Theoretical and Experimental Aspects of Quantum Discord and Related Measures

Céleri, Lucas C.; Maziero, Jonas; Serra, R. M.

doi:10.1142/s0219749911008374

Cited by 116 publications

(158 citation statements)

References 138 publications

(240 reference statements)

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“…The probability distribution landscape, P (f θ , φ), over the plane of (f θ , φ), in the case of a two-qubit state ρAB of the form in Eq. (11) in the case of QD (a) and QWD (c). The regions 1-5 are marked on the maps of the distribution landscape in the case of QD (b) and QWD (d) so that the corresponding quantum correlation for majority of the states is optimized in the marked regions.…”

Section: B Two-qubit States In Parameter Spacementioning

confidence: 99%

“…Parallely, various counter-intuitive findings such as substantial non-classical efficiency of quantum states with vanishingly small entanglement, and locally indistinguishable orthogonal product states [5][6][7][8] have motivated the search for quantum correlations not belonging to the entanglement-separability paradigm. This has led to the possibility of introducing more fine-grained quantum correlation measures than entanglement, such as quantum discord (QD) [9], quantum work deficit (QWD) [10], and various 'discord-like' measures [11,12], opening up a new direction of research in quantum information theory. Although establishing a link between the measures of quantum correlations belonging to the two different genres has also been tried [13], a decisive result is yet to be found in the case of mixed bipartite quantum states.…”

Section: Introductionmentioning

confidence: 99%

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Reducing computational complexity of quantum correlations

et al. 2015

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We address the issue of reducing the resource required to compute information-theoretic quantum correlation measures like quantum discord and quantum work deficit in two qubits and higher dimensional systems. We show that determination of the quantum correlation measure is possible even if we utilize a restricted set of local measurements. We find that the determination allows us to obtain a closed form of quantum discord and quantum work deficit for several classes of states, with a low error. We show that the computational error caused by the constraint over the complete set of local measurements reduces fast with an increase in the size of the restricted set, implying usefulness of constrained optimization, especially with the increase of dimensions. We perform quantitative analysis to investigate how the error scales with the system size, taking into account a set of plausible constructions of the constrained set. Carrying out a comparative study, we show that the resource required to optimize quantum work deficit is usually higher than that required for quantum discord. We also demonstrate that minimization of quantum discord and quantum work deficit is easier in the case of two-qubit mixed states of fixed ranks and with positive partial transpose in comparison to the corresponding states having non-positive partial transpose. Applying the methodology to quantum spin models, we show that the constrained optimization can be used with advantage in analyzing such systems in quantum information-theoretic language. For bound entangled states, we show that the error is significantly low when the measurements correspond to the spin observables along the three Cartesian coordinates, and thereby we obtain expressions of quantum discord and quantum work deficit for these bound entangled states.

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Section: B Two-qubit States In Parameter Spacementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Reducing computational complexity of quantum correlations

et al. 2015

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“…(9), has an absolute minimum for a 1 = a 2 = b 1 = b 2 = 0 and for a 3 =ā 3 , b 3 =b 3 solutions of Eqs. (13) when an X state is considered.…”

Section: Appendix Amentioning

confidence: 99%

“…The properties of quantum discord have been widely investigated in the last years [13]. It has been shown that it is present in almost all quantum states [14] and the relation between discord and entanglement has been discussed [15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Unified view of correlations using the square-norm distance

et al. 2012

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The distance between a quantum state and its closest state not having a certain property has been used to quantify the amount of correlations corresponding to that property. This approach allows a unified view of the various kinds of correlations present in a quantum system. In particular, using relative entropy as a distance measure, total correlations can be meaningfully separated in a quantum and a classical part thanks to an additive relation involving only distances between states. Here, we investigate a unified view of correlations using as distance measure the square norm, already used to define the so-called geometric quantum discord. We thus consider geometric quantifiers also for total and classical correlations finding, for a quite general class of bipartite states, their explicit expressions. We analyze the relationship among geometric total, quantum and classical correlations and we find that they do not satisfy anymore a closed additivity relation.

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“…It has been also shown [20,21] that discord quantifies the minimum damage made by a decoherence process to the performance of many quantum information processing protocols, including teleportation, distillation and dense coding.…”

mentioning

confidence: 99%

Discording Power of Quantum Evolutions

et al. 2013

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We introduce the discording power of a unitary transformation, which assesses its capability to produce quantum discord, and analyze in detail the generation of discord by relevant classes of two-qubit gates. Our measure is based on the Cartan decomposition of two-qubit unitaries and on evaluating the maximum discord achievable by a unitary upon acting on classical-classical states at fixed purity. We found that there exist gates which are perfect discorders for any value of purity, and that they belong to a class of operators that includes the √ SWAP. Other gates, even those universal for quantum computation, do not posses the same property: the CNOT, for example, is a perfect discorder only for states with low or unit purity, but not for intermediate values. The discording power of a two-qubit unitary also provides a generalization of the corresponding measure defined for entanglement to any value of the purity. The primary aim of the science of quantum information is the exploitation of the quantum structure of nature for information processing and communication tasks. Among the quantum features of a physical system, entanglement is usually considered the prominent resource, providing speed-up in various quantum information and communication tasks [1]. In the realm of mixed-state quantum-information, however, instances are known where quantum advantages are obtained in the presence of little or no entanglement. In fact, quantum discord [2,3] has been proposed as the source behind this enhancement [4], and some indications in this direction have been given [5][6][7][8]. The notion of nonclassicality springing from information theory has been also discussed in comparison with that coming from phase-space constraints [9].Although introduced in the context of environment induced decoherence, quantum discord has been then related to the performance of quantum and classical Maxwell's demons [10] and to the thermodynamic efficiency of a photo-Carnot engine [11], as well as the total entanglement consumption [12], and the minimum possible increase of quantum communication cost [13] in state merging protocols. Furthermore, its propagation properties have been studied in [14] in connection with micro-causality and in [15] for quantum spin channels.Quantum discord can be activated into distillable entanglement [16,17], and has been shown to be a resource in quantum state discrimination [18] and quantum locking [19]. It has been also shown [20,21] that discord quantifies the minimum damage made by a decoherence process to the performance of many quantum information processing protocols, including teleportation, distillation and dense coding.In continuous variable systems, Gaussian quantum discord [22,23] has been experimentally measured [24][25][26] and represents a measure of the advantage provided by coherent quantum systems over their classical counterpart. It has been also suggested [27] that the geometric quantum discord [28] is the optimal resource for remote quantum state preparation, though the interpretation of ...

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Theoretical and Experimental Aspects of Quantum Discord and Related Measures

Cited by 116 publications

References 138 publications

Reducing computational complexity of quantum correlations

Reducing computational complexity of quantum correlations

Unified view of correlations using the square-norm distance

Discording Power of Quantum Evolutions

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