scholarly journals Quantum combinatorial designs and k-uniform states

2021 ◽  
Author(s):  
Yajuan Zang ◽  
Paolo Facchi ◽  
Zihong Tian
Keyword(s):  
Orthogonal Arrays ◽  
Latin Squares ◽  
Quantum States ◽  
Entangled States ◽  
Combinatorial Designs ◽  
Construction Methods ◽  
Pure States

Abstract Goyeneche et al.\ [Phys.\ Rev.\ A \textbf{97}, 062326 (2018)] introduced several classes of quantum combinatorial designs, namely quantum Latin squares, quantum Latin cubes, and the notion of orthogonality on them. They also showed that mutually orthogonal quantum Latin arrangements can be entangled in the same way in which quantum states are entangled. Moreover, they established a relationship between quantum combinatorial designs and a remarkable class of entangled states called $k$-uniform states, i.e., multipartite pure states such that every reduction to $k$ parties is maximally mixed. In this article, we put forward the notions of incomplete quantum Latin squares and orthogonality on them and present construction methods for mutually orthogonal quantum Latin squares and mutually orthogonal quantum Latin cubes. Furthermore, we introduce the notions of generalized mutually orthogonal quantum Latin squares and generalized mutually orthogonal quantum Latin cubes, which are equivalent to quantum orthogonal arrays of size $d^2$ and $d^3$, respectively, and thus naturally provide $2$- and $3$-uniform states.

scholarly journals Optimal verification of general bipartite pure states

2019 ◽  
Vol 5 (1) ◽  
Author(s):  
Xiao-Dong Yu ◽  
Jiangwei Shang ◽  
Otfried Gühne
Keyword(s):  
Quantum Information ◽  
Quantum Information Processing ◽  
Optimization Problems ◽  
Optimal Strategies ◽  
Adaptive Strategies ◽  
Quantum States ◽  
Entangled States ◽  
Classical Communication ◽  
Pure States ◽  
Projective Measurements

AbstractThe efficient and reliable verification of quantum states plays a crucial role in various quantum information processing tasks. We consider the task of verifying entangled states using one-way and two-way classical communication and completely characterize the optimal strategies via convex optimization. We solve these optimization problems using both analytical and numerical methods, and the optimal strategies can be constructed for any bipartite pure state. Compared with the nonadaptive approach, our adaptive strategies significantly improve the efficiency of quantum state verification. Moreover, these strategies are experimentally feasible, as only few local projective measurements are required.

“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.

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

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.

MULTIPARTY REMOTELY PREPARING MULTIPARTITE EQUATORIAL ENTANGLED STATES IN HIGH DIMENSIONS

2011 ◽  
Vol 09 (06) ◽  
pp. 1437-1448
Author(s):  
YI-BAO LI ◽  
KUI HOU ◽  
SHOU-HUA SHI
Keyword(s):  
Quantum State ◽  
Quantum Channel ◽  
Success Probability ◽  
Quantum States ◽  
Remote State Preparation ◽  
Entangled States ◽  
Entangled State ◽  
High Dimensions ◽  
Original State ◽  
State Preparation

We propose two kinds of schemes for multiparty remote state preparation (MRSP) of the multiparticle d-dimensional equatorial quantum states by using partial entangled state as the quantum channel. Unlike more remote state preparation scheme which only one sender knows the original state to be remotely prepared, the quantum state is shared by two-party or multiparty in this scheme. We show that if and only if all the senders agree to collaborate with each other, the receiver can recover the original state with certain probability. It is found that the total success probability of MRSP is only by means of the smaller coefficients of the quantum channel and the dimension d.

scholarly journals Clustering and enhanced classification using a hybrid quantum autoencoder

2021 ◽  
Author(s):  
Maiyuren Srikumar ◽  
Charles Daniel Hill ◽  
Lloyd Hollenberg
Keyword(s):  
Machine Learning ◽  
Supervised Classification ◽  
Quantum Information Theory ◽  
Quantum States ◽  
Data Sets ◽  
New Paradigm ◽  
Novel Approach ◽  
Representational Space ◽  
Quantum Machine Learning ◽  
Pure States

Abstract Quantum machine learning (QML) is a rapidly growing area of research at the intersection of classical machine learning and quantum information theory. One area of considerable interest is the use of QML to learn information contained within quantum states themselves. In this work, we propose a novel approach in which the extraction of information from quantum states is undertaken in a classical representational-space, obtained through the training of a hybrid quantum autoencoder (HQA). Hence, given a set of pure states, this variational QML algorithm learns to identify – and classically represent – their essential distinguishing characteristics, subsequently giving rise to a new paradigm for clustering and semi-supervised classification. The analysis and employment of the HQA model are presented in the context of amplitude encoded states – which in principle can be extended to arbitrary states for the analysis of structure in non-trivial quantum data sets.

Most robust and fragile two-qubit entangled states under deploarizing channels

2013 ◽  
Vol 13 (7&8) ◽  
pp. 645-660
Author(s):  
Chao-Qian Pang ◽  
Fu-Lin Zhang ◽  
Yue Jiang ◽  
Mai-Lin Liang ◽  
Jing-Ling Chen
Keyword(s):  
Evolution Equation ◽  
Numerical Calculations ◽  
Entangled States ◽  
Fragile States ◽  
Qubit System ◽  
Uniform Channel ◽  
Pure States ◽  
The One ◽  
Major Factors ◽  
The Impact

For a two-qubit system under local depolarizing channels, the most robust and most fragile states are derived for a given concurrence or negativity. For the one-sided channel, the pure states are proved to be the most robust ones, with the aid of the evolution equation for entanglement given by Konrad \emph{et al.} [Nat. Phys. 4, 99 (2008)]. Based on a generalization of the evolution equation for entanglement, we classify the ansatz states in our investigation by the amount of robustness, and consequently derive the most fragile states. For the two-sided channel, the pure states are the most robust for a fixed concurrence. Under the uniform channel, the most fragile states have the minimal negativity when the concurrence is given in the region $[1/2,1]$. For a given negativity, the most robust states are the ones with the maximal concurrence, and the most fragile ones are the pure states with minimum of concurrence. When the entanglement approaches zero, the most fragile states under general nonuniform channels tend to the ones in the uniform channel. Influences on robustness by entanglement, degree of mixture, and asymmetry between the two qubits are discussed through numerical calculations. It turns out that the concurrence and negativity are major factors for the robustness. When they are fixed, the impact of the mixedness becomes obvious. In the nonuniform channels, the most fragile states are closely correlated with the asymmetry, while the most robust ones with the degree of mixture.

scholarly journals Pure States of Maximum Uncertainty with Respect to a Given POVM

2020 ◽  
Vol 27 (01) ◽  
pp. 2050002
Author(s):  
Anna Szymusiak
Keyword(s):  
Shannon Entropy ◽  
Pure State ◽  
Quantum States ◽  
Maximal Amount ◽  
Dimension 2 ◽  
Pure States

One of the differences between classical and quantum world is that in the former we can always perform a measurement that gives certain outcomes for all pure states, while such a situation is not possible in the latter one. The degree of randomness of the distribution of the measurement outcomes can be quantified by the Shannon entropy. While it is well known that this entropy, as a function of quantum states, needs to be minimized by some pure states, we would like to address the question how ‘badly’ can we end by choosing initially any pure state, i.e., which pure states produce the maximal amount of uncertainty under given measurement. We find these maximizers for all highly symmetric POVMs in dimension 2, and for all SIC-POVMs in any dimension.

scholarly journals An elementary introduction to the geometry of quantum states with pictures

2019 ◽  
Vol 32 (02) ◽  
pp. 2030001 ◽  
Author(s):  
J. Avron ◽  
O. Kenneth
Keyword(s):  
Convex Body ◽  
Cross Sections ◽  
Convex Bodies ◽  
Quantum States ◽  
Entangled States ◽  
High Dimensions ◽  
Geometric Properties ◽  
Precise Sense ◽  
Entanglement Witnesses ◽  
Elementary Methods

This is a review of the geometry of quantum states using elementary methods and pictures. Quantum states are represented by a convex body, often in high dimensions. In the case of [Formula: see text] qubits, the dimension is exponentially large in [Formula: see text]. The space of states can be visualized, to some extent, by its simple cross sections: Regular simplexes, balls and hyper-octahedra. a When the dimension gets large, there is a precise sense in which the space of states resembles, almost in every direction, a ball. The ball turns out to be a ball of rather low purity states. We also address some of the corresponding, but harder, geometric properties of separable and entangled states and entanglement witnesses. “All convex bodies behave a bit like Euclidean balls.” Keith Ball

scholarly journals On Graph-Orthogonal Arrays by Mutually Orthogonal Graph Squares

Symmetry ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 1895 ◽  
Author(s):  
M. Higazy ◽  
A. El-Mesady ◽  
M. S. Mohamed
Keyword(s):  
Computer Science ◽  
Finite Fields ◽  
Orthogonal Array ◽  
Orthogonal Arrays ◽  
Latin Squares ◽  
Error Correcting Codes ◽  
Recursive Construction ◽  
Orthogonal Latin Squares ◽  
Mutually Orthogonal Latin Squares ◽  
Definition Of

During the last two centuries, after the question asked by Euler concerning mutually orthogonal Latin squares (MOLS), essential advances have been made. MOLS are considered as a construction tool for orthogonal arrays. Although Latin squares have numerous helpful properties, for some factual applications these structures are excessively prohibitive. The more general concepts of graph squares and mutually orthogonal graph squares (MOGS) offer more flexibility. MOGS generalize MOLS in an interesting way. As such, the topic is attractive. Orthogonal arrays are essential in statistics and are related to finite fields, geometry, combinatorics and error-correcting codes. Furthermore, they are used in cryptography and computer science. In this paper, our current efforts have concentrated on the definition of the graph-orthogonal arrays and on proving that if there are k MOGS of order n, then there is a graph-orthogonal array, and we denote this array by G-OA(n2,k,n,2). In addition, several new results for the orthogonal arrays obtained from the MOGS are given. Furthermore, we introduce a recursive construction method for constructing the graph-orthogonal arrays.

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