposal3. Rather than using a single copy of an interacting system, the scheme involves implementing similar time evolution on two copies of an interacting system of qubits in parallel (Fig. 1). The copies are initially highly correlated — all but one qubit in the first copy is entangled with an equivalent qubit in the second copy. The remaining qubit in the first copy is called the input, and is encoded with some quantum information. The remaining qubit in the second copy is entangled with an external qubit called the target, which is prepared in its lowest-energy state. This external qubit does not take part in the interactions, but has a crucial role in the verification.

Figure 1 | Verified quantum-information scrambling. Landsman et al.1 report an experiment involving two copies of a system of three quantum bits (qubits). Two qubits in the first copy are entangled (correlated in a non-classical way) with two qubits in the second copy. The remaining qubit in the first copy is called the input (red). The remaining qubit in the second copy is entangled with an external qubit called the target (yellow). The authors allow the qubits in each copy to interact. They then take a measurement of two qubits to check for the existence of a particular entangled state. They also check to see whether the quantum state of the input has been transferred through the two interacting systems to the target by the phenomenon of quantum teleportation. The combination of these checks provides an unambiguous test for whether an effect called quantum-information scrambling has occurred.

After allowing the qubits to interact, the experimenters determine whether information scrambling has occurred. The first step consists of checking whether a specific entangled state exists between two equivalent qubits in the two copies. The probability of the answer ‘yes’ is equivalent to the result obtained by computing out-of-time-ordered correlation functions. However, in the current approach, the scrambling that is suggested by the presence of the entangled state is verified using a second step. This step involves seeing whether the arbitrary state of the input has been transferred to the target through the two linked systems by quantum teleportation, which happens only if true scrambling occurs. To show this feature, Landsman et al. use different quantum circuits to introduce various amounts of scrambling, and neatly illustrate the advantages of the two-step scheme.

The ability of the researchers to carry out these experiments results from the exquisite level of control that they attain over the qubits — in this case, trapped atomic ions. Aside from implementing a new protocol, this work extends such control to a larger system than one for which the same authors had demonstrated it previously4. Nevertheless, the delocalization in the current work occurs in systems of three qubits, which are not strictly systems of ‘many’ bodies, and the method relies on there being a direct correspondence between the dynamics in the two copies. Whether this approach can be extended to larger systems remains an open question. Crucially, however, the main effect of noise or other imperfections might be to take the probability of observing a successful correlation to zero, rather than to produce a false indication of scrambling.

The measurement implemented in this work is chiefly applicable to many-body physics in the laboratory, but, intriguingly, it arose from considerations of information flow in simplified models of purely quantum-mechanical black holes, which rapidly scramble information. In a previous study5, it was shown that information falling into an aged black hole is almost immediately recoverable from Hawking radiation — light that is released by the black hole. The current experimental protocol mimics this theoretical scenario, with the input quantum state to be teleported playing the part of the infalling information, and the output being viewed as the Hawking radiation. Although we are unlikely to operate a trapped-ion quantum computer in the vicinity of a black hole, the use of these concepts in an experimental technique illustrates the value of pursuing and connecting diverse avenues of research to stimulate the advancement of science.

Nature 567, 36-37 (2019)

doi: 10.1038/d41586-019-00743-4

References

  1. 1.

    Landsman, K. A. et al. Nature 567, 61–65 (2019).

  2. 2.

    Swingle, B. & Yao, N. Y. Physics 10, 82 (2017).

  3. 3.

    Yoshida, B. & Kitaev, A. Preprint at https://arXiv.org/abs/1710.03363 (2017).

  4. 4.

    Debnath, S. et al. Nature 536, 63–66 (2016).

  5. 5.

    Hayden, P. & Preskill, J. J. High Energy Phys. 2007, 120 (2007).

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