Experiment describes the effects of memory on quantum systems

Article on research conducted by Brazilian physicists is published in the journal Physical Review Letters.

By José Tadeu Arantes

Agência FAPESP – Andrei Andreyevich Markov (1856-1922) was a Russian mathematician recognized for his libertarian political views and his work in probability and stochastic processes. Nearly a century after his death, the nouns “Markovianity” and “non-Markovianity” have become keywords in the study of quantum information and computer science.

A system is said to be “Markovian” when its current behavior does not depend on its past behavior. In contrast, a “non-Markovian” system is one in which present behavior depends on past behavior. The concept of “non-Markovianity” implicitly carries the notion of memory.

A better understanding of the relationship between non-Markovian behavior and the flow of information between the system and the environment is provided in the article Non-Markovianity through Accessible Information, published by Felipe Fernandes Fanchini and colleagues in the journal Physical Review Letters, May 29, 2014.

A professor at the São Paulo State University (Unesp), Bauru campus, and research fellow at the Abdus Salam International Center for Theoretical Physics (ICTP) in Trieste, Italy, Fanchini works with quantum information and computer science and is currently working on a FAPESP-funded study titled “A study of quantum correlations in open quantum systems.”

“Our paper presented an interpretation of non-Markovian measurement based on the dynamics of quantum entanglement in terms of information flow,” the researcher told Agência FAPESP.

To understand this statement, one needs to take a few steps back to establish certain concepts more precisely. First, consider “non-Markovianity.”

“Non-Markovianity is basically an effect of memory of the environment. A dissipative system that is losing coherence, that loses information to the environment, is said to be non-Markovian if what happens in the present depends on what happened in the past; in other words, if the way it dissipates now depends on the way it dissipated before,“ Fanchini said.

The system in this case is made up of qubits, or units of quantum information, which are the quantum analog of the classical bits. Any system that allows the existence of two quantum states may be considered a qubit. An example of this is the polarization of the photon, which may be vertical or horizontal. Another example is the quantum number for spin, which may be +1/2 or -1/2.

The bit is also a two-state system. However, the key difference with regard to the qubit is that the bit can only assume one state at a time, corresponding to the number zero (0) or the number one (1). That property is what is known as basic binary logic. The quantum bit, however, can overlap the two states – and this constitutes the great advantage of quantum computing, which, in practical terms, is still in its embryonic phase.

Measuring the memory of the interaction between qubits and the environment was the topic that received the attention of the Brazilian researchers. “In 2009, Heinz-Peter Breuer of the University of Freiburg [Germany] and his partners submitted a proposal to measure non-Markovianity based on the reflow of information. If part of the information lost by the system is returned by the environment and flows back to the system, the process is characterized as non-Markovian,” Fanchini said.

“Subsequently, Ángel Rivas [University of Ulm, Germany and the University of Hertfordshire, United Kingdom], Susana Huelga [University of Ulm, Germany and the University of Hertfordshire, United Kingdom] and Martin Plenio [University of Ulm, Germany and Imperial College London, United Kingdom] developed another non-Markovian measurement based on the dynamics of entanglement,” he said.

“They considered two systems: one that was interacting with the environment and the other used as backup. These two systems became entangled, and the researchers observed that the entanglement exhibited non-monotonic behavior. In other words, measurement of the entanglement revealed that after declining, it rose again. If the entanglement had only declined, it would be characterized as Markovian behavior. If it had declined and risen, or if there was oscillation, it would be characterized as non-Markovian behavior,” the researcher explained.

Here we need to remember that entanglement occurs when pairs or groups of particles are generated or interact in such a way that the quantum state of each particle cannot be independently described but rather depends on the whole, no matter how distant the particles may be in relation to the others.

The quintessential example of entanglement is the Einstein-Podolsky-Rosen (EPR) paradox proposed by Albert Einstein (1879-1955), Boris Podolsky (1896-1966) and Nathan Rosen (1909-1995) in 1935 in their controversy with the Copenhagen School regarding the interpretation of quantum theory.

“What was lacking was an association between the two ideas: that of the dynamics of entanglement and that of the reflow of information. That is what our work contributed. We were able to present an interpretation for the non-Markovian measure based on the entanglement dynamics in terms of the flow of information. We show that at the exact moment that the entanglement, which had declined, rose again, the environment was losing information to the system. This had never been proven before,” Fanchini said.

The demonstration was based not only on the mathematical treatment of the theory but also on experimental results obtained through an optical device. With the help of photons (the quanta of electromagnetic radiation), a pair of entangled quantum systems was created which, in turn, interacted with a third qubit that represented the environment. Utilizing the photon polarization (vertical or horizontal) to represent the two states of quantum bits, and through controlled interactions between the systems, they were able to prove what had been theoretically predicted.

“If the entanglement only declines, it would mean that the environment was capturing information the entire time. The fact that the entanglement rose again is because of the reflow of information from the environment to the system,” Fanchini explained.

“Let’s imagine a measurement process in quantum mechanics. This process consists of the system that is being measured, the measuring device and the observer. The observer looks to the device to obtain information about the system. If he is able to obtain increasing amounts of information, the process is said to be Markovian because the information is flowing from the system to the observer, which represents the environment,” he said.

“This is assisted knowledge because the system is not directly measured. What is being measured is the device, which in turn is in contact with the system. What takes place in a non-Markovian process – and this is what we demonstrated – is that the information about the system begins to diminish during the process of being measured. That is, the information is flowing back to the system,” he said.

In addition to Fanchini, the article was written by Göktuğ Karpat (School of Sciences at Unesp Bauru); Baris Çakmak (Faculty of Engineering and Natural Sciences, Sabanci University, Istanbul, Turkey); Leonardo Castelano (Department of Physics at the Federal University of São Carlos); Gabriel Aguilar, Osvaldo Jiménez Farías, Stephen Walborn, Paulo Souto Ribeiro (all four from the Physics Institute of the Federal University of Rio de Janeiro); and Marcos César de Oliveira (Gleb Wataghin Physics Institute at the University of Campinas).

The article Non-Markovianity through Accessible Information, by Felipe Fernandes Fanchini and colleagues (DOI: http://dx.doi.org/10.1103/PhysRevLett.112.210402), may be read by subscribers of Physical Review Letters at https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.210402.