Quantum networks are promising tools for the implementation of long-range quantum communication. The characterization of quantum correlations in networks and their usefulness for information ...processing is therefore central for the progress of the field, but so far only results for small basic network structures or pure quantum states are known. Here we show that symmetries provide a versatile tool for the analysis of correlations in quantum networks. We provide an analytical approach to characterize correlations in large network structures with arbitrary topologies. As examples, we show that entangled quantum states with a bosonic or fermionic symmetry can not be generated in networks; moreover, cluster and graph states are not accessible. Our methods can be used to design certification methods for the functionality of specific links in a network and have implications for the design of future network structures.
Recent advances have led towards first prototypes of quantum networks in which entanglement is distributed by sources producing bipartite entangled states. This raises the question of which states ...can be generated in quantum networks based on bipartite sources using local operations and classical communication. In this work, we study state transformations under finite rounds of local operations and classical communication (LOCC) in networks based on maximally entangled two-qubit states. We first derive the symmetries for arbitrary network structures, as these determine which transformations are possible. Then, we show that contrary to tree graphs, for which it has already been shown that any state within the same entanglement class can be reached, there exist states which can be reached probabilistically but not deterministically if the network contains a cycle. Furthermore, we provide a systematic way to determine states which are not reachable in networks consisting of a cycle. Moreover, we provide a complete characterization of the states which can be reached in a cycle network with a protocol where each party measures only once, and each step of the protocol results in a deterministic transformation. Finally, we present an example which cannot be reached with such a simple protocol, and constitutes, up to our knowledge, the first example of a LOCC transformation among fully entangled states requiring three rounds of classical communication.
Recently, various nonclassical properties of quantum states and channels have been characterized through an advantage they provide in quantum information tasks over their classical counterparts. Such ...advantage can be typically proven to be quantitative, in that larger amounts of quantum resources lead to better performance in the corresponding tasks. So far, these characterizations have been established only in the finite-dimensional setting, hence, leaving out central resources in continuous variable systems such as entanglement and nonclassicality of states as well as entanglement breaking and broadcasting channels. In this Letter, we present a fully general framework for resource quantification in infinite-dimensional systems. The framework is applicable to a wide range of resources with the only premises being that classical randomness cannot create a resource and that the resourceless objects form a closed set in an appropriate sense. As the latter may be hard to establish for the abstract topologies of continuous variable systems, we provide a relaxation of the condition with no reference to topology. This envelopes the aforementioned resources and various others, hence, giving them an interpretation as performance enhancement in so-called input-output games.
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One of the basic distinctions between classical and quantum mechanics is the existence of fundamentally incompatible quantities. Such quantities are present on all levels of quantum objects: states, ...measurements, quantum channels, and even higher order dynamics. In this manuscript, we show that two seemingly different aspects of quantum incompatibility: the quantum marginal problem of states and the incompatibility on the level of quantum channels are in many-to-one correspondence. Importantly, as incompatibility of measurements is a special case of the latter, it also forms an instance of the quantum marginal problem. The generality of the connection is harnessed by solving the marginal problem for Gaussian and Bell diagonal states, as well as for pure states under depolarizing noise. Furthermore, we derive entropic criteria for channel compatibility, and develop a converging hierarchy of semi-definite programs for quantifying the strength of quantum memories.
Four wild berry species, Amelanchier alnifolia, Viburnum trilobum, Prunus virginiana, and Shepherdia argentea, all integral to the traditional subsistence diet of Native American tribal communities, ...were evaluated to elucidate phytochemical composition and bioactive properties related to performance and human health. Biological activity was screened using a range of bioassays that assessed the potential for these little-known dietary berries to affect diabetic microvascular complications, hyperglycemia, pro-inflammatory gene expression, and metabolic syndrome symptoms. Nonpolar constituents from berries, including carotenoids, were potent inhibitors of aldose reductase (an enzyme involved in the etiology of diabetic microvascular complications), whereas the polar constituents, mainly phenolic acids, anthocyanins, and proanthocyanidins, were hypoglycemic agents and strong inhibitors of IL-1β and COX-2 gene expression. Berry samples also showed the ability to modulate lipid metabolism and energy expenditure in a manner consistent with improving metabolic syndrome. The results demonstrate that these berries traditionally consumed by tribal cultures contain a rich array of phytochemicals that have the capacity to promote health and protect against chronic diseases, such as diabetes.
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Stabilizer states and graph states find application in quantum error correction, measurement-based quantum computation and various other concepts in quantum information theory. In this work, we study ...party-local Clifford (PLC) transformations among stabilizer states. These transformations arise as a physically motivated extension of local operations in quantum networks with access to bipartite entanglement between some of the nodes of the network. First, we show that PLC transformations among graph states are equivalent to a generalization of the well-known local complementation, which describes local Clifford transformations among graph states. Then, we introduce a mathematical framework to study PLC equivalence of stabilizer states, relating it to the classification of tuples of bilinear forms. This framework allows us to study decompositions of stabilizer states into tensor products of indecomposable ones, that is, decompositions into states from the entanglement generating set (EGS). While the EGS is finite up to
3
parties Bravyi et al., J. Math. Phys.
47
, 062106 (2006), we show that for
4
and more parties it is an infinite set, even when considering party-local unitary transformations. Moreover, we explicitly compute the EGS for
4
parties up to
10
qubits. Finally, we generalize the framework to qudit stabilizer states in prime dimensions not equal to
2
, which allows us to show that the decomposition of qudit stabilizer states into states from the EGS is unique.
Genuine correlated coherence Kraft, Tristan; Piani, Marco
Journal of physics. A, Mathematical and theoretical,
10/2018, Volume:
51, Issue:
41
Journal Article
Peer reviewed
Open access
We introduce a notion of genuine correlated coherence. Such a notion is based on the possibility of concentrating on individual systems the coherence present in a distributed system, by making use of ...incoherent unitary transformations. We define an entropic quantifier of genuine correlated multipartite coherence for generic mixed states, and we focus on the bipartite pure-state case. In the latter case we derive necessary and sufficient conditions for the possibility of fully localizing the coherence, hence identifying the conditions for genuine correlated bipartite coherence. We analyze in detail the quantitative problem for the case of two-qubit pure states, identifying the states with the largest amount of genuine correlated coherence. Interestingly, such states do not have maximal global coherence nor maximal coherence rank.
Resource theories can be used to formalize the quantification and manipulation of resources in quantum information processing such as entanglement, asymmetry and coherence of quantum states, and ...incompatibility of quantum measurements. Given a certain state or measurement, one can ask whether there is a task in which it performs better than any resourceless state or measurement. Using conic programming, we prove that any general robustness measure (with respect to a convex set of free states or measurements) can be seen as a quantifier of such outperformance in some discrimination task. We apply the technique to various examples, e.g., joint measurability, positive operator valued measures simulable by projective measurements, and state assemblages preparable with a given Schmidt number.
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Entanglement of high-dimensional quantum systems has become increasingly important for quantum communication and experimental tests of nonlocality. However, many effects of high-dimensional ...entanglement can be simulated by using multiple copies of low-dimensional systems. We present a general theory to characterize those high-dimensional quantum states for which the correlations cannot simply be simulated by low-dimensional systems. Our approach leads to general criteria for detecting multilevel entanglement in multiparticle quantum states, which can be used to verify these phenomena experimentally.
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Some measurements in quantum mechanics disturb each other. This has puzzled physicists since the formulation of the theory, but only in recent decades has the incompatibility of measurements been ...analyzed in depth and detail, using the notion of joint measurability of generalized measurements. In this Colloquium joint measurability and incompatibility are reviewed from the perspective of quantum information science. The Colloquium starts by discussing the basic definitions and concepts. An overview on applications of incompatibility, such as in measurement uncertainty relations, the characterization of quantum correlations, or information processing tasks like quantum state discrimination, is then presented. Finally, emerging directions of research, such as a resource theory of incompatibility as well as other concepts to grasp the nature of measurements in quantum mechanics, are discussed.
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