Vanishing Quantum Discord is Necessary and Sufficient for Completely Positive Maps

Shabani, Alireza; Lidar, Daniel A.

doi:10.1103/physrevlett.102.100402

Cited by 295 publications

(133 citation statements)

References 18 publications

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“…It has been used to understand the completely positive evolution of a system [17,18,19], local broadcasting [20,21]. Thus, finding zero discord quantum states is important in quantum information theory.…”

Section: Let {ρ (A)mentioning

confidence: 99%

Quantum discord of states arising from graphs

Dutta

Adhikari

Banerjee

2017

Quantum Inf Process

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Quantum discord refers to an important aspect of quantum correlations for bipartite quantum systems. In our earlier works we have shown that corresponding to every graph (combinatorial) there are quantum states whose properties are reflected in the structure of the corresponding graph. Here, we attempt to develop a graph theoretic study of quantum discord that corresponds to a necessary and sufficient condition of zero quantum discord states which says that the blocks of density matrix corresponding to a zero quantum discord state are normal and commute with each other. These blocks have a one to one correspondence with some specific subgraphs of the graph which represents the quantum state. We obtain a number of graph theoretic properties representing normality and commutativity of a set of matrices which are indeed arising from the given graph. Utilizing these properties we define graph theoretic measures for normality and commutativity that results a formulation of graph theoretic quantum discord. We identify classes of quantum states with zero discord using the said formulation.

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Section: Let {ρ (A)mentioning

confidence: 99%

Quantum discord of states arising from graphs

Dutta

Adhikari

Banerjee

2017

Quantum Inf Process

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“…Several approaches have been proposed to quantify this generalized quantum correlation present in a bipartite mixed quantum state [5,[7][8][9], one of which, quantum discord [5], has received special attention [10][11][12][13][14][15][16]. Beyond the importance of nonclassical correlations (other than entanglement) for the foundations of quantum mechanics, the relevance of such an issue is increasing in several fields as well as in QIS applications.…”

mentioning

confidence: 99%

“…In the context of quantum field theory, it has been shown that the Unruh effect may also lead to an abrupt change in the behavior of correlations [17]. For applications in QIS, it is interesting to know that states with nonzero quantum discord cannot be locally broadcast [18], and this kind of nonclassicality is also related to a condition for a complete positive map [12]. Quantum discord was proposed as a figure of merit for the quantum advantage in some computational models without or with little entanglement [13,14].…”

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confidence: 99%

Environment-Induced Sudden Transition in Quantum Discord Dynamics

et al. 2011

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Non-classical correlations play a crucial role in the development of quantum information science. The recent discovery that non-classical correlations can be present even in separable (unentangled) states has broadened this scenario. This generalized quantum correlation has been increasing relevance in several fields, among them quantum communication, quantum computation, quantum phase transitions, and biological systems. We demonstrate here the occurrence of the suddenchange phenomenon and immunity against some sources of noise for the quantum discord and its classical counterpart, in a room temperature nuclear magnetic resonance setup. The experiment is performed in a decohering environment causing loss of phase relations among the energy eigenstates and exchange of energy between system and environment, resulting in relaxation to a Gibbs ensemble.

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“…(49) that whenever ρ 0 = ρ 1 (which is the case when W 0 W 1 and K 0 K 1 ), the above commutator does not vanish and thus, as shown in [39], the state has nonvanishing quantum discord. Although it is not a sufficient condition, an initial state with nonvanishing discord indicates that the reduced spin dynamics (E and N ) may not be completely positive (CP) [40][41][42].…”

Section: Relativistic Quantum Mapmentioning

confidence: 99%

Sending classical information through relativistic quantum channels

Landulfo

Torres

2013

Phys. Rev. A

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We investigate how special relativity influences the transmission of classical information through quantum channels by evaluating the Holevo bound when the sender and the receiver are in (relativistic) relative motion. By using the spin degrees of freedom of spin-1/2 fermions to encode the classical information, we show that, for some configurations, the accessible information in the receiver can be increased when the spin detector moves fast enough. This is possible by allowing the momentum wave packet of one of the particles to be sufficiently wide while the momentum wave packets of other particles are kept relatively narrow. In this way, one can take advantage of the fact that boosts entangle the spin and momentum degrees of freedom of spin-1/2 fermions to increase the accessible information in the former. We close the paper with a discussion of how this relativistic quantum channel cannot in general be described by completely positive quantum maps.

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Vanishing Quantum Discord is Necessary and Sufficient for Completely Positive Maps

Cited by 295 publications

References 18 publications

Quantum discord of states arising from graphs

Quantum discord of states arising from graphs

Environment-Induced Sudden Transition in Quantum Discord Dynamics

Sending classical information through relativistic quantum channels

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