Quantum Information and Many-Body Physics

From a quantum foundational viewpoint, a big question still stands: how far in the macroscopic regime can we witness quantum effects? Is there any fundamental mechanism that leads to the emergence of classical physics at certain scales? In a modern perspective, this is also connected to the afore-mentioned technological revolution, at least to the extent of understanding its potential limitations. A common intuition is that at large scales there is inevitable decoherence which erases quantum effects. In this respect, to make more precise and quantitative statements, it can be very helpful to link more and more deeply the physics of quantum many-body systems with information-theoretic concepts, in particular entanglement. This is particularly important since one of the main applications of near-future quantum devices is precisely in simulating the dynamics of complex many-body Hamiltonians.

At the same time, entanglement theory has also proved useful for characterizing phases of matter and it could be therefore very important to further develop such a toolbox and look for novel potential implementations in deepening the understanding of the most complex phases.  Within this perspective, we aim at investigating more concretely quantum-information-theoretic aspects of many-body physics, following the research on questions like: How can we quantify quantum correlations in many-body experiments? How are they related to thermodynamic/statistical physics concepts? How is entanglement connected with crucial properties of quantum matter? Can we overcome Landau theory of phase transitions and find universal (i.e., model-independent) properties of complex phases connected with entanglement?

In dynamical non-equilibrium situations there is not just entanglement that plays a fundamental role. As noticed already by Heisenberg in the early days of quantum theory, measurements of “complementary” observables such as position and momentum are incompatible, which means that, for example, one disturbs the other if performed in a sequence. Again, this is clearly visible in the microscopic regime, where, e.g., a photon hits an electron to measure its position, but starts to become counter-intuitive in the macroscopic regime, when the sources of noise should be negligible as compared to the measured value. In this case it is perhaps even more counter-intuitive the fact that this incompatibility can be actually also seen as a basic resource for computation. 

In the light of this, the natural question is: Is there a relation between entanglement and some notion of sequential incompatibility? While entanglement by now has been quite long investigated and has also a clear foundational and operational definition, notions of temporal quantum correlations have been considered only recently. Nevertheless, their role as resources has been already explored to some extent, in particular connected to notions of memory. In this respect, the idea is to follow this path and in particular investigate the role of memory and temporal correlations and their trade-off with entanglement for a specific, yet fundamental task: measuring time. In fact, one motivation for choosing this concrete task is precisely it being the simplest and most fundamental (for example as compared to universal computation), although still highly nontrivial. In recent times it has become clear that entanglement helps in metrological tasks, and this is in fact one of the main practical applications that is already implemented. However, much less is known about the role of temporal correlations. Moreover, in the case of clocks, the most precise current standards, i.e., atomic clocks, still don’t make use of any quantum “resource”. This clashes with theoretical quantum models that could in principle overcome classical limits and could as well work in a many-body regime. Thus, another question arises: is there any fundamental reason for the optimal practical clocks being classical and microscopic (like inevitable decoherence)?

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