scholarly journals Multipartite entanglement and topology in holography

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Jonathan Harper
Keyword(s):  
Minimal Surface ◽  
Cross Section ◽  
Mixed State ◽  
Homology Class ◽  
Boundary Region ◽  
Multipartite Entanglement ◽  
Purification Procedure ◽  
Bipartite Entanglement ◽  
Original Boundary ◽  
And Topology

Abstract Starting from the entanglement wedge of a multipartite mixed state we describe a purification procedure which involves the gluing of several copies. The resulting geometry has non-trivial topology and a single oriented boundary for each original boundary region. In the purified geometry the original multipartite entanglement wedge cross section is mapped to a minimal surface of a particular non-trivial homology class. In contrast, each original bipartite entanglement wedge cross section is mapped to the minimal wormhole throat around each boundary. Using the bit thread formalism we show how maximal flows for the bipartite and multipartite entanglement wedge cross section can be glued together to form maximal multiflows in the purified geometry. The defining feature differentiating the flows is given by the existence of threads which cross between different copies of the original entanglement wedge. Together these demonstrate a possible connection between multipartite entanglement and the topology of holographic spacetimes.

Evolution of Genuine Multipartite Entanglement of Specific and Random States Under non-Markovian Noise

2014 ◽  
Vol 21 (04) ◽  
pp. 1450008 ◽  
Author(s):  
Mazhar Ali
Keyword(s):  
Mixed State ◽  
Weighted Graph ◽  
Ghz State ◽  
W State ◽  
Multipartite Entanglement ◽  
Fragile State ◽  
Graph States ◽  
Random States ◽  
Genuine Multipartite Entanglement

We study the dynamics of genuine multipartite entanglement under non-Markovian noise. Using a computable entanglement monotone for multipartite systems, we investigate a system of three qubits each of which is individually exposed to classical Ornstein–Uhlenbeck noise. We found that the W state mixed with the maximally mixed state is the most fragile state, whereas a similar mixture of GHZ state exhibits robust behaviour. We compare dynamics of these states with dynamics of similar mixtures of random states and weighted graph states. We also discuss the limiting cases.

scholarly journals Correlation loss and multipartite entanglement across a black hole horizon (

2009 ◽  
Vol 9 (7&8) ◽  
pp. 657-665
Author(s):  
G. Adesso ◽  
I. Fuentes-Schuller
Keyword(s):  
Black Hole ◽  
Small Mass ◽  
Point Of View ◽  
Multipartite Entanglement ◽  
Squeezed State ◽  
Schwarzschild Black Hole ◽  
Bipartite Entanglement ◽  
Hawking Effect ◽  
Entanglement Distribution ◽  
Quantum And Classical Correlations

We investigate the Hawking effect on entangled fields. By considering a scalar field which is in a two-mode squeezed state from the point of view of freely falling (Kruskal) observers crossing the horizon of a Schwarzschild black hole, we study the degradation of quantum and classical correlations in the state from the perspective of physical (Schwarzschild) observers confined outside the horizon. Due to monogamy constraints on the entanglement distribution, we show that the lost bipartite entanglement is recovered as multipartite entanglement among modes inside and outside the horizon. In the limit of a small-mass black hole, no bipartite entanglement is detected outside the horizon, while the genuine multipartite entanglement interlinking the inner and outer regions grows infinitely.

scholarly journals Multipartite entanglement outperforming bipartite entanglement under limited quantum system sizes

2018 ◽  
Vol 98 (5) ◽  
Author(s):  
Hayata Yamasaki ◽  
Alexander Pirker ◽  
Mio Murao ◽  
Wolfgang Dür ◽  
Barbara Kraus
Keyword(s):  
Quantum System ◽  
Multipartite Entanglement ◽  
Bipartite Entanglement

scholarly journals CHARACTERIZING AND MEASURING MULTIPARTITE ENTANGLEMENT

2007 ◽  
Vol 05 (01n02) ◽  
pp. 97-103 ◽  
Author(s):  
P. FACCHI ◽  
G. FLORIO ◽  
S. PASCAZIO
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Multipartite Entanglement ◽  
Bipartite Entanglement ◽  
Pure States

A method is proposed to characterize and quantify multipartite entanglement in terms of the probability density function of bipartite entanglement over all possible balanced bipartitions of an ensemble of qubits. The method is tested on a class of random pure states.

scholarly journals Dressed minimal surfaces in AdS4

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Dimitrios Katsinis ◽  
Dimitrios Manolopoulos ◽  
Ioannis Mitsoulas ◽  
Georgios Pastras
Keyword(s):  
Minimal Surface ◽  
Minimal Surfaces ◽  
Arbitrary Number ◽  
Sigma Model ◽  
Boundary Region ◽  
Linear Sigma Model ◽  
Area Element ◽  
Non Linear

Abstract We apply an arbitrary number of dressing transformations to a static minimal surface in AdS4. Interestingly, a single dressing transformation, with the simplest dressing factor, interrelates the latter to solutions of the Euclidean non linear sigma model in dS3. We present an expression for the area element of the dressed minimal surface in terms of that of the initial one and comment on the boundary region of the dressed surface. Finally, we apply the above formalism to the elliptic minimal surfaces and obtain new ones.

scholarly journals Genuine multipartite entanglement in time

2021 ◽  
Vol 10 (6) ◽  
Author(s):  
Simon Milz ◽  
Cornelia Spee ◽  
Zhen-Peng Xu ◽  
Felix Pollock ◽  
Kavan Modi ◽  
...  
Keyword(s):  
Sufficient Conditions ◽  
Quantum Correlations ◽  
Multipartite Entanglement ◽  
Quantum Processes ◽  
Bipartite Entanglement ◽  
Temporal Correlations ◽  
Crucial Difference ◽  
Comprehensive Picture ◽  
Quantum Steering ◽  
Genuine Multipartite Entanglement

While spatial quantum correlations have been studied in great detail, much less is known about the genuine quantum correlations that can be exhibited by temporal processes. Employing the quantum comb formalism, processes in time can be mapped onto quantum states, with the crucial difference that temporal correlations have to satisfy causal ordering, while their spatial counterpart is not constrained in the same way. Here, we exploit this equivalence and use the tools of multipartite entanglement theory to provide a comprehensive picture of the structure of correlations that (causally ordered) temporal quantum processes can display. First, focusing on the case of a process that is probed at two points in time -- which can equivalently be described by a tripartite quantum state -- we provide necessary as well as sufficient conditions for the presence of bipartite entanglement in different splittings. Next, we connect these scenarios to the previously studied concepts of quantum memory, entanglement breaking superchannels, and quantum steering, thus providing both a physical interpretation for entanglement in temporal quantum processes, and a determination of the resources required for its creation. Additionally, we construct explicit examples of W-type and GHZ-type genuinely multipartite entangled two-time processes and prove that genuine multipartite entanglement in temporal processes can be an emergent phenomenon. Finally, we show that genuinely entangled processes across multiple times exist for any number of probing times.

Bipartite entanglement of decohered mixed states generated from maximally entangled cluster states

2021 ◽  
Vol 36 (03) ◽  
pp. 2150010
Author(s):  
Mostafa Mansour ◽  
Saeed Haddadi
Keyword(s):  
Mixed State ◽  
Entangled States ◽  
Entangled State ◽  
Mixed States ◽  
Density Matrices ◽  
Bipartite Entanglement ◽  
Cluster States ◽  
Maximally Entangled State ◽  
Qubit System ◽  
Maximally Entangled States

In this work, we investigate the bipartite entanglement of decohered mixed states generated from maximally entangled cluster states of [Formula: see text] qubits physical system. We introduce the disconnected cluster states for an ensemble of [Formula: see text] non-interacting qubits and we give the corresponding separable density matrices. The maximally entangled states can be generated from disconnected cluster states, by assuming that the dynamics of the multi-qubit system is governed by a quadratic Hamiltonian of Ising type. When exposed to a local noisy interaction with the environment, the multi-qubit system evolves from its initial pure maximally entangled state to a decohered mixed state. The decohered mixed states generated from bipartite, tripartite and multipartite maximally entangled cluster states are explicitly expressed and their bipartite entanglements are investigated.

scholarly journals ENTANGLEMENT FRUSTRATION IN MULTIMODE GAUSSIAN STATES

2012 ◽  
Vol 09 (02) ◽  
pp. 1260022 ◽  
Author(s):  
COSMO LUPO ◽  
STEFANO MANCINI ◽  
PAOLO FACCHI ◽  
GIUSEPPE FLORIO ◽  
SAVERIO PASCAZIO
Keyword(s):  
Pure State ◽  
High Energy ◽  
Quantum Systems ◽  
Entangled States ◽  
Multipartite Entanglement ◽  
Total System ◽  
Continuous Variables ◽  
Bipartite Entanglement ◽  
Gaussian States ◽  
Composite Quantum System

Bipartite entanglement between two parties of a composite quantum system can be quantified in terms of the purity of one party and there always exists a pure state of the total system that maximizes it (and minimizes purity). When many different bipartitions are considered, the requirement that purity be minimal for all bipartitions gives rise to the phenomenon of entanglement frustration. This feature, observed in quantum systems with both discrete and continuous variables, can be studied by means of a suitable cost function whose minimizers are the maximally multipartite-entangled states (MMES). In this paper we extend the analysis of multipartite entanglement frustration of Gaussian states in multimode bosonic systems. We derive bounds on the frustration, under the constraint of finite mean energy, in the low- and high-energy limits.

scholarly journals Entanglement wedge cross section inequalities from replicated geometries

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Ning Bao ◽  
Aidan Chatwin-Davies ◽  
Grant N. Remmen
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
General Algorithm ◽  
Multipartite Entanglement

Abstract We generalize the constructions for the multipartite reflected entropy in order to construct spacetimes capable of representing multipartite entanglement wedge cross sections of differing party number as Ryu-Takayanagi surfaces on a single replicated geometry. We devise a general algorithm for such constructions for arbitrary party number and demonstrate how such methods can be used to derive novel inequalities constraining mulipartite entanglement wedge cross sections.

scholarly journals SEMITRANSPARENT PISTONS

2010 ◽  
Vol 25 (11) ◽  
pp. 2196-2200 ◽  
Author(s):  
P. MORALES ◽  
K. KIRSTEN
Keyword(s):  
Cross Section ◽  
Extra Dimensions ◽  
And Topology ◽  
The Cross

We consider semitransparent pistons in the presence of extra dimensions. It is shown that the piston is always attracted to the closest wall irrespective of details of the geometry and topology of the extra dimensions and of the cross section of the piston. Furthermore, we evaluate the zeta regularized determinant for this configuration.

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