Does entanglement have a weight? This might seems a very strange question. Entanglement is just correlations, what does it mean that it can have a weight? Entanglement in a quantum state can be prepared, detected, used, and this about it. Not only the theory but overwhelming experimental evidence seem to indicate that weight and entanglement do not have much to do with each other.
In the past few years, advances in quantum thermodynamics have shown that work can be stored in the quantum correlations of a state. A thermal state is the most entropic state one can prepare given a fixed amount of energy. However, with the same amount of energy, one can prepare a state with some entanglement, which can be used in clever protocols to perform for, i.e., to "store energy". If this is true, entanglement should have a weight, since we have known for more than a century that energy has a weight.
I have worked on answering a preliminary question, which could set a challenge and a direction of research : understanding which type of entanglement weighs, and why.
Broad research lines: Relativistic and Quantum Information
Introduction: I have mainly focused my research in the field of Relativistic Quantum Information (RQI). This wonderful and exciting field merges Relativity with Quantum Information (QI), aiming at understanding how QI tasks are affected when relativistic effects are taken into consideration. Pioneering work [1-3] began to address these issues and unexpected features were found.Although the first results were indeed groundbreaking, not much attention was drawn until the last 5-6 years, when more researchers focused their attention onto moving beyond purely quantum mechanical predictions.
Core ideas in RQI: The main idea that lies behind RQI is that relativistic effects should affect quantum information protocols and processing. Although it might seems specific to QI only, this idea can be extended even further. Relativity should affect anything that involves information.Standard predictions from Quantum Field Theory suggest that since the concept of particle is not observer independent, different observers will in general observe different amount of particles as content of a quantum state. For example, an inertial observer (i.e. moving with constant velocity) might say that a state contains no particles (the Minkowski vacuum). An accelerated observer will not agree. If he or she is uniformly accelerated, we call him or her Rindler observer, it is a standard result from Unruh ( see ) that this observer will perceive the Minkowski vacuum (which is empty as described by the inertial observer) as full of particles.
Localized system for relativistic quantum information processing: While the first results were obtained using global fields, which "live" on the entire spacetime, it has remained an open question how to address issues such as the influence of motion on entanglement when fields are confined, for example within cavities. I have mainly contributed to this field by introducing and developing techniques to treat mode entanglement of modes within one or two cavities. I have shown, mainly together with my colleagues at Nottingham, that when one cavity moves, entanglement between the modes of a quantum field is affected and can be degraded, preserved or created. I have provided the techniques to fully characterized the phenomena that occurred in such localized systems. My results have attracted the interest of experimental scientists and we are now looking at possible experimental proposals.
A recent avenue that has been proposed by myself and collaborators investigates how to employ localized detectors, modeled by harmonic oscillators, for tasks that are typically investigated with Unruh-deWitt detectors. Unruh-deWitt detectors require perturbation theory which, a part from mathematical challenges, does not provide a full understanding on the physics under investigation. We have shown that, contrary to setups involving Unruh-deWitt, it is possible to employ this new scheme to analytically solve the time evolution of interacting quantum systems.
Space-based relativistic and quantum science
It is still an open question which are the effects, if any, of space-time curvature and gravity on quantum physics at large scales i.e., the scales at which relativity becomes important. Space agencies across the world are interested in bringing quantum technologies, such as quantum key distribution (QKD), to space!
QKD explains how you and I can exchange information and make sure that only the two of us can access it. In addition, we would like to know if somebody is messing around with the information we are exchanging. QKD offers a recipe, based on quantum mechanics, which allows us to do this! What we need to do is share a secret key, which allows us (and only us) to encode and decode any information we exchange. There are clever protocols which allow us to share the secret key (the original BB84 is described in ) and there are companies that now sell technology based on these principles! Furthermore, ICT roadmaps of different countries envision that going to space is the future for quantum (and perhaps relativistic?) technologies !
I have investigated the effects of gravity on quantum communication schemes. The research was partly inspired by . I was able to show that if a user on the earth tries to exchange a secret key with a user on a spaceship, for example the International Space Station (ISS), the key will be affected by the curvature of space-time around the earth and these effects are measurable with current technology! Furthermore, we have shown that by employing relativistic quantum metrology, one can aim at exploiting the effects described above for ultra-precise measurements of relevant parameters, such as distances in a future quantum GPS.
Quantum Thermodynamics of relativistic systems
About thermodynamics: Thermodynamics is arguably the most long lived and successfully exploited theory of all physical theories. It can be used to understand the physics and performance of heat machines, to study black holes and condensed matter systems, to investigate properties of the cosmos. It has been so successful that it has barely changed in the past two hundred years. However, a fundamental aspect of thermodynamics is that it applies to systems that are composed of (very) large amounts of constituents. A gas, like the air in a bottle, is a good example of a system which can be studied with thermodynamics to (extremely) good approximation.
A very basic question naturally arises: can thermodynamics can be exported to single (and small) systems? The answer is yes, and many new features arise. This has led many scientists to work in the area pf physics loosely named quantum thermodynamics. The aim is to understand how to extend concepts such as heat, work and temperature to systems with one or few constituents.
I have recently applied state of the art tools from quantum thermodynamics to relativistic fields, such as bosons and fermions. The results are very interesting because it is still not well understood what is the interplay between relativity, quantum correlations, energy and entropy. One can show that quantum correlations come at a cost, and we try to understand how this cost depends on the relativistic nature of the fundamental constituents of our universe. Together with my collaborators, I found the ultimate bound on how many correlations can be created given a fixed amount of work that can be used in a unitary process. This will help me develop more the quantum thermodynamics of relativistic systems.
Entanglement in Analogue gravity systems
About Analogue gravity: Black holes are among the most fascinating predictions of modern physics. They are known to "eat" everything that is around them and not even light can escape. However, they are not completely "one-way" systems. Stephen Hawking showed that black holes emit radiation, now known as the celebrated Hawking effect . Ten years later, it was shown by Bill Unruh that systems that can be realized in the laboratory (i.e., flowing water tanks) can be manipulated to exhibit regimes where small perturbations (i.e., surface ripples) propagate as if on a curved space-time and in the presence of a black hole . This opened a huge avenue opportunities, namely the possibility of testing Hawking's prediction in systems that are experimentally accessible so far (nobody has volunteered to fall in a black hole to see what happens, never being able to come back out and tell us what they witnessed...). In particular, new systems were found that could be led to exhibit these regimes, for example light wave guides and Bose-Einstein Condensates (BECs); these systems are now commonly employed in laboratories across the globe to study features typical of gravitational processes. Great progress has been made and analogue radiation from analogue black holes has been observed. However, its most prominent feature, the quantum character of the correlations trademark of this radiation, are hard to be observed.
I have contributed to this area of research by providing a simple analytical understanding of the role of the initial temperature of the system that is being used (temperature that can never be brought to zero) and how this affects the correlations in the analogue radiation. My work is the first to give the experimental groups a temperature threshold above which no matter how good they are, they cannot observe quantum correlations.
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Quantum Information and Communication European roadmap: http://qurope.eu/projects/quie2t/wp2/deliverables; Roadmap of Quantum ICT Laboratory of National Institute of Information and Communications Technology of Japan: http://www.nict.go.jp/en/advanced\_ict/quantum/roadmap.html; Quantum Information Science and Technology Roadmap of USA: http://qist.lanl.gov/qcomp\_map.shtml
"Quantum communication with an accelerated partner", T. G. Downes, T. C. Ralph and N. Walk, Phys. Rev. A 87, 012327 (2013)
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