scholarly journals Symmetry-resolved entanglement detection using partial transpose moments

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Antoine Neven ◽  
Jose Carrasco ◽  
Vittorio Vitale ◽  
Christian Kokail ◽  
Andreas Elben ◽  
...  
Keyword(s):  
Ordered Set ◽  
Empirical Studies ◽  
Moment Inequalities ◽  
Mixed States ◽  
Independent State ◽  
Relevant Situation ◽  
Partial Transpose ◽  
Detection Capabilities ◽  
Entanglement Detection ◽  
Random Measurements

AbstractWe propose an ordered set of experimentally accessible conditions for detecting entanglement in mixed states. The k-th condition involves comparing moments of the partially transposed density operator up to order k. Remarkably, the union of all moment inequalities reproduces the Peres-Horodecki criterion for detecting entanglement. Our empirical studies highlight that the first four conditions already detect mixed state entanglement reliably in a variety of quantum architectures. Exploiting symmetries can help to further improve their detection capabilities. We also show how to estimate moment inequalities based on local random measurements of single state copies (classical shadows) and derive statistically sound confidence intervals as a function of the number of performed measurements. Our analysis includes the experimentally relevant situation of drifting sources, i.e. non-identical, but independent, state copies.

scholarly journals Experimental test of the Greenberger–Horne–Zeilinger-type paradoxes in and beyond graph states

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Zheng-Hao Liu ◽  
Jie Zhou ◽  
Hui-Xian Meng ◽  
Mu Yang ◽  
Qiang Li ◽  
...  
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Success Probability ◽  
Quantum Foundations ◽  
Mixed States ◽  
Graph States ◽  
Hardy Type ◽  
Realistic Description ◽  
Entanglement Detection ◽  
Quantum Paradoxes

AbstractThe Greenberger–Horne–Zeilinger (GHZ) paradox is an exquisite no-go theorem that shows the sharp contradiction between classical theory and quantum mechanics by ruling out any local realistic description of quantum theory. The investigation of GHZ-type paradoxes has been carried out in a variety of systems and led to fruitful discoveries. However, its range of applicability still remains unknown and a unified construction is yet to be discovered. In this work, we present a unified construction of GHZ-type paradoxes for graph states, and show that the existence of GHZ-type paradox is not limited to graph states. The results have important applications in quantum state verification for graph states, entanglement detection, and construction of GHZ-type steering paradox for mixed states. We perform a photonic experiment to test the GHZ-type paradoxes via measuring the success probability of their corresponding perfect Hardy-type paradoxes, and demonstrate the proposed applications. Our work deepens the comprehension of quantum paradoxes in quantum foundations, and may have applications in a broad spectrum of quantum information tasks.

scholarly journals Bounds on Mixed State Entanglement

Entropy ◽  
2020 ◽  
Vol 22 (1) ◽  
pp. 62 ◽  
Author(s):  
Bruno Leggio ◽  
Anna Napoli ◽  
Hiromichi Nakazato ◽  
Antonino Messina
Keyword(s):  
Mixed State ◽  
General Framework ◽  
Quantum Correlations ◽  
Thermal Entanglement ◽  
Mixed States ◽  
Clear Explanation ◽  
Finite Dimensionality ◽  
Partial Transpose ◽  
The Subject

In the general framework of d 1 × d 2 mixed states, we derive an explicit bound for bipartite negative partial transpose (NPT) entanglement based on the mixedness characterization of the physical system. The derived result is very general, being based only on the assumption of finite dimensionality. In addition, it turns out to be of experimental interest since some purity-measuring protocols are known. Exploiting the bound in the particular case of thermal entanglement, a way to connect thermodynamic features to the monogamy of quantum correlations is suggested, and some recent results on the subject are given a physically clear explanation.

scholarly journals A Genetic Algorithm-Based Approach for Composite Metamorphic Relations Construction

Information ◽  
2019 ◽  
Vol 10 (12) ◽  
pp. 392
Author(s):  
Zhenglong Xiang ◽  
Hongrun Wu ◽  
Fei Yu
Keyword(s):  
Genetic Algorithm ◽  
Empirical Studies ◽  
High Quality ◽  
Testing Technique ◽  
Metamorphic Testing ◽  
The Core ◽  
Test Oracle ◽  
Detection Capabilities ◽  
Optimal Set ◽  
Core Problem

The test oracle problem exists widely in modern complex software testing, and metamorphic testing (MT) has become a promising testing technique to alleviate this problem. The inference of efficient metamorphic relations (MRs) is the core problem of metamorphic testing. Studies have proven that the combination of simple metamorphic relations can construct more efficient metamorphic relations. In most previous studies, metamorphic relations have been mainly manually inferred by experts with professional knowledge, which is an inefficient technique and hinders the application. In this paper, a genetic algorithm-based approach is proposed to construct composite metamorphic relations automatically for the program to be tested. We use a set of relation sequences to represent a particular class of MRs and turn the problem of inferring composite MRs into a problem of searching for suitable sequences. We then dynamically implement multiple executions of the program and use a genetic algorithm to search for the optimal set of relation sequences. We conducted empirical studies to evaluate our approach using scientific functions in the GNU scientific library (abbreviated as GSL). From the empirical results, our approach can automatically infer high-quality composite MRs, on average, five times more than basic MRs. More importantly, the inferred composite MRs can increase the fault detection capabilities by at least 30 % more than the original metamorphic relations.

Covering Array Constructors: An Experimental Analysis of Their Interaction Coverage and Fault Detection

2020 ◽  
Author(s):  
Rubing Huang ◽  
Haibo Chen ◽  
Yunan Zhou ◽  
Tsong Yueh Chen ◽  
Dave Towey ◽  
...  
Keyword(s):  
Fault Detection ◽  
Empirical Studies ◽  
Specific Interaction ◽  
Interaction Strength ◽  
The Other ◽  
Test Cases ◽  
Covering Array ◽  
Interaction Testing ◽  
Detection Capabilities ◽  
Combinatorial Interaction Testing

Abstract Combinatorial interaction testing (CIT) aims at constructing a covering array (CA) of all value combinations at a specific interaction strength, to detect faults that are caused by the interaction of parameters. CIT has been widely used in different applications, with many algorithms and tools having been proposed to support CA construction. To date, however, there appears to have been no studies comparing different CA constructors when only some of the CA test cases are executed. In this paper, we present an investigation of five popular CA constructors: ACTS, Jenny, PICT, CASA and TCA. We conducted empirical studies examining the five programs, focusing on interaction coverage and fault detection. The experimental results show that when there is no preference or special justification for using other CA constructors, then Jenny is recommended—because it achieves better interaction coverage and fault detection than the other four constructors in many cases. Our results also show that when using ACTS or CASA, their CAs must be prioritized before testing. The main reason for this is that these CAs can result in considerable interaction coverage or fault detection capabilities when executing a large number of test cases; however, they may also produce the lowest rates of fault detection and interaction coverage.

scholarly journals Characterization of Combinatorially Independent Permutation Separability Criteria

2005 ◽  
Vol 12 (04) ◽  
pp. 331-345 ◽  
Author(s):  
Paweł Wocjan ◽  
Michał Horodecki
Keyword(s):  
Density Matrix ◽  
The State ◽  
Necessary Condition ◽  
Trace Norm ◽  
Mixed States ◽  
Graphical Notation ◽  
Operational Conditions ◽  
Separability Criteria ◽  
Partial Transpose

The so-called permutation separability criteria are simple operational conditions that are necessary for separability of mixed states of multipartite systems: (1) permute the indices of the density matrix and (2) check if the trace norm of at least one of the resulting operators is greater than one. If it is greater than one then the state is necessarily entangled. A shortcoming of the permutation separability criteria is that many permutations give rise to equivalent separability criteria. Therefore, we introduce a necessary condition for two permutations to yield independent criteria called combinatorial independence. This condition basically means that the map corresponding to one permutation cannot be obtained by concatenating the map corresponding to the second permutation with a norm-preserving map. We characterize completely combinatorially independent criteria, and determine simple permutations that represent all independent criteria. The representatives can be visualized by means of a simple graphical notation. They are composed of three basic operations: partial transpose, and two types of so-called reshufflings. In particular, for a four-partite system all criteria except one are composed of partial transpose and only one type of reshuffling; the exceptional one requires the second type of reshuffling. Furthermore, we show how to obtain efficiently a simple representative for every permutation. This method allows to check easily if two permutations are combinatorially equivalent or not.

scholarly journals Inequalities detecting entanglement for arbitrary bipartite systems

2014 ◽  
Vol 12 (03) ◽  
pp. 1450013 ◽  
Author(s):  
Hui Zhao ◽  
Shao-Ming Fei ◽  
Jiao Fan ◽  
Zhi-Xi Wang
Keyword(s):  
Quantum Entanglement ◽  
Sufficient Condition ◽  
Mixed States ◽  
Entanglement Detection

Based on the generators of SU(n) we present inequalities for detecting quantum entanglement for 2 ⊗ d and M ⊗ N systems. These inequalities provide a sufficient condition of entanglement for bipartite mixed states and give rise to an experimental way of entanglement detection.

scholarly journals NUMERICAL SIMULATIONS OF MIXED STATE QUANTUM COMPUTATION

2005 ◽  
Vol 03 (01) ◽  
pp. 195-199 ◽  
Author(s):  
P. GAWRON ◽  
J. A. MISZCZAK
Keyword(s):  
Quantum Algorithms ◽  
Building Blocks ◽  
Quantum Error Correction ◽  
Quantum Mechanical ◽  
Error Correction Codes ◽  
Mixed States ◽  
Partial Trace ◽  
Shor's Algorithm ◽  
Partial Transpose ◽  
Quantum Error

We describe the [Formula: see text] package of functions useful for simulations of quantum algorithms and protocols. The presented package allows one to perform simulations with mixed states. We present numerical implementation of important quantum mechanical operations — partial trace and partial transpose. Those operations are used as building blocks of algorithms for analysis of entanglement and quantum error correction codes. A simulation of Shor's algorithm is presented as an example of package capabilities.

An empirical review of gambling expansion and gambling-related harm

2018 ◽  
Vol 64 (5-6) ◽  
pp. 295-306 ◽  
Author(s):  
Debi A. LaPlante ◽  
Heather M. Gray ◽  
Pat M. Williams ◽  
Sarah E. Nelson
Keyword(s):  
Literature Review ◽  
Peer Review ◽  
Empirical Data ◽  
Empirical Studies ◽  
Expansion Method ◽  
Responsible Gambling ◽  
Review Literature ◽  
Evidence Based ◽  
Empirical Comparison ◽  
Related Harm

Abstract. Aims: To discuss and review the latest research related to gambling expansion. Method: We completed a literature review and empirical comparison of peer reviewed findings related to gambling expansion and subsequent gambling-related changes among the population. Results: Although gambling expansion is associated with changes in gambling and gambling-related problems, empirical studies suggest that these effects are mixed and the available literature is limited. For example, the peer review literature suggests that most post-expansion gambling outcomes (i. e., 22 of 34 possible expansion outcomes; 64.7 %) indicate no observable change or a decrease in gambling outcomes, and a minority (i. e., 12 of 34 possible expansion outcomes; 35.3 %) indicate an increase in gambling outcomes. Conclusions: Empirical data related to gambling expansion suggests that its effects are more complex than frequently considered; however, evidence-based intervention might help prepare jurisdictions to deal with potential consequences. Jurisdictions can develop and evaluate responsible gambling programs to try to mitigate the impacts of expanded gambling.

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