Lectures on General Quantum Correlations and their Applications

Abstract

Monogamy is an intrinsic feature of quantum correlations that gives rise to several interesting quantum characteristics which are not amenable to classical explanations. The monogamy property imposes physical restrictions on unconditional sharability of quantum correlations between the different parts of a multipartite quantum system, and thus has a direct bearing on the cooperative properties of states of multiparty systems, including large many-body systems. On the contrary, a certain party can be maximally classical correlated with an arbitrary number of parties in a multiparty system. In recent years, the monogamy property of quantum correlations has been applied to understand several key aspects of quantum physics, including distribution of quantum resources, security in quantum communication, critical phenomena, and quantum biology. In this chapter, we look at some of the salient developments and applications in quantum physics that have been closely associated with the monogamy of quantum discord, and "discord-like" quantum correlation measures.

Quantum synchronisation enabled by dynamical symmetries and dissipation

“…For the following results, we start in a specified initial state and then time-evolve it under the Liouvillian in equation (9) measuring various time-dependent quantities in order to observe the formation of synchronisation. As a first synchronisation measure for the local observables in our model we consider the time-dependent Pearson-correlation factor [14,34]. It can be used to measure the correlation over time for two functions f, g .…”

Time dilation in quantum systems and decoherence

“…This case is the one considered in [1][2][3], where the superposed paths have common initial and final points (which may correspond to the first and second beam-splitter, or the source and detection points on a screen in a double-slit experiment). The outcomes do not depend on the choice of reference frame to describe the experiments, as is apparent from equation (7) (see also [24]). One may however also consider superimposed world-lines that do not meet on a final beam splitter.…”

“…is the mean internal energy (see also methods in [3]). This decoherence is therefore in the opposite limit than the Markovian models (see also [24] for a discussion of non-Markovianity in this context). A few other models are of similar form, as for example the one by Cucchietti, Paz and Zurek [56] in which a spin couples to the bath spin operators, ( ) s = å B i z i , and which also results in a Gaussian decay of coherence.…”

“…Focusing on the evolution of the internal degrees of freedom, the fundamental limits on the stability of clocks due to the time dilation induced entanglement between internal and external degrees of freedom were discussed in [22]. All these effects on quantum systems stem from the relativistic coupling between internal and external degrees of freedom due to time dilation, which was further studied in [23][24][25].…”

“…Like time dilation induced decoherence, this effect can take place due to the mass-energy equivalence, but these two decoherence mechanisms are not the same. The time dilation induced entanglement and decoherence in a free-falling scenario was studied in [24], where also the difference to Newtonian effects was highlighted.…”