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arXiv:quant-ph/0103057

The Foundations of Quantum Information and Feasible Experiments

Christoph Simon

Published Mar 12, 2001• 2 citations
arXivHTMLPDF

Abstract

This thesis consists of four parts. In the first part it is shown that optimal universal cloning of photons can be realized with the help of stimulated emission. Possible schemes based on three-level systems and on parametric down-conversion are analyzed in detail. The second part shows that the dynamical rules of quantum physics can be derived from its static properties and the condition that superluminal communication is forbidden. In the third part a very simple form of the Kochen-Specker theorem is presented, which leads to a proposal for a simple experimental test of non-contextual hidden variables. The fourth part shows how hidden-variable theorems can be derived in a completely operational way. In particular a Kochen-Specker theorem is derived that applies to experiments with finite precision.

DOI
10.48550/arxiv.quant-ph/0103057

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This thesis consists of four parts. In the first part it is shown that optimal universal cloning of photons can be realized with the help of stimulated emission. Possible schemes based on three-level systems and on parametric down-conversion are analyzed in detail. The second part shows that the dynamical rules of quantum physics can be derived from its static properties and the condition that superluminal communication is forbidden. In the third part a very simple form of the Kochen-Specker theorem is presented, which leads to a proposal for a simple experimental test of non-contextual hidden variables. The fourth part shows how hidden-variable theorems can be derived in a completely operational way. In particular a Kochen-Specker theorem is derived that applies to experiments with finite precision.
The rapidly developing interdisciplinary field of quantum information, which merges quantum and information science, studies non-classical aspects of quantum systems. These studies are motivated by the promise that the non-classicality can be used to solve tasks more efficiently than classical methods would allow. In many quantum informational studies, non-classical behaviour is attributed to the notion of entanglement. In this thesis we use photons to experimentally investigate fundamental questions such as: What happens to the entanglement in a system when it is affected by noise? In our study of noisy entanglement we pursue the challenging task of creating bound entanglement. Bound entangled states are created through an irreversible process that requires entanglement. Once in the bound regime, entanglement cannot be distilled out through local operations assisted by classical communication. We show that it is possible to experimentally produce four-photon bound entangled states and that a violation of a Bell inequality can be achieved. Moreover, we demonstrate an entanglement-unlocking protocol by relaxing the condition of local operations. We also explore the non-classical nature of quantum mechanics in several single-photon experiments. In these experiments, we show the violation of various inequalities that were derived under the assumption of non-contextuality. Using qutrits we construct and demonstrate the simplest possible test that offers a discrepancy between classical and quantum theory. Furthermore, we perform an experiment in the spirit of the Kochen-Specker theorem to illustrate the state-independence of this theorem. Here, we investigate whether or not measurement outcomes exhibit fully contextual correlations. That is, no part of the correlations can be attributed to the non-contextual theory. Our results show that only a small part of the experimental generated correlations are amenable to a non-contextual interpretation.
We present ways of realizing quantum cloning via stimulated emission. Universality of the cloning procedure is achieved by choosing systems that have appropriate symmetries. We first discuss a scheme based on certain three-level systems, e.g. atoms in a cavity. Our numerical results show that this scheme approaches optimal cloning for short interaction times. Then we demonstrate that optimal universal cloning can be realized using parametric down-conversion. At the same time, our down-conversion scheme also implements the optimal universal NOT operation. We conclude with some remarks on cloning and superluminal signalling, using our cloner as an illustrative example.
Entanglement is a key resource in many quantum information schemes and in the last years the research on multi-qubit entanglement has drawn lots of attention. In this thesis the experimental generation and characterisation of multi-qubit entanglement is presented. Specifically we have prepared entangled states of up to six qubits. The qubits were implemented in the polarisation degree of freedom of single photons. We emphasise that one type of states that we produce are rotationally invariant states, remaining unchanged under simultaneous identical unitary transformations of all their individual constituents. Such states can be applied to e.g. decoherence-free encoding, quantum communication without sharing a common reference frame, quantum telecloning, secret sharing and remote state preparation schemes. They also have properties which are interesting in studies of foundations of quantum mechanics. In the experimental implementation we use a single source of entangled photon pairs, based on parametric down-conversion, and extract the first, second and third order events. Our experimental setup is completely free from interferometric overlaps, making it robust and contributing to a high fidelity of the generated states. To our knowledge, the achieved fidelity is the highest that has been observed for six-qubit entangled states and our measurement results are in very good agreement with predictions of quantum theory. We have also performed another novel test of the foundations of quantum mechanics. It is based on an inequality that is fulfilled by any non-contextual hidden variable theory, but can be violated by quantum mechanics. This test is similar to Bell inequality tests, which rule out local hidden variable theories as possible completions of quantum mechanics. Here, however, we show that non-contextual hidden variable theories cannot explain certain experimental results, which are consistent with quantum mechanics. Hence, neither of these theories can be used to make quantum mechanics complete.
Although perfect copying of unknown quantum systems is forbidden by the laws of quantum mechanics, approximate cloning is possible. A natural way of realizing quantum cloning of photons is by stimulated emission. In this context, the fundamental quantum limit to the quality of the clones is imposed by the unavoidable presence of spontaneous emission. In our experiment, a single input photon stimulates the emission of additional photons from a source on the basis of parametric down-conversion. This leads to the production of quantum clones with near-optimal fidelity. We also demonstrate universality of the copying procedure by showing that the same fidelity is achieved for arbitrary input states.
A recent proposal to experimentally test quantum mechanics against noncontextual hidden-variable theories [Phys. Rev. Lett.80, 1797 (1998)] is shown to be related with the smallest proof of the Kochen–Specker theorem currently known [Phys. Lett.A212, 183 (1996)]. This proof contains eighteen yes-no questions about a four-dimensional physical system, combined in nine mutually incompatible tests. When these tests are considered as tests about a two-part two-state system, then quantum mechanics and noncontextual hidden variables make the same predictions for eight of them, but make different predictions for the ninth. Therefore, this ninth test would allow us to discriminate between quantum mechanics and noncontextual hidden-variable theories in a (gedanken) single run experiment.