Quantum Networks and Symmetries

Abstract 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.

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Quantum Mappings and Characterization of Entangled Quantum States

Journal of Mathematical Sciences ◽

10.1007/s10958-019-04418-3 ◽

2019 ◽

Vol 241 (2) ◽

pp. 210-236 ◽

Cited By ~ 6

Author(s):

S. N. Filippov

Keyword(s):

Quantum States ◽

Entangled Quantum States

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“Non-locality”

10.1093/oso/9780198714057.003.0004 ◽

2017 ◽

Author(s):

Richard Healey

Keyword(s):

Quantum Theory ◽

Quantum Entanglement ◽

Quantum States ◽

Entangled States ◽

Entangled Quantum States ◽

Action At A Distance ◽

Insight Into ◽

Non Locality

Quantum entanglement is popularly believed to give rise to spooky action at a distance of a kind that Einstein decisively rejected. Indeed, important recent experiments on systems assigned entangled states have been claimed to refute Einstein by exhibiting such spooky action. After reviewing two considerations in favor of this view I argue that quantum theory can be used to explain puzzling correlations correctly predicted by assignment of entangled quantum states with no such instantaneous action at a distance. We owe both considerations in favor of the view to arguments of John Bell. I present simplified forms of these arguments as well as a game that provides insight into the situation. The argument I give in response turns on a prescriptive view of quantum states that differs both from Dirac’s (as stated in Chapter 2) and Einstein’s.

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Computing conditional entropies for quantum correlations

Nature Communications ◽

10.1038/s41467-020-20018-1 ◽

2021 ◽

Vol 12 (1) ◽

Author(s):

Peter Brown ◽

Hamza Fawzi ◽

Omar Fawzi

Keyword(s):

Quantum Key Distribution ◽

Detection Efficiency ◽

Conditional Entropy ◽

Key Distribution ◽

Quantum Correlations ◽

Upper Bounds ◽

Cryptographic Protocols ◽

Quantum States ◽

Security Proofs

AbstractThe rates of quantum cryptographic protocols are usually expressed in terms of a conditional entropy minimized over a certain set of quantum states. In particular, in the device-independent setting, the minimization is over all the quantum states jointly held by the adversary and the parties that are consistent with the statistics that are seen by the parties. Here, we introduce a method to approximate such entropic quantities. Applied to the setting of device-independent randomness generation and quantum key distribution, we obtain improvements on protocol rates in various settings. In particular, we find new upper bounds on the minimal global detection efficiency required to perform device-independent quantum key distribution without additional preprocessing. Furthermore, we show that our construction can be readily combined with the entropy accumulation theorem in order to establish full finite-key security proofs for these protocols.

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Introduction, generation and entanglement of entangled displaced even and odd squeezed states

International Journal of Quantum Information ◽

10.1142/s0219749920500471 ◽

2021 ◽

pp. 2050047

Author(s):

Amir Karimi

Keyword(s):

Quantum States ◽

Entangled States ◽

Squeezed States ◽

Displacement Operator ◽

Text Type ◽

Level Atom ◽

Displacement Parameter ◽

Entangled Quantum States ◽

Quantized Field ◽

Classical Fields

In this paper, first, we introduce special types of entangled quantum states named “entangled displaced even and odd squeezed states” by using displaced even and odd squeezed states which are constructed via the action of displacement operator on the even and odd squeezed states, respectively. Next, we present a theoretical scheme to generate the introduced entangled states. This scheme is based on the interaction between a [Formula: see text]-type three-level atom and a two-mode quantized field in the presence of two strong classical fields. In the continuation, we consider the entanglement feature of the introduced entangled states by evaluating concurrence. Moreover, we study the influence of the displacement parameter on the entanglement degree of the introduced entangled states and compare the results. It will be observed that the concurrence of the “entangled displaced odd squeezed states” has less decrement with respect to the “entangled displaced even squeezed states” by increasing the displacement parameter.

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The memory effect of nanoscale memristors investigated by conducting scanning probe microscopy methods

Beilstein Journal of Nanotechnology ◽

10.3762/bjnano.3.82 ◽

2012 ◽

Vol 3 ◽

pp. 722-730 ◽

Cited By ~ 5

Author(s):

César Moreno ◽

Carmen Munuera ◽

Xavier Obradors ◽

Carmen Ocal

Keyword(s):

Memory Effect ◽

Scanning Probe Microscopy ◽

Electrical Characterization ◽

Scanning Force Microscopy ◽

Scanning Probe ◽

Force Microscopy ◽

Versatile Tool ◽

Scanning Force ◽

Memristor Device

We report on the use of scanning force microscopy as a versatile tool for the electrical characterization of nanoscale memristors fabricated on ultrathin La0.7Sr0.3MnO3 (LSMO) films. Combining conventional conductive imaging and nanoscale lithography, reversible switching between low-resistive (ON) and high-resistive (OFF) states was locally achieved by applying voltages within the range of a few volts. Retention times of several months were tested for both ON and OFF states. Spectroscopy modes were used to investigate the I–V characteristics of the different resistive states. This permitted the correlation of device rectification (reset) with the voltage employed to induce each particular state. Analytical simulations by using a nonlinear dopant drift within a memristor device explain the experimental I–V bipolar cycles.

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Quantum limit of genuine tripartite correlations by bipartite extremality

International Journal of Quantum Information ◽

10.1142/s0219749920500148 ◽

2020 ◽

Vol 18 (04) ◽

pp. 2050014

Author(s):

Hiroyuki Ozeki ◽

Satoshi Ishizaka

Keyword(s):

Probability Space ◽

Quantum Correlations ◽

Quantum Limit ◽

Sufficient Criterion ◽

Extremal Points ◽

Chsh Inequality ◽

Nonlocal Correlations ◽

Necessary And Sufficient

The characterization of the extremal points of the set of quantum correlations has attracted wide interest. In the simplest bipartite Bell scenario, a necessary and sufficient criterion for identifying extremal correlations has recently been conjectured, but extremality of tripartite correlations is not well known. In this study, we analyze tripartite extremal correlations in terms of the conjectured bipartite extremal criterion, and we demonstrate that the bipartite part of some extremal correlations satisfies the bipartite criterion, even though they violate Svetlichny’s inequality, and therefore are considered (stronger) genuine tripartite nonlocal correlations. This phenomenon arises from the fact that the conjectured extremal criterion is automatically satisfied when the violation of the Clauser–Horne–Shimony–Holt (CHSH) inequality exceeds a certain threshold, the value of which is given by the maximum CHSH violation at the edges of the probability space. This also suggests the possibility that the extremality of bipartite correlations can be certified by verifying whether the CHSH violation exceeds the threshold.

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Designing locally maximally entangled quantum states with arbitrary local symmetries

Quantum ◽

10.22331/q-2021-05-01-450 ◽

2021 ◽

Vol 5 ◽

pp. 450

Author(s):

Oskar Słowik ◽

Adam Sawicki ◽

Tomasz Maciążek

Keyword(s):

Quantum State ◽

Quantum States ◽

Local Mode ◽

Trivial Representation ◽

Tensor Power ◽

Technical Result ◽

Combinatorial Objects ◽

Local Symmetries ◽

Entangled Quantum States ◽

Group Of Symmetries

One of the key ingredients of many LOCC protocols in quantum information is a multiparticle (locally) maximally entangled quantum state, aka a critical state, that possesses local symmetries. We show how to design critical states with arbitrarily large local unitary symmetry. We explain that such states can be realised in a quantum system of distinguishable traps with bosons or fermions occupying a finite number of modes. Then, local symmetries of the designed quantum state are equal to the unitary group of local mode operations acting diagonally on all traps. Therefore, such a group of symmetries is naturally protected against errors that occur in a physical realisation of mode operators. We also link our results with the existence of so-called strictly semistable states with particular asymptotic diagonal symmetries. Our main technical result states that the Nth tensor power of any irreducible representation of SU(N) contains a copy of the trivial representation. This is established via a direct combinatorial analysis of Littlewood-Richardson rules utilising certain combinatorial objects which we call telescopes.

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