Grothendieck’s constant and local models for noisy entangled quantum states

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.

Download Full-text

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

International Journal of Quantum Information ◽

10.1142/s0219749920500471 ◽

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.

Download Full-text

Designing locally maximally entangled quantum states with arbitrary local symmetries

Quantum ◽

10.22331/q-2021-05-01-450 ◽

2021 ◽

Vol 5 ◽

pp. 450

Author(s):

Oskar Słowik ◽

Adam Sawicki ◽

Tomasz Maciążek

Keyword(s):

Quantum State ◽

Quantum States ◽

Local Mode ◽

Trivial Representation ◽

Tensor Power ◽

Technical Result ◽

Combinatorial Objects ◽

Local Symmetries ◽

Entangled Quantum States ◽

Group Of Symmetries

One of the key ingredients of many LOCC protocols in quantum information is a multiparticle (locally) maximally entangled quantum state, aka a critical state, that possesses local symmetries. We show how to design critical states with arbitrarily large local unitary symmetry. We explain that such states can be realised in a quantum system of distinguishable traps with bosons or fermions occupying a finite number of modes. Then, local symmetries of the designed quantum state are equal to the unitary group of local mode operations acting diagonally on all traps. Therefore, such a group of symmetries is naturally protected against errors that occur in a physical realisation of mode operators. We also link our results with the existence of so-called strictly semistable states with particular asymptotic diagonal symmetries. Our main technical result states that the Nth tensor power of any irreducible representation of SU(N) contains a copy of the trivial representation. This is established via a direct combinatorial analysis of Littlewood-Richardson rules utilising certain combinatorial objects which we call telescopes.

Download Full-text