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Detection of genuine n-qubit entanglement via the proportionality of two vectors [article]

Dafa Li
2018 arXiv   pre-print
Thus, we avoid decomposing a coefficient vector into a tensor product of two vectors to detect the genuine entanglement. We also present the full decomposition theorem for product states of n qubits.  ...  In terms of " proportionality" , we can rephrase that a pure state of n qubits is genuinely entangled if and only if there are two non-zero block vectors of the coefficient vector which are not proportional  ...  Thus, we give another necessary and sufficient condition for the genuine entanglement via "proportionality" of two vectors and permutations of qubits.  ... 
arXiv:1810.03674v1 fatcat:nx64hpsb4vepzbpiwwrrm7tcjq

Reducing the detection of genuine entanglement of n qubits to two qubits [article]

Dafa Li
2021 arXiv   pre-print
We also show that a pure n-qubit state is genuinely entangled provided that the state has at least two genuinely entangled (n-1)-qubit projected states.  ...  By repeating the losing process, we reduce the detection of entanglement of pure n-qubit states to the one of pure two-qubit states. Also we write a LISP program for the reduction process.  ...  The genuine n-qubit entanglement can be detected via the proportionality of two coefficient vectors [11] . In this paper, we propose the losing one qubit operator.  ... 
arXiv:2110.01479v1 fatcat:iua7wmlzkrhgtpccgmn5dc7xmu

Quantifying entanglement resources

Christopher Eltschka, Jens Siewert
2014 Journal of Physics A: Mathematical and Theoretical  
We present an overview of the quantitative theory of single-copy entanglement in finite-dimensional quantum systems.  ...  In particular we emphasize the point of view that different entanglement measures quantify different types of resources which leads to a natural interdependence of entanglement classification and quantification  ...  Via this method, various interesting bounds for white-noise tolerance could be found, i.e., the maximum weight 1 − p * for which an entangled N -qubit state ψ ent remains genuinely entangled in a mixture  ... 
doi:10.1088/1751-8113/47/42/424005 fatcat:4kyiz4hyozh7xnjlhxdyunb5jq

Heisenberg-Weyl Observables: Bloch vectors in phase space

Ali Asadian, Paul Erker, Marcus Huber, Claude Klöckl
2016 Physical Review A  
Such bounds can be used in entanglement detection and we show that Heisenberg-Weyl observables provide a first non-trivial example beyond the dichotomic case.  ...  The complete set of Heisenberg-Weyl observables allows us to identify a real-valued Bloch vector for an arbitrary density operator in discrete phase space, with a smooth transition to infinite dimensions  ...  The convenient convexity of the moduli also allows a trivial extension to detect genuine multipartite entanglement.  ... 
doi:10.1103/physreva.94.010301 fatcat:lbsmsc46hfbblnm3yiq5yolsfa

Experimental verification of multidimensional quantum steering

Che-Ming Li, Hsin-Pin Lo, Liang-Yu Chen, Atsushi Yabushita
2018 Optics Communications  
The designed scenario offers a new method to study further the genuine multipartite steering of large dimensionality and potential uses in quantum information processing.  ...  We use multidimensional steering witnesses to verify EPR steering of polarization-entangled pairs and SS steering of single photons.  ...  ACKNOWLEDGEMENTS This work is supported by the Ministry of Science and Technology, Taiwan, under Grant No. MOST 104-2112-M-006 -016 -MY3 and 104-2112-M-009 -001 -MY2.  ... 
doi:10.1016/j.optcom.2017.11.070 fatcat:ito3eytqkrdpna2w5yqiieiit4

Self-testing non-projective quantum measurements in prepare-and-measure experiments [article]

Armin Tavakoli, Massimiliano Smania, Tamás Vértesi, Nicolas Brunner, Mohamed Bourennane
2018 arXiv   pre-print
In the latter case, the data certifies a genuine four-outcome qubit POVM. Our results open interesting perspective for strong 'black-box' certification of quantum devices.  ...  Self-testing represents the strongest form of certification of a quantum system. Here we investigate theoretically and experimentally the question of self-testing non-projective quantum measurements.  ...  A well-known example is that the maximal violation of the Clauser-Horne-Shimony-Holt (CHSH) Bell inequality [14] implies (self-tests) a maximally entangled two-qubit state, and pairs of anti-commuting  ... 
arXiv:1811.12712v2 fatcat:yk7nwq4plbe45gafzmmp3muqvy

Quantum chaos, delocalization, and entanglement in disordered Heisenberg models

Winton G. Brown, Lea F. Santos, David J. Starling, Lorenza Viola
2008 Physical Review E  
characterize the onset of chaos in the presence of disorder.  ...  A distinctive correlation between entanglement, delocalization, and integrability is uncovered, which may be generic to systems described by the two-body random ensemble and may point to a new diagnostic  ...  · ជ ͑j͒ , ͑6͒ where ជ ͑i͒ is the vector of Pauli matrices ͑ x ͑i͒ , y ͑i͒ , z ͑i͒ ͒ acting on the two-dimensional Hilbert space of the ith site.  ... 
doi:10.1103/physreve.77.021106 pmid:18351986 fatcat:mesn5mndcratfctumixrfxgvpq

Quantum information with top quarks in QCD production [article]

Yoav Afik, Juan Ramón Muñoz de Nova
2022 arXiv   pre-print
In the case of entanglement, this signature represents the violation of a Cauchy-Schwarz inequality.  ...  Finally, we argue that the CHSH violation detected in a collider is only a weak form of violation of Bell's theorem, necessarily containing a number of loopholes.  ...  JR-MdN acknowledges funding from European Union's Horizon 2020 research and innovation programme under the Marie Sk lodowska-Curie grant agreement No 847635, and also partially from Grant FIS2017-84368  ... 
arXiv:2203.05582v1 fatcat:gxv764gm5varzpj63wtcvvkw5y

Subsystem symmetries, quantum cellular automata, and computational phases of quantum matter [article]

David T. Stephen, Hendrik Poulsen Nautrup, Juani Bermejo-Vega, Jens Eisert, Robert Raussendorf
2019 arXiv   pre-print
structure of entanglement that is uniformly present throughout these phases.  ...  We show that states within a non-trivial SPT phase protected by these symmetries are indicated by the presence of the same QCA in a tensor network representation of the state, thereby characterizing the  ...  If we contract the physical (upwards-directed) leg of the tensor A T with the N -qubit state vector |j = |j 1 , j 2 , . . . , j N , the result is a 2 N × 2 N matrix acting in the virtual space of the tensor  ... 
arXiv:1806.08780v3 fatcat:uwkom534xngkrkbpzcb2nsegda

Subsystem symmetries, quantum cellular automata, and computational phases of quantum matter

David T. Stephen, Hendrik Poulsen Nautrup, Juani Bermejo-Vega, Jens Eisert, Robert Raussendorf
2019 Quantum  
structure of entanglement that is uniformly present throughout these phases.  ...  We show that states within a non-trivial SPT phase protected by these symmetries are indicated by the presence of the same QCA in a tensor network representation of the state, thereby characterizing the  ...  If we contract the physical (upwards-directed) leg of the tensor A T with the N -qubit state vector |j = |j 1 , j 2 , . . . , j N , the result is a 2 N × 2 N matrix acting in the virtual space of the tensor  ... 
doi:10.22331/q-2019-05-20-142 fatcat:2gkssin55ffgriijwvourqss2i

Echoing the recent Google success: Foundational Roots of Quantum Supremacy [article]

Andrei Khrennikov
2019 arXiv   pre-print
(Our analysis also includes comparison of classical vs genuine quantum entanglements.)  ...  Consequently, classical probabilistic algorithms involving calculation of jpd for n random variables can be over-performed by quantum algorithms (for big values of n).  ...  A qubit is a two-state (or two-level) quantum-mechanical system, one of the simplest quantum systems displaying the peculiarity of quantum mechanics."  ... 
arXiv:1911.10337v1 fatcat:57qstze6nbf6fcacz73qklxbqe

Entanglement-Enhanced Classical Communication [article]

David A. Herrera-Martí
2009 arXiv   pre-print
The technical content of the thesis is twofold. On one hand, a quadratic classification based on optimization programs that I devised for distinguishing entangled states is presented in Chapter 4.  ...  This thesis will be focused on the classical capacity of quantum channels, one of the first areas treated by quantum information theorists. The problem is fairly solved since some years.  ...  , only 12.7% of the "entangled vectors" are detected.  ... 
arXiv:0810.2041v2 fatcat:veooopfzp5gsllf6hn5kuhc3ku

Genuine multipartite nonlocality of entangled thermal states

G. McKeown, F. L. Semião, H. Jeong, M. Paternostro
2010 Physical Review A. Atomic, Molecular, and Optical Physics  
We discuss the conditions for maximizing the degree of violation against the local thermal character of the states and the inefficiency of the detection apparatuses.  ...  This opens up the possibility for coherent exploitation of multipartite quantum channels made out of entangled thermal states.  ...  [15] , where the entanglement in a mixed two-mode non-Gaussian state has been examined under the assumption that each mode-qubit subsystem interacts via a local Jaynes-Cummings model.  ... 
doi:10.1103/physreva.82.022315 fatcat:wd43ang2ujelpf3nptx23pw6li

Quantum repeaters and quantum key distribution: Analysis of secret-key rates

Silvestre Abruzzo, Sylvia Bratzik, Nadja K. Bernardes, Hermann Kampermann, Peter van Loock, Dagmar Bruß
2013 Physical Review A. Atomic, Molecular, and Optical Physics  
Additionally, we examine in detail the impact of device imperfections on the final secret key rate and on the optimal number of rounds of distillation when the entangled states are purified right after  ...  spin qubits, and the Duan-Lukin-Cirac-Zoller-type repeater using atomic ensembles together with linear optics and, in its most recent extension, heralded qubit amplifiers.  ...  Acknowledgments The authors acknowledge financial support by the German Federal Ministry of  ... 
doi:10.1103/physreva.87.052315 fatcat:nrvjskqtqjgxnapg4hevflndaq

Entanglement Evolution in Finite Dimensions

Markus Tiersch, Fernando de Melo, Andreas Buchleitner
2008 Physical Review Letters  
We provide a relation which describes how the entanglement of two d-level systems evolves as either system undergoes an arbitrary physical process.  ...  The dynamics of the entanglement turns out to be of a simple form, and is fully captured by a single quantity.  ...  although G-concurrence detects only a very specific type of entanglement, that is entanglement in exactly d levels.  ... 
doi:10.1103/physrevlett.101.170502 pmid:18999731 fatcat:px5j5jyml5bulnfvnussl7gese
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