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arXiv:1204.4349 · International Journal of Modern Physics B

CORRELATIONS OF DECAY TIMES OF ENTANGLED COMPOSITE UNSTABLE SYSTEMS

Thomas Durt

Published Oct 19, 2012• 5 citations
arXivHTMLPDF

Abstract

The role played by time in the quantum theory is still mysterious by many aspects. In particular it is not clear today whether the distribution of decay times of unstable particles could be described by a time operator (TO). As we shall discuss, different approaches to this problem (one could say interpretations) can be found in the literature on the subject. As we shall show, it is possible to conceive crucial experiments aimed at distinguishing the different approaches, by measuring with accuracy the statistical distribution of decay times of entangled particles. Such experiments can be realized in principle with entangled kaon pairs.

DOI
10.1142/s021797921345015x

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The role played by time in the quantum theory is still mysterious by many aspects. In particular it is not clear today whether the distribution of decay times of unstable particles could be described by a time operator (TO). As we shall discuss, different approaches to this problem (one could say interpretations) can be found in the literature on the subject. As we shall show, it is possible to conceive crucial experiments aimed at distinguishing the different approaches, by measuring with accuracy the statistical distribution of decay times of entangled particles. Such experiments can be realized in principle with entangled kaon pairs.
The status of Time in the Quantum Theory remains even today a largely open question. In particular, the existence of a Quantum Time Operator that would describe the distribution of decay times of an unstable quantum system (in analogy with the Position operator that is associated to the position distribution) remained a polemichal question during several decades. Recently, we conceived experimental proposals involving CP violating processes (of single mesons and entangled pairs of mesons) that can be considered as crucial experiments aimed at testing the existence of a Quantum Time Operator. In the present paper, we shall present a similar proposal that can be realized with a single trapped ion. These proposals aim at bringing fundamental problems related to the status of Time in the Quantum Theory to the realm of experimental physics.
We investigate the role of time ordering in entanglement experiments involving unstable particles, focusing on μ+μ−\mu^+ \mu^-μ+μ− pairs produced in a maximally-entangled spin state. We analyse the correlations between measurements performed by two experimenters, Alice (who measures μ−\mu^-μ− spin) and Bob (who measures μ+\mu^+μ+ decay products). Remarkably, the observed correlations persist irrespective of whether Bob's muon decays before or after Alice's spin measurement. We further discuss different interpretations of the same empirical results depending on the observer's reference frame. The findings reinforce the viewpoint that the Copenhagen interpretation of measurement is a mathematical tool rather than a literal account of physical reality.
It is cu~tomary in the pedagogica.ldevelopment of quantum mechanics • ...and field theory to mention'the limitations on correlated measurements of observables at different space-time points.Little attention has .•8been given, however, to actual experiments for making such observations, or their usefulness.In this paper and in a subsequent one, we shall •,• discuss both of these subjects from a general point of view and w1 th •.particular applications to scattering processes. :! .This work is an outgrowth from a recent paper on the correlated :1 .counting rate of two detectors recording particles scattered from a 1 . .
The study and characterisation of quantum entanglement represents an extended effort within the field of quantum information. This thesis addresses two problems. The first regards entanglement in open systems, where it’s more difficult to define a dichotomic (two outcome) observable due to population loss. The second problem concerns genuine multipartite entanglement, that is entanglement between many particles in states that cannot be separable with respect to any possible bipartition of a system.\nThe first chapter consists of an introduction to the basic elements of quantum mechanics and quantum information theory. We briefly describe a few historical facts about quantum mechanics and the study of entanglement, to help put things into perspective.\nThe second chapter is a detailed discussion of the neutral kaon system. These particles are produced in pairs and are described as a particle-antiparticle system. This system displays some unique properties like the violation of CP-symmetry, and shares some characteristics with other mesons, such as neutral particle oscillation and decay. This makes formulating Bell-type inequalities for them more difficult, but also provides the opportunity for new tests.\nThe third chapter continues with the presentation of an already existent effective formalism for performing Bell tests on neutral kaons. The essence of the formalism is a switch to the Heisenberg picture, transferring the time evolution and dependence on measurement directions to a so-called effective operator. This has many advantages, some of the most important being a proper normalization during population loss (due to decay), an easy application to\nthe case of multiple particles and the fact that it allows one to observe entanglement within the system for a relatively long amount of time. The final part presents a way to simulate neutral kaons with atomic systems, namely with Ytterbium isotopes and discuss what are the differences between these atomic systems and neutral kaons.\nThe second part of the thesis treats the problem of proving genuine multipartite entanglement from separable two-body marginals. For this, an introduction to semidefinite programming is necessary due to the fact that the problem under study can be formulated in terms of this method. We will briefly discuss linear and semidefinite programming as well as the concept of duality and provide some basic examples.\nThe formal description of this problem and previous results are provided in the fifth chapter. Our result shows that, through a cyclic iteration between two SDPs, one obtains states with the desired properties. Using this method we managed to go up to six qubit states for various configurations. From this we can construct higher-dimensional states having the same properties.
The present review article is aimed at a clear formulation of the basic problematics of the decay and at a description of the various recent attempts to solve this delicate problem, illustrating both their successes and limitations. The organisation of the article is as follows. After a short summary of the classical description of the decay, a detailed study of the quantum non-decay probability is given. Then the peculiar dynamical situation leading to the formation of an unstable system is identified and the formal and physical aspects of the process are discussed. A detailed analysis is then made of the preparation procedure of an unstable system which is shown to amount to a localisation of the decay fragments within a distance of the order of the range of the forces acting between them. After this the discussion of the general properties of the non-decay probability at all times is completed.