ASSESSMENT OF CURRENT RESULTS AND OUTLOOK ON FUTURE EFFORTS

FUNDAMENTAL ISSUES ABOUT QIPC PHYSICS

QIPC relies on the manipulation and control of ensembles of qubits behaving according to the counter-intuitive laws of quantum physics. Most generally, though, quantum features are washed out in systems made of large numbers of particles. This decoherence phenomenon defines a kind of boundary between the microscopic world, where the quantum laws are dominant, and the macroscopic world, which behaves classically in spite of its underlying quantum nature. This boundary is fuzzy however. It largely reflects our lack of ability to isolate completely the system under study from its environment, made of a very big number of uncontrolled particles. By developing clever schemes, physicists and quantum information scientists are finding ways to fight this environment-induced decoherence. Some methods rely on the observation and manipulation of the environment itself, combined with feedback procedures counteracting the effects of decoherence on the system under study. Other methods, borrowing from the error correction schemes of classical computers, are at least in principle even more powerful. They are based on the redundant coding of the information in an ensemble of entangled qubits, monitoring the effects of decoherence on a subset of these qubits and applying correction procedures on others to restore the initial quantum state affected by decoherence. The progress towards the implementation of these methods, a prerequisite for large scale quantum computing to ever become feasible, is discussed in other parts of this report.

Here, we focus on other aspects of this field of research. The first is of a pedagogical nature. By attempting to "harness" the quantum laws and make them useful to achieve logical tasks, QIPC scientists are, in some way, changing our view of the quantum-classical boundary. In the discussions of the founding fathers of quantum theory, this boundary was explored in thought experiments dealing with the principles of quantum measurements where microscopic systems are put in contact with macroscopic meters. Many QIPC experiments with atoms and photons can be viewed as modern realizations of these thought experiments. By doing them, physicists get more familiar with quantum concepts such as complementarity and wave particle duality. These experiments are now included in all modern textbooks of quantum physics. This pedagogical element must not be underestimated. The formation of an intuition for the quantum world is certainly an important ingredient in the education of students in physics and the study of QIPC is an excellent way to acquire this intuition. The students attracted by the esthetical qualities of this physics will be the researchers of tomorrow, who will apply their skills to QIPC or to other fields.

More fundamentally, these experiments also raise some issues at the forefront of physics. In QIPC, physicists learn to build systems of increasing size in quantum superposition, the Schrödinger cat states. This research is still in its infancy and many important issues remain to be explored, some of which are listed here non-exhaustively:

• Size of mesoscopic superpositions. This concept remains to be defined in a more quantitative way. Present experiments involve big molecules following spatially separated paths in an interferometer, large numbers of photons stored in different states in boxes or propagating freely in laser beams and currents rotating in opposite directions in superconducting circuits. Large ensembles of atoms entangled with each other via their interaction with polarized laser beams share common features with these mesoscopic superpositions. Experiments with entangled Bose Einstein condensates of ultra cold atoms are also developing, completing this zoo of Schrödinger cat states. Clearly, the mass of the system (what about the photonic cat states?) or the number of particles involved (should we count the quarks in the molecular cat systems?) are not universal parameters to measure the magnitude of a given state superposition. Attempts to define a universal distance between the parts of the mesoscopic wave functions have been made and should be refined, to permit a meaningful comparison between experiments performed under very different conditions on disparate systems.

• Non locality of mesoscopic superpositions. Non locality has been investigated in great details so far on simple microscopic systems (pairs of photons or ions). It remains to be studied on larger systems. Mesoscopic objects made of many atoms or photons can now be built, in which the two parts of the wave function correspond to different locations in space, separated by a truly macroscopic distance. In the case of photons, this relies on the realization of some kind of non linear beam splitter device which, in a way very different from an ordinary beam splitter, collectively channels all the photons, at the same time, in one arm and in the other of an interferometer. Experiments with up to four photons have already been realized and non local cat states involving much larger photon numbers are in the making. Similar ideas are being developed to channel Bose Einstein condensed atoms collectively in different final positions. These systems combine the weirdness of the Schrödinger cat (large objects in state superpositions) and the strangeness of non locality. In simple two-particle systems, the amount of non-locality is measured by the degree of violation of Bell's inequalities. Versions of these inequalities for mesoscopic systems have been proposed. Testing them on large non local Schrödinger cat states remains to be done. The effect of decoherence on the violation of these mesoscopic versions of Bell's inequalities remains largely to be studied.

• QIPC, gravitation and beyond. In QIPC physics, the coupling to environment is considered to be electromagnetic. There is however another kind of environment against which no shielding exists, due to the gravitational field permeating all space. Decoherence induced by the fluctuations of gravitational waves of cosmological origin has been estimated theoretically. It is found to be negligibly small on atoms or molecules, and exceedingly efficient on large objects, for which it is by far more important than electromagnetic decoherence. The transition appears to occur for objects of the order of Planck's mass (22 micrograms). Observing gravitational decoherence would be a daunting task, the challenge being to isolate effectively from electromagnetic influence objects made of many trillions of atoms. Experiments attempting to prepare quantum superpositions of states of a tiny mirror placed at the tip of a cantilever could be a first step in this direction. Even if gravitational effects are not of concern for QIPC applications, they are of a fundamental interest because they link the quantum-classical boundary to fundamental cosmological issues. Experiments on gravitational decoherence will not be realized in the near future, but thinking about them brings together scientists from quantum optics, mesoscopic physics, theoretical physics and cosmology. Deep questions such as the connection between information theory and black hole physics are also fruitfully debated, even though applications are not to be expected. Finally, these issues cannot be separated from a fundamental question about the future of quantum theory itself. Including gravitation into a comprehensive quantum framework has up to now eluded the efforts of theorists. A majority believes that such a comprehensive theory will retain the essential features of the present quantum theory, notably state superpositions and probabilistic behavior. Some however, who dislike the idea that "God is playing dice", hope that the new theory will reestablish some kind of classical determinism. There would then exist another kind of decoherence, more fundamental than the environment induced one. All attempts to build such theories so far have failed, but this does not deter their advocates. To test experimentally possible theories of this kind will be exceedingly difficult. It will imply, as a prerequisite, a very good control of the largely dominant environment induced decoherence. If a limitation to quantum laws as we know them were found at a given size scale, it would have tremendous consequences on our view of Nature, going far beyond the discussion about the feasibility of a quantum computer.