scholarly journals The type-independent resource theory of local operations and shared randomness

Quantum ◽  
2020 ◽  
Vol 4 ◽  
pp. 262 ◽  
Author(s):  
David Schmid ◽  
Denis Rosset ◽  
Francesco Buscemi
Keyword(s):  
Quantum Theory ◽  
Quantum Information Processing ◽  
Full Range ◽  
Quantum States ◽  
Resource Theory ◽  
Independent Manner ◽  
Common Cause ◽  
Entanglement Witnesses ◽  
Different Types ◽  
Common Resource

In space-like separated experiments and other scenarios where multiple parties share a classical common cause but no cause-effect relations, quantum theory allows a variety of nonsignaling resources which are useful for distributed quantum information processing. These include quantum states, nonlocal boxes, steering assemblages, teleportages, channel steering assemblages, and so on. Such resources are often studied using nonlocal games, semiquantum games, entanglement-witnesses, teleportation experiments, and similar tasks. We introduce a unifying framework which subsumes the full range of nonsignaling resources, as well as the games and experiments which probe them, into a common resource theory: that of local operations and shared randomness (LOSR). Crucially, we allow these LOSR operations to locally change the type of a resource, so that players can convert resources of any type into resources of any other type, and in particular into strategies for the specific type of game they are playing. We then prove several theorems relating resources and games of different types. These theorems generalize a number of seminal results from the literature, and can be applied to lessen the assumptions needed to characterize the nonclassicality of resources. As just one example, we prove that semiquantum games are able to perfectly characterize the LOSR nonclassicality of every resource of any type (not just quantum states, as was previously shown). As a consequence, we show that any resource can be characterized in a measurement-device-independent manner.

scholarly journals Postquantum common-cause channels: the resource theory of local operations and shared entanglement

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 419
Author(s):  
David Schmid ◽  
Haoxing Du ◽  
Maryam Mudassar ◽  
Ghi Coulter-de Wit ◽  
Denis Rosset ◽  
...  
Keyword(s):  
Systematic Study ◽  
Quantum Channel ◽  
Resource Theory ◽  
Valuable Resource ◽  
Common Cause ◽  
Special Cases ◽  
Common Causes ◽  
Different Types ◽  
Distributed Tasks

We define the type-independent resource theory of local operations and shared entanglement (LOSE). This allows us to formally quantify postquantumness in common-cause scenarios such as the Bell scenario. Any nonsignaling bipartite quantum channel which cannot be generated by LOSE operations requires a postquantum common cause to generate, and constitutes a valuable resource. Our framework allows LOSE operations that arbitrarily transform between different types of resources, which in turn allows us to undertake a systematic study of the different manifestations of postquantum common causes. Only three of these have been previously recognized, namely postquantum correlations, postquantum steering, and non-localizable channels, all of which are subsumed as special cases of resources in our framework. Finally, we prove several fundamental results regarding how the type of a resource determines what conversions into other resources are possible, and also places constraints on the resource's ability to provide an advantage in distributed tasks such as nonlocal games, semiquantum games, steering games, etc.

“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.

Quantum Theory

2017 ◽  
Author(s):  
Frank S. Levin
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Uncertainty Principle ◽  
Quantum Spin ◽  
Quantum States ◽  
Wave Functions ◽  
Symbolic Representations ◽  
Quantum Numbers ◽  
The Subject ◽  
Heisenberg's Uncertainty Principle

The subject of Chapter 8 is the fundamental principles of quantum theory, the abstract extension of quantum mechanics. Two of the entities explored are kets and operators, with kets being representations of quantum states as well as a source of wave functions. The quantum box and quantum spin kets are specified, as are the quantum numbers that identify them. Operators are introduced and defined in part as the symbolic representations of observable quantities such as position, momentum and quantum spin. Eigenvalues and eigenkets are defined and discussed, with the former identified as the possible outcomes of a measurement. Bras, the counterpart to kets, are introduced as the means of forming probability amplitudes from kets. Products of operators are examined, as is their role underpinning Heisenberg’s Uncertainty Principle. A variety of symbol manipulations are presented. How measurements are believed to collapse linear superpositions to one term of the sum is explored.

Do Relative Status of Women and Marriage Characteristics Matter for the Intimate Partner Violence?

2021 ◽  
pp. 0192513X2110300
Author(s):  
Aysegul Kayaoglu
Keyword(s):  
Intimate Partner Violence ◽  
Partner Violence ◽  
Emotional Abuse ◽  
Intimate Partner ◽  
Resource Theory ◽  
Bargaining Model ◽  
Different Types ◽  
Relative Status ◽  
Turkish Case ◽  
Status Of Women

This article analyzes intimate partner violence (IPV) in a developing country context, namely, Turkey, which faces an enormous increase in femicide cases over the last decade. Analyzing a very rich nationwide representative survey on IPV, we show that it is not only the absolute status of women but also their relative status in terms of income and education that affects different types of domestic violence, ranging from emotional abuse to physical and sexual violence. Besides, factors related to marriage setting are found to have a significant role in the effect of women’s superior status on IPV. Overall, we provide evidence to support the relative resource theory and invalidate the intra-household bargaining model in the Turkish case.

scholarly journals Generation and Detection of Structured Light: A Review

2021 ◽  
Vol 9 ◽  
Author(s):  
Jian Wang ◽  
Yize Liang
Keyword(s):  
Quantum Information Processing ◽  
Structured Light ◽  
Super Resolution ◽  
Research Progress ◽  
Free Space Optical ◽  
The Past ◽  
Integrated Devices ◽  
Different Types ◽  
Resolution Imaging ◽  
Light Beams

Structured light beams have rapidly advanced over the past few years, from specific spatial-transverse/longitudinal structure to tailored spatiotemporal structure. Such beams with diverse spatial structures or spatiotemporal structures have brought various breakthroughs to many fields, including optical communications, optical sensing, micromanipulation, quantum information processing, and super-resolution imaging. Thus, plenty of methods have been proposed, and lots of devices have been manufactured to generate structured light beams by tailoring the structures of beams in the space domain and the space–time domain. In this paper, we firstly give a brief introduction of different types of structured light. Then, we review the recent research progress in the generation and detection of structured light on different platforms, such as free space, optical fiber, and integrated devices. Finally, challenges and perspectives are also discussed.

Proposal for dimensionality testing in QPQ

2018 ◽  
Vol 18 (13&14) ◽  
pp. 1125-1142
Author(s):  
Arpita Maitra ◽  
Bibhas Adhikari ◽  
Satyabrata Adhikari
Keyword(s):  
Information Processing ◽  
Quantum Information ◽  
Quantum System ◽  
Quantum State ◽  
Quantum Information Processing ◽  
Quantum States ◽  
Quantum Private Query ◽  
Unfair Advantage ◽  
Security Proofs

Recently, dimensionality testing of a quantum state has received extensive attention (Ac{\'i}n et al. Phys. Rev. Letts. 2006, Scarani et al. Phys. Rev. Letts. 2006). Security proofs of existing quantum information processing protocols rely on the assumption about the dimension of quantum states in which logical bits are encoded. However, removing such assumption may cause security loophole. In the present paper, we show that this is indeed the case. We choose two players' quantum private query protocol by Yang et al. (Quant. Inf. Process. 2014) as an example and show how one player can gain an unfair advantage by changing the dimension of subsystem of a shared quantum system. To resist such attack we propose dimensionality testing in a different way. Our proposal is based on CHSH like game. As we exploit CHSH like game, it can be used to test if the states are product states for which the protocol becomes completely vulnerable.

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 The Strange (Hi)story of Particles and Waves

2016 ◽  
Vol 71 (3) ◽  
pp. 195-212
Author(s):  
H. Dieter Zeh
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Quantum Theory ◽  
Excited States ◽  
Configuration Space ◽  
Historical Context ◽  
Quantum States ◽  
Wave Functions ◽  
General Readership ◽  
Boson Fields

AbstractThis is an attempt of a non-technical but conceptually consistent presentation of quantum theory in a historical context. While the first part is written for a general readership, Section 5 may appear a bit provocative to some quantum physicists. I argue that the single-particle wave functions of quantum mechanics have to be correctly interpreted as field modes that are “occupied once” (i.e. first excited states of the corresponding quantum oscillators in the case of boson fields). Multiple excitations lead to apparent many-particle wave functions, while the quantum states proper are defined by wave function(al)s on the “configuration” space of fundamental fields, or on another, as yet elusive, fundamental local basis.

scholarly journals Theoretical framework for higher-order quantum theory

2019 ◽  
Vol 475 (2225) ◽  
pp. 20180706 ◽  
Author(s):  
Alessandro Bisio ◽  
Paolo Perinotti
Keyword(s):  
Quantum Theory ◽  
Convex Sets ◽  
Mathematical Structure ◽  
Higher Order ◽  
Equivalence Relations ◽  
Full Generality ◽  
Special Cases ◽  
Different Types ◽  
Causal Structures

Higher-order quantum theory is an extension of quantum theory where one introduces transformations whose input and output are transformations, thus generalizing the notion of channels and quantum operations. The generalization then goes recursively, with the construction of a full hierarchy of maps of increasingly higher order. The analysis of special cases already showed that higher-order quantum functions exhibit features that cannot be tracked down to the usual circuits, such as indefinite causal structures, providing provable advantages over circuital maps. The present treatment provides a general framework where this kind of analysis can be carried out in full generality. The hierarchy of higher-order quantum maps is introduced axiomatically with a formulation based on the language of types of transformations. Complete positivity of higher-order maps is derived from the general admissibility conditions instead of being postulated as in previous approaches. The recursive characterization of convex sets of maps of a given type is used to prove equivalence relations between different types. The axioms of the framework do not refer to the specific mathematical structure of quantum theory, and can therefore be exported in the context of any operational probabilistic theory.

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