Learning quantum states from their classical shadows

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.

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Quantum optics with nitrogen-vacancy centres in diamond

10.1093/oso/9780198768609.003.0005 ◽

2017 ◽

Cited By ~ 1

Author(s):

Yiwen Chu ◽

Mikhail D. Lukin

Keyword(s):

Optical Properties ◽

Quantum Information ◽

Solid State ◽

Quantum Optics ◽

Quantum States ◽

Nitrogen Vacancy ◽

Common Theme ◽

External Effects ◽

Promising Candidate ◽

Optical Photons

A common theme in the implementation of quantum technologies involves addressing the seemingly contradictory needs for controllability and isolation from external effects. Undesirable effects of the environment must be minimized, while at the same time techniques and tools must be developed that enable interaction with the system in a controllable and well-defined manner. This chapter addresses several aspects of this theme with regard to a particularly promising candidate for developing applications in both metrology and quantum information, namely the nitrogen-vacancy (NV) centre in diamond. The chapter describes how the quantum states of NV centres can be manipulated, probed, and efficiently coupled with optical photons. It also discusses ways of tackling the challenges of controlling the optical properties of these emitters inside a complex solid state environment.

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Quantum Theory

10.1093/oso/9780198808275.003.0009 ◽

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.

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