Role of complementary correlations in the evolution of classical and quantum correlations under Markovian decoherence

Deb, Prasenjit; Banik, Manik

doi:10.1088/1751-8113/48/18/185303

Cited by 5 publications

(5 citation statements)

References 62 publications

(98 reference statements)

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“…Hence, the freezing of coherence might provide a deeper insight into the peculiar phenomenon of frozen quantum correlations under local flip channels (see also Ref. [67]), as the latter just reduce to coherence for t ≤ t ⋆ under the conditions we identified.…”

Section: 210401 (2015) P H Y S I C a L R E V I E W L E T T E R Smentioning

confidence: 73%

Frozen Quantum Coherence

2015

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We analyze under which dynamical conditions the coherence of an open quantum system is totally unaffected by noise. For a single qubit, specific measures of coherence are found to freeze under different conditions, with no general agreement between them. Conversely, for an N-qubit system with even N, we identify universal conditions in terms of initial states and local incoherent channels such that all bona fide distance-based coherence monotones are left invariant during the entire evolution. This finding also provides an insightful physical interpretation for the freezing phenomenon of quantum correlations beyond entanglement. We further obtain analytical results for distance-based measures of coherence in two-qubit states with maximally mixed marginals. Introduction.-The coherent superposition of states stands as one of the characteristic features that mark the departure of quantum mechanics from the classical realm, if not the most essential one [1]. Quantum coherence constitutes a powerful resource for quantum metrology [2,3] and entanglement creation [4,5] and is at the root of a number of intriguing phenomena of wide-ranging impact in quantum optics [6-9], quantum information [10], solidstate physics [11,12], and thermodynamics [13][14][15][16][17][18]. In recent years, research on the presence and functional role of quantum coherence in biological systems has also attracted considerable interest [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35].Despite the fundamental importance of quantum coherence, only very recently have relevant first steps been achieved towards developing a rigorous theory of coherence as a physical resource [36][37][38] and necessary constraints have been put forward to assess valid quantifiers of coherence [36,39]. A number of coherence measures have been proposed and investigated, such as the l 1 norm and relative entropy of coherence [36] and the skew information [40,41]. Attempts to quantify coherence via a distancebased approach, which has been fruitfully adopted for entanglement and other correlations [42][43][44][45][46][47][48][49][50][51][52], have revealed some subtleties [53].A lesson learned from natural sciences is that coherencebased effects can flourish and persist at significant time scales under suitable exposure to decohering environments. Recent evidence suggests that a fruitful interplay between long-lived quantum coherence and tailored noise may be in fact crucial to enhance certain biological processes, such as light harvesting [27,28,30,31]. This surprising cooperation between traditionally competing phenomena provides an inspiration to explore other physical contexts, such as quantum information science, in order to look for general conditions under which coherence can be sustained in the

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Section: 210401 (2015) P H Y S I C a L R E V I E W L E T T E R Smentioning

confidence: 73%

Frozen Quantum Coherence

2015

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“…Considering two complementary observables acting on each one of the subsystems of a bipartite system, it was shown that the sum of the local correlations between such observables is a good measure of the quantum correlations shared by the composite system. The general conclusion is that the mixedness of the initial bipartite state is not enough for the SCP, but the state also needs to present certain asymmetry with respect to local complementary observables [145]. Moreover, they also proved that a pure state will never present the SCP and that the freezing phenomena is not a general property of all the Bell-diagonal states.…”

Section: A Markovian Dynamics Of Correlationsmentioning

confidence: 96%

“…A new interpretation of the SCP was introduced employing the idea of complementary correlations [145]. Considering two complementary observables acting on each one of the subsystems of a bipartite system, it was shown that the sum of the local correlations between such observables is a good measure of the quantum correlations shared by the composite system.…”

Section: A Markovian Dynamics Of Correlationsmentioning

confidence: 99%

The Sudden Change Phenomenon of Quantum Discord

Céleri

Maziero

2017

Quantum Science and Technology

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Even if the parameters determining a system's state are varied smoothly, the behavior of quantum correlations alike to quantum discord, and of its classical counterparts, can be very peculiar, with the appearance of non-analyticities in its rate of change. Here we review this sudden change phenomenon (SCP) discussing some important points related to it: Its uncovering, interpretations, and experimental verifications, its use in the context of the emergence of the pointer basis in a quantum measurement process, its appearance and universality under Markovian and non-Markovian dynamics, its theoretical and experimental investigation in some other physical scenarios, and the related phenomenon of double sudden change of trace distance discord. Several open questions are identified, and we envisage that in answering them we will gain significant further insight about the relation between the SCP and the symmetry-geometric aspects of the quantum state space.

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“…Although E t,0 and E tp,0 should be completely positive by construction, the map E t,tp need not be completely positive and not even positive because the inverse E −1 tp of a completely positive map E tp need not be positive. Composition (18), originating from the existence of the inverse for all positive times, allows us to introduce the notion of divisibility. The family of dynamical maps is said to be P-divisible when propagator E t,tp is positive as well as trace-preserving, and CP-divisible if E t,tp is CPTP for all 0 < t p < t [14].…”

Section: Non-markovianity Measuresmentioning

confidence: 99%

“…[17], considering the case of Bell-diagonal states under the action of non-dissipative environments, the authors proved that all bona fide measures of quantum correlations virtually present the freezing effect under the same dynamical conditions. Besides, using the quantum discord as a measure for quantum correlations, the authors of [18] proved that a pure state never present the SCP and that the freezing phenomena is not a general property of all the Bell-diagonal states.…”

Section: Introductionmentioning

confidence: 99%

Quantum memory and quantum correlations of Majorana qubits used for magnetometry

Jahromi¹,

Haseli²

2019

Preprint

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We address how the non-local nature of the topological qubits, realized by Majorana modes and driven by an external magnetic field, can be used to control the non-Markovian dynamics of the system. It is also demonstrated that the non-local characteristic plays a key role in control and protection of quantum correlations between Majorana qubits. Moreover, we discuss how those non-local qubits help us to enhance quantum magnetometry.

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Role of complementary correlations in the evolution of classical and quantum correlations under Markovian decoherence

Cited by 5 publications

References 62 publications

Frozen Quantum Coherence

Frozen Quantum Coherence

The Sudden Change Phenomenon of Quantum Discord

Quantum memory and quantum correlations of Majorana qubits used for magnetometry

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