Measures and applications of quantum correlations

Abstract

Abstract. Quantum information theory is built upon the realisation that quantum resources like coherence and entanglement can be exploited for novel or enhanced ways of transmitting and manipulating information, such as quantum cryptography, teleportation, and quantum computing. We now know that there is potentially much more than entanglement behind the power of quantum information processing. There exist more general forms of non-classical correlations, stemming from fundamental principles such as the necessary disturbance induced by a local measurement, or the persistence of quantum coherence in all possible local bases. These signatures can be identified and are resilient in almost all quantum states, and have been linked to the enhanced performance of certain quantum protocols over classical ones in noisy conditions. Their presence represents, among other things, one of the most essential manifestations of quantumness in cooperative systems, from the subatomic to the macroscopic domain. In this work we give an overview of the current quest for a proper understanding and characterisation of the frontier between classical and quantum correlations in composite states. We focus on various approaches to define and quantify general quantum correlations, based on different yet interlinked physical perspectives, and comment on the operational significance of the ensuing measures for quantum technology tasks such as information encoding, distribution, discrimination and metrology. We then provide a broader outlook of a few applications in which quantumness beyond entanglement looks fit to play a key role.

Generation of Quantum Correlations in Bipartite Gaussian Open Quantum Systems

“…In order to prove the possible generation of the Gaussian quantum discord, we have to consider an initial state of the form of a product state, which is the only kind of states which do not contain quantum discord [3]. The uni-modal squeezed states represent an interesting example of such product states with zero discord, described by the covariance matrix …”

“…Characterizing and quantifying quantum correlations represent a key subject in the theory of quantum information [1][2][3]. In particular, quantum correlations in states of continuous variable systems play a crucial role in applications of quantum information processing and transmission [4].…”

Versatile Gaussian probes for squeezing estimation

“…This is because any local probe undergoing a unitary evolution is left unchanged by a Hamiltonian diagonal in its same eigenbasis and the worst-case precision becomes trivially zero. Although entangled states guarantee the highest minimal precision, interestingly the presence of entanglement is not a necessary condition in order to obtain a nonzero worst-case performance [18][19][20][21]. Indeed, the key resource in this and similar discrimination tasks is a weaker form of correlation known as "quantum discord" [22,23].…”

Approximate broadcasting of quantum correlations

“…Quantum discord is a quite useful concept in many fields of quantum information processing, such as local broadcasting of correlations [4,25], quantum computing [26], quantum data hiding [27], quantum data locking [28], entanglement distribution [29,30], common randomness distillation [31], quantum state merging [32][33][34], entanglement distillation [34,35], superdense coding [34], quantum teleportation [34], quantum metrology [36], and quantum cryptography [37]. Quantum discord has become an active research topic over the past few years [38,39].…”

“…[40] which considers pure states ρ AB only. However, it remains open whether there is an analogous connection for the two-sided setting of redistributing correlations [39].…”