scholarly journals Quantum entanglement, supersymmetry, and the generalized Yang-Baxter equation

2020 ◽  
Vol 20 (1&2) ◽  
pp. 37-64
Author(s):  
Pramod Padmanabhan ◽  
Fumihiko Sugino ◽  
Diego Trancanelli
Keyword(s):  
Quantum Entanglement ◽  
Communication Protocol ◽  
Quantum Information Theory ◽  
Entangled States ◽  
Baxter Equation ◽  
Classical Communication ◽  
Separable States ◽  
Qubit System ◽  
Large Families ◽  
Parameter Dependent

Entangled states, such as the Bell and GHZ states, are generated from separable states using matrices known to satisfy the Yang-Baxter equation and its generalization. This remarkable fact hints at the possibility of using braiding operators as quantum entanglers, and is part of a larger speculated connection between topological and quantum entanglement. We push the analysis of this connection forward, by showing that supersymmetry algebras can be used to construct large families of solutions of the spectral parameter-dependent generalized Yang-Baxter equation. We present a number of explicit examples and outline a general algorithm for arbitrary numbers of qubits. The operators we obtain produce, in turn, all the entangled states in a multi-qubit system classified by the Stochastic Local Operations and Classical Communication protocol introduced in quantum information theory.

scholarly journals Braiding quantum gates from partition algebras

Quantum ◽  
2020 ◽  
Vol 4 ◽  
pp. 311
Author(s):  
Pramod Padmanabhan ◽  
Fumihiko Sugino ◽  
Diego Trancanelli
Keyword(s):  
Statistical Mechanics ◽  
Braid Group ◽  
Quantum Gates ◽  
Entangled States ◽  
Baxter Equation ◽  
Classical Communication ◽  
Qubit System ◽  
Partition Algebras

Unitary braiding operators can be used as robust entangling quantum gates. We introduce a solution-generating technique to solve the (d,m,l)-generalized Yang-Baxter equation, for m/2≤l≤m, which allows to systematically construct such braiding operators. This is achieved by using partition algebras, a generalization of the Temperley-Lieb algebra encountered in statistical mechanics. We obtain families of unitary and non-unitary braiding operators that generate the full braid group. Explicit examples are given for a 2-, 3-, and 4-qubit system, including the classification of the entangled states generated by these operators based on Stochastic Local Operations and Classical Communication.

The impact of resource on remote quantum correlation Preparation

2015 ◽  
Vol 15 (13&14) ◽  
pp. 1223-1232
Author(s):  
Chengjun Wu ◽  
Bin Luo ◽  
Hong Guo
Keyword(s):  
Quantum Entanglement ◽  
Quantum Correlation ◽  
Quantum Discord ◽  
Entangled States ◽  
Shared Resources ◽  
Classical Communication ◽  
Bell Measurement ◽  
Measurement Results ◽  
The Impact

When Alice and Bob share two pairs of quantum correlated states, Alice can remotely prepare quantum entanglement and quantum discord in Bob’s side by measuring the parts in her side and telling Bob the measurement results by classical communication. For remote entanglement preparation, entanglement is necessary . We find that for some shared resources having the same amount of entanglement, when Bell measurement is used, the entanglement remotely prepared can be different, and more discord in the resources actually decreases the entanglement prepared. We also find that for some resources with more entanglement, the entanglement remotely prepared may be less. Therefore, we conclude that entanglement is a necessary resource but may not be the only resource responsible for the entanglement remotely prepared, and discord does not likely to assist this process. Also, for the preparation of discord, we find that some states with no entanglement could outperform entangled states.

Gaussian (N, z)-generalized Yang-Baxter operators

2016 ◽  
pp. 105-114
Author(s):  
Eric Rowell
Keyword(s):  
Bell States ◽  
Entangled States ◽  
Unitary Matrix ◽  
Baxter Equation ◽  
Careful Study ◽  
Standard Measurement ◽  
Measurement Basis ◽  
Parameter Dependent

We find unitary matrix solutions R˜(a) to the (multiplicative parameter-dependent) (N, z)-generalized Yang-Baxter equation that carry the standard measurement basis to m-level N-partite entangled states that generalize the 2-level bipartite entangled Bell states. This is achieved by a careful study of solutions to the Yang-Baxter equation discovered by Fateev and Zamolodchikov in 1982.

scholarly journals Generating W states with braiding operators

2020 ◽  
Vol 20 (13&14) ◽  
pp. 1154-1162
Author(s):  
Pramod Padmanabhan ◽  
Fumihiko Sugino ◽  
Diego Trancanelli
Keyword(s):  
Quantum Entanglement ◽  
W State ◽  
Entangled States ◽  
Classical Communication ◽  
Ghz States ◽  
W States ◽  
Partition Algebras ◽  
Baxter Operator

Braiding operators can be used to create entangled states out of product states, thus establishing a correspondence between topological and quantum entanglement. This is well-known for maximally entangled Bell and GHZ states and their equivalent states under Stochastic Local Operations and Classical Communication, but so far a similar result for W states was missing. Here we use generators of extraspecial 2-groups to obtain the W state in a four-qubit space and partition algebras to generate the W state in a three-qubit space. We also present a unitary generalized Yang-Baxter operator that embeds the W_n state in a (2n-1)-qubit space.

Efficient and Secure Two-Way Asynchronous Quantum Secure Direct Communication Protocol by Using Entangled States

2011 ◽  
Vol 135-136 ◽  
pp. 1171-1178
Author(s):  
Min Cang Fu ◽  
Jia Chen Wang
Keyword(s):  
Communication Protocol ◽  
Quantum Secure Direct Communication ◽  
Entangled States ◽  
Secret Message ◽  
Classical Communication ◽  
Bell Measurement ◽  
Direct Communication ◽  
Von Neumann ◽  
Asymmetric Quantum ◽  
Quantum Protocol

An efficient and secure two-way asynchronous quantum secure direct communication protocol by using entangled states is proposed in this paper. Decoy photons are utilized to check eavesdropping; the securities of the protocol are equal to BB84 protocol. After ensuring the security of the quantum channel, both parties encode the secret message by using CNOT operation and local unitary operation separately. The two-way asynchronous direct transition of secret message can be realized by using Bell measurement and von Neumann measurement, combined with classical communication. Different from the present quantum secure direct communication protocols, the two parties encode secret message through different operations which is equivalent to sharing two asymmetric quantum channels, and the protocol is secure for a noise quantum protocol. The protocol is efficient in that all entangled states are used to transmit secret message.

Qubit masking in multipartite qubit system

2021 ◽  
pp. 2150156
Author(s):  
Wei-Min Shang ◽  
Fu-Lin Zhang ◽  
Jie Zhou ◽  
Hui-Xian Meng ◽  
Jing-Ling Chen
Keyword(s):  
Recent Work ◽  
Quantum Entanglement ◽  
Quantum Correlation ◽  
Entangled States ◽  
Qubit System ◽  
Qubit States

The no-masking theories show that it is impossible to mask the set of all qubit states into the quantum correlation of bipartite qubit system or tripartite qubit system. In this paper, we give a new proof of the no-masking situation of the tripartite qubit system. Recent work has shown that there exists a universal masker which can mask an arbitrary set of qubit states in four-qubit systems perfectly by means of the maximum entangled states. Here we show that there exist more than one masking scheme even for the same multipartite qubit system. Basing on the maximum entangled states we give the deterministic masking scenario for N-qubit system. In practice, decoherence hinders us from obtaining the maximum entangled states. From this viewpoint, the masking scenario based on non-maximum entangled states becomes more universal. Furthermore, we provide an approximate quantum masking scenario and investigate the relation between approximate masking and quantum entanglement.

GEOPHYSICS OF ENTANGLED STATES OF THE COVID-19 PANDEMIC AND QUANTUM TELEPORTATION OF SARS COV-2 IN THE PLANET'S BIOGEOSPHERE

2020 ◽  
Author(s):  
Vladimir Gavrilov ◽  
Tatyana Antipova ◽  
Yan Vlasov ◽  
Sergey Ardatov ◽  
Anastasia Ardatova
Keyword(s):  
Entangled States ◽  
Classical Communication ◽  
Special Services ◽  
External Relations ◽  
Useful Signal ◽  
Experimental Process ◽  
The Russian Federation ◽  
Academy Of Sciences ◽  
Principle Of Complementarity

In their previous works , leading their history since 1988, the authors of this article have repeatedly conceptually shown and experimentally verified the results of research on the teleportation of information between macro objects. Early author's works were performed during the existence of the Russian Federation – as a country called the Union of Soviet Socialist Republics (USSR). Some of which were marked "Top Secret" - links further down the text. Since they were performed under the supervision of the relevant special services and further "Department of external relations of the Russian Academy of Sciences". The authors used numerous examples to demonstrate the possibility of teleportation of information in macro-systems, including ecosystem, biogeocenotic levels, and then tissue and organism levels. Successful experimental verifications occurred only in cases when all the principles and rules laid down in the theory of quantum information, applied to biological objects, were correctly combined. Namely, the preparation of cascades of entangled States was performed both on the mental and somatic levels. In full accordance with the principle of complementarity and taking into account the fact that the observer and the observed are actively connected by the sum of similarities. In addition, the role of the classical communication channel in this process was performed by carrier electromagnetic fields modulated by a useful signal. This signal represented a cast of the simulated experimental process. An example of a real COVID-19 pandemic is the verification of author's works in nature on a biogeocenotic scale. And certainly with anthropogenic – so to speak-participation.

“Non-locality”

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.

scholarly journals Local Information as an Essential Factor for Quantum Entanglement

Entropy ◽  
2021 ◽  
Vol 23 (6) ◽  
pp. 728
Author(s):  
Zhaofeng Su
Keyword(s):  
Quantum Entanglement ◽  
Quantum Information Processing ◽  
Local Information ◽  
Essential Factor ◽  
Qubit System ◽  
Local Vectors ◽  
Correlation Parameters ◽  
The One ◽  
Local Parameters

Quantum entanglement is not only a fundamental concept in quantum mechanics but also a special resource for many important quantum information processing tasks. An intuitive way to understand quantum entanglement is to analyze its geometric parameters which include local parameters and correlation parameters. The correlation parameters have been extensively studied while the role of local parameters have not been drawn attention. In this paper, we investigate the question how local parameters of a two-qubit system affect quantum entanglement in both quantitative and qualitative perspective. Firstly, we find that the concurrence, a measure of quantum entanglement, of a general two-qubit state is bounded by the norms of local vectors and correlations matrix. Then, we derive a sufficient condition for a two-qubit being separable in perspective of local parameters. Finally, we find that different local parameters could make a state with fixed correlation matrix separable, entangled or even more qualitatively entangled than the one with vanished local parameters.

Entanglement classification of relaxed Greenberger-Horne-Zeilinger-symmetric states

2014 ◽  
Vol 14 (11&12) ◽  
pp. 937-948
Author(s):  
Eylee Jung ◽  
DaeKil Park
Keyword(s):  
Separable States ◽  
Qubit System ◽  
Symmetric States

In this paper we analyze entanglement classification of relaxed Greenberger-Horne-Zeilinger-symmetric states $\rho^{ES}$, which is parametrized by four real parameters $x$, $y_1$, $y_2$ and $y_3$. The condition for separable states of $\rho^{ES}$ is analytically derived. The higher classes such as bi-separable, W, and Greenberger-Horne-Zeilinger classes are roughly classified by making use of the class-specific optimal witnesses or map from the relaxed Greenberger-Horne-Zeilinger symmetry to the Greenberger-Horne-Zeilinger symmetry. From this analysis we guess that the entanglement classes of $\rho^{ES}$ are not dependent on $y_j \hspace{.2cm} (j=1,2,3)$ individually, but dependent on $y_1 + y_2 + y_3$ collectively. The difficulty arising in extension of analysis with Greenberger-Horne-Zeilinger symmetry to the higher-qubit system is discussed.

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