scholarly journals Sum-of-squares decompositions for a family of noncontextuality inequalities and self-testing of quantum devices

Quantum ◽  
2020 ◽  
Vol 4 ◽  
pp. 302
Author(s):  
Debashis Saha ◽  
Rafael Santos ◽  
Remigiusz Augusiak
Keyword(s):  
Quantum Theory ◽  
Quantum State ◽  
Three Dimensional ◽  
Sum Of Squares ◽  
Quantum Devices ◽  
Fundamental Feature ◽  
Quantum Contextuality ◽  
Sequential Measurement ◽  
Self Testing ◽  
Odd Cycle

Violation of a noncontextuality inequality or the phenomenon referred to `quantum contextuality' is a fundamental feature of quantum theory. In this article, we derive a novel family of noncontextuality inequalities along with their sum-of-squares decompositions in the simplest (odd-cycle) sequential-measurement scenario capable to demonstrate Kochen-Specker contextuality. The sum-of-squares decompositions allow us to obtain the maximal quantum violation of these inequalities and a set of algebraic relations necessarily satisfied by any state and measurements achieving it. With their help, we prove that our inequalities can be used for self-testing of three-dimensional quantum state and measurements. Remarkably, the presented self-testing results rely on weaker assumptions than the ones considered in Kochen-Specker contextuality.

Probability and Explanation

2017 ◽  
Author(s):  
Richard Healey
Keyword(s):  
Quantum Theory ◽  
Quantum State ◽  
Causal Explanation ◽  
Born Rule ◽  
Correct Application

We can use quantum theory to explain an enormous variety of phenomena by showing why they were to be expected and what they depend on. These explanations of probabilistic phenomena involve applications of the Born rule: to accept quantum theory is to let relevant Born probabilities guide one’s credences about presently inaccessible events. We use quantum theory to explain a probabilistic phenomenon by showing how its probabilities follow from a correct application of the Born rule, thereby exhibiting the phenomenon’s dependence on the quantum state to be assigned in circumstances of that type. This is not a causal explanation since a probabilistic phenomenon is not constituted by events that may manifest it: but each of those events does depend causally on events that actually occur in those circumstances. Born probabilities are objective and sui generis, but not all Born probabilities are chances.

Entanglement

2017 ◽  
Author(s):  
Richard Healey
Keyword(s):  
Quantum Theory ◽  
Quantum State ◽  
Physical Condition ◽  
Physical System ◽  
Polarization State ◽  
Quantum Systems ◽  
Ghz State ◽  
Mathematical Representation ◽  
Entangled State ◽  
Physical Relation

Often a pair of quantum systems may be represented mathematically (by a vector) in a way each system alone cannot: the mathematical representation of the pair is said to be non-separable: Schrödinger called this feature of quantum theory entanglement. It would reflect a physical relation between a pair of systems only if a system’s mathematical representation were to describe its physical condition. Einstein and colleagues used an entangled state to argue that its quantum state does not completely describe the physical condition of a system to which it is assigned. A single physical system may be assigned a non-separable quantum state, as may a large number of systems, including electrons, photons, and ions. The GHZ state is an example of an entangled polarization state that may be assigned to three photons.

Losing Sight of the Forest for the ψ‎

2020 ◽  
pp. 185-211
Author(s):  
Alisa Bokulich
Keyword(s):  
Quantum Theory ◽  
Quantum State ◽  
Configuration Space ◽  
Mathematical Formalism ◽  
Alternative Formulation ◽  
Quantum Hydrodynamics ◽  
Many Body ◽  
Quantum Realism ◽  
The World ◽  
The Many

Traditionally \1 is used to stand for both the mathematical wavefunction (the representation) and the quantum state (thing in the world). This elision has been elevated to a metaphysical thesis by advocates of wavefunction realism. The aim of Chapter 10 is to challenge the hegemony of the wavefunction by calling attention to a littleknown formulation of quantum theory that does not make use of the wavefunction in representing the quantum state. This approach, called Lagrangian quantum hydrodynamics (LQH), is a full alternative formulation, not an approximation scheme. A consideration of alternative formalisms is essential for any realist project that attempts to read the ontology of a theory off the mathematical formalism. The chapter shows that LQH falsifies the claim that one must represent the many-body quantum state as living in 3n-dimensional configuration space. When exploring quantum realism, regaining sight of the proverbial forest of quantum representations beyond the \1 is just the beginning.

Three-Dimensional Point Cloud Registration Based on Maximum Sum of Squares of Correlation Coefficients

2019 ◽  
Vol 56 (22) ◽  
pp. 221504
Author(s):  
苗长伟 Miao Changwei ◽  
唐志荣 Tang Zhirong ◽  
唐英杰 Tang Yingjie
Keyword(s):  
Point Cloud ◽  
Three Dimensional ◽  
Correlation Coefficients ◽  
Sum Of Squares ◽  
Point Cloud Registration

Three-dimensional quantum mechanics in a curved space based on the q-addition

2019 ◽  
Vol 34 (29) ◽  
pp. 1950177
Author(s):  
Won Sang Chung ◽  
Hassan Hassanabadi
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Coordinate System ◽  
Three Dimensional ◽  
One Dimension ◽  
Cartesian Coordinate System ◽  
Spherical Coordinate ◽  
Curved Space ◽  
Dimension Formula ◽  
Cartesian Coordinate

In this paper, we extend the theory of the [Formula: see text]-deformed quantum mechanics in one dimension[Formula: see text] into three-dimensional case. We relate the [Formula: see text]-deformed quantum theory to the quantum theory in a curved space. We discuss the diagonal metric based on [Formula: see text]-addition in the Cartesian coordinate system and core radius of neutron star. We also discuss the diagonal metric based on [Formula: see text]-addition in the spherical coordinate system and [Formula: see text]-deformed Heisenberg atom model.

scholarly journals Revealing universal quantum contextuality through communication games

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
A. K. Pan
Keyword(s):  
Quantum Theory ◽  
Success Probability ◽  
Quantum Contextuality ◽  
Communication Games ◽  
Qubit System ◽  
Operational Theory ◽  
Universal Quantum ◽  
Local Bound ◽  
Ontological Model ◽  
Non Locality

AbstractAn ontological model of an operational theory is considered to be universally noncontextual if both preparation and measurement noncontextuality assumptions are satisfied in that model. In this report, we first generalize the logical proofs of quantum preparation and measurement contextuality for qubit system for any odd number of preparations and measurements. Based on the logical proof, we derive testable universally non-contextual inequalities violated by quantum theory. We then propose a class of two-party communication games and show that the average success probability of winning such games is solely linked to suitable Bell expression whose local bound is greater than universal non-contextual bound. Thus, for a given state, even if quantum theory does not exhibit non-locality, it may still reveal non-classicality by violating the universal non-contextual bound. Further, we consider a different communication game to demonstrate that for a given choices of observables in quantum theory, even if there is no logical proof of preparation and measurement contextuality exist, the universal quantum contextuality can be revealed through that communication game. Such a game thus test a weaker form of universal non-contextuality with minimal assumption.

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