Measure-independent freezing of quantum coherence

Abstract

We find that all measures of coherence are frozen for an initial state in a strictly incoherent channel if and only if the relative entropy of coherence is frozen for the state. Our finding reveals the existence of measure-independent freezing of coherence, and provides an entropy-based dynamical condition in which the coherence of an open quantum system is totally unaffected by noise.Quantum coherence is a fundamental feature of quantum mechanics, describing the capability of a quantum state to exhibit quantum interference phenomena. The coherence effect of a state is usually ascribed to the offdiagonal elements of its density matrix with respect to a particular reference basis, which is determined according to the physical problem under consideration. It is an essential ingredient in quantum information processing [1], and plays a central role in emergent fields, such as quantum metrology [2][3][4], nanoscale thermodynamics [5][6][7][8][9][10][11], and quantum biology [12][13][14][15][16].It is only recent years that the quantification of coherence has become a hot topic due to the development of quantum information science, although the theory of quantum coherence is historically well developed in quantum optics [17][18][19]. A rigorous framework to quantify the coherence of quantum states in the resource theories has been recently proposed after a series of efforts [20][21][22][23][24][25][26][27][28][29]. By following the rigorous framework comprising four postulates [20], a number of coherence measures based on various physical contexts have been put forward. The l 1 norm of coherence and the relative entropy of coherence were first suggested as two coherence measures based on distance. The coherence measures based on entanglement [30], the coherence measures based on operation [31,32], and the coherence measures based on convex-roof construction [33,34] were subsequently proposed. With coherence measures, various properties of quantum coherence, such as the relations between quantum coherence and other quantum resources [30,35,36], the quantum coherence in infinite-dimensional systems [37,38], the complementarity relations of quantum coherence [39], and the measure of macroscopic coherence [40], have been discussed. Quantum coherence is a useful physical resource, but coherence of a quantum state is often destroyed by noise. A challenge in exploiting the resource is to protect coherence from the decoherence caused by noise, as the loss of coherence may weaken the abilities of a state to perform quantum information processing tasks. Today, after having been equipped with the knowledge of coherence measures, it becomes possible to analyze under which dynamical conditions the coherence of an open system is frozen in a noisy channel. Studies on this topic have been started in Ref. [41], where the authors found that the coherence measures based on bona fide distances are frozen for some initial states of a quantum system with even number of qubits undergoing local identical bit flip channels. This finding illu...

Detecting coherence via spectrum estimation

“…The freezing of coherence means that the coherence of the quantum system (quantified by some coherence measure) is not affected by noise. When the freezing of coherence is independent of the choice of measures, it is called universal freezing [36,37]. Especially, in Ref.…”

“…Especially, in Ref. [37], it is shown that under a strictly incoherent channel, the universal freezing of coherence occurs if and only if the relative entropy of coherence is frozen. This implies that if we can witness the freezing of relative entropy of coherence, we can assure that the coherence of the quantum system is completely unaffected by noise.…”

“…These coherence measures make it possible to quantitatively study the role of coherence in various physical contexts. Further important properties of coherence, such as the distillation of coherence [24,29], the relation between coherence and quantum correlations [20,[30][31][32][33][34][35], and the freezing phenomenon of coherence [36,37], can be studied based on the coherence measures that have been proposed.…”

Quantum Field Theory of Nematic Transitions in Spin-Orbit-Coupled Spin-1 Polar Bosons

“…A majority of the theoretical [28, 32-35, 37, 38] and experimental [17][18][19][20][21] work has focused on quantum phase transitions (QPTs) that are driven by the strength of the Raman field and are accessible in both pseudospin-1/2 and spin-1 bosons. Interestingly, for polar spin-1 bosons, the phenomena and nematic QPTs that can be evoked by SOC goes beyond transverse field induced transitions, and remains largely unexplored apart from mean field (MF) [35,39] and variational solutions [33,36,40]. Our work aims to fill this gap by developing a field theory description of nematic QPTs.…”

Spin-exchange-induced spin-orbit coupling in a superfluid mixture

“…We have considered here, perhaps, the simplest spinor mixtures. This can be naturally extended to mixtures of high spin systems [31][32][33][34][35][36][37], where both the interand intra-species spin-exchange interactions exist, the interplay between which may lead to even richer physics. The system considered here is quasi-one dimensional.…”