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.
We call attention on the fact that recent unprecedented technological achievements, in particular in the field of quantum optics, seem to open the way to new experimental tests which might be relevant both for the foundational problems of quantum mechanics as well as for investigating the perceptual processes.
Quantum interferometry and quantum information processing have been proposed for Bose-Einstein condensates (BECs), but BECs are described in complicated ways such as using quantum field theory or using a nonlinear differential equation. Nonlinear quantum mechanics does not mesh well with the superposition principle at the heart of interferometry and quantum information processing but could be compatible. Thus, we develop a rigorous foundation for quantum gates, obtained by solving the equation for evolution, and then we employ this foundation, combined with quantum-control techniques and appro…
We discuss foundation of quantum mechanics (interpretations, superposition, principle of complementarity, locality, hidden variables) and quantum information theory.
This is a collection of references (papers, books, preprints, book reviews, Ph. D. thesis, patents, web sites, etc.), sorted alphabetically and (some of them) classified by subject, on foundations of quantum mechanics and quantum information. Specifically, it covers hidden variables (``no-go'' theorems, experiments), interpretations of quantum mechanics, entanglement, quantum effects (quantum Zeno effect, quantum erasure, ``interaction-free'' measurements, quantum ``non-demolition'' measurements), quantum information (cryptography, cloning, dense coding, teleportation), and quantum computation…
The purpose of this paper is to survey some topics on mathematical foundations of quantum information developed mainly by the present author and co-workers for the last three decades. The topics include an axiomatic construction of quantum measurement theory based on completely positive map-valued measures, a universally valid new formulation of the uncertainty principle for error and disturbance in quantum measurements, the Wigner-Araki-Yanase limit of quantum measurements, the accuracy limit of quantum computing based on conservation laws, and a quantum interpretation based on quantum set th…
This thesis is a contribution to the debate on the implications of quantum information theory for the foundations of quantum mechanics. In Part 1, the logical and conceptual status of various notions of information is assessed. It is emphasized that the everyday notion of information is to be firmly distinguished from the technical notions arising in information theory; however it is maintained that in both settings `information' functions as an abstract noun, hence does not refer to a particular or substance (the worth of this point is illustrated in application to quantum teleportation). The…
We present a simple experimental scheme which can be used to demonstrate an all-or-nothing type contradiction between non-contextual hidden variables and quantum mechanics. The scheme, which is inspired by recent ideas by Cabello and Garcia-Alcaine, shows that even for a single particle, path and spin information cannot be predetermined in a non-contextual way.
We believe that the hypothesis `it from bit' originates from the assumption that probabilities have a fundamental, irremovable status in quantum theory. We argue against this assumption and highlight four well-known reformulations / modifications of the theory in which probabilities and the measuring apparatus do not play a fundamental role. These are: Bohmian Mechanics, Dynamical Collapse Models, Trace Dynamics, and Quantum Theory without Classical Time. Here the `it' is primary and the `bit' is derived from the `it'.
In this thesis, we have proposed some novel thought experiments involving foundations of quantum mechanics and quantum information theory, using quantum entanglement property. Concerning foundations of quantum mechanics, we have suggested some typical systems including two correlated particles which can distinguish between the two famous theories of quantum mechanics, i.e. the standard and Bohmian quantum mechanics, at the individual level of pair of particles. Meantime, the two theories present the same predictions at the ensemble level of particles. Regarding quantum information theory, two …
Three-level quantum systems, which possess some unique characteristics beyond two-level ones, such as electromagnetically induced transparency, coherent trapping, and Raman scatting, play important roles in solid-state quantum information processing. Here, we introduce an approach to implement the physically feasible three-level transitionless quantum driving with multiple Schrödinger dynamics (MSDs). It can be used to control accurately population transfer and entanglement generation for three-level quantum systems in a nonadiabatic way. Moreover, we propose an experimentally realizable hybri…
This thesis establishes a number of connections between foundational issues in quantum theory, and some quantum information applications. It starts with a review of quantum contextuality and non-locality, multipartite entanglement characterisation, and of a few quantum information protocols. Quantum non-locality and contextuality are shown to be essential for different implementations of quantum information protocols known as quantum random access codes and quantum communication complexity protocols. I derive sufficient experimental conditions for tests of these quantum properties. I also disc…
Prediction is the making of statements, usually probabilistic, about future events based on current information. Retrodiction is the making of statements about past events based on current information. We present the foundations of quantum retrodiction and highlight its intimate connection with the Bayesian interpretation of probability. The close link with Bayesian methods enables us to explore controversies and misunderstandings about retrodiction that have appeared in the literature. To be clear, quantum retrodiction is universally applicable and draws its validity directly from conventiona…
We review some recent experimental progresses concerning Foundations of Quantum Mechanics and Quantum Information obtained in Quantum Optics Laboratory "Carlo Novero" at IENGF. More in details, after a short presentation of our polarization entangled photons source (based on precise superposition of two Type I PDC emission) and of the results obtained with it, we describe an innovative double slit experiment where two degenerate photons produced by PDC are sent each to a specific slit. Beyond representing an interesting example of relation between visibility of interference and "welcher weg" k…
Logical information theory is the quantitative version of the logic of partitions just as logical probability theory is the quantitative version of the dual Boolean logic of subsets. The resulting notion of information is about distinctions, differences, and distinguishability, and is formalized using the distinctions (`dits') of a partition (a pair of points distinguished by the partition). All the definitions of simple, joint, conditional, and mutual entropy of Shannon information theory are derived by a uniform transformation from the corresponding definitions at the logical level. The purp…
This paper reports three almost trivial theorems that nevertheless appear to have significant import for quantum foundations studies. 1) A Gleason-like derivation of the quantum probability law, but based on the positive operator-valued measures as the basic notion of measurement (see also Busch, quant-ph/9909073). Of note, this theorem also works for 2-dimensional vector spaces and for vector spaces over the rational numbers, where the standard Gleason theorem fails. 2) A way of rewriting the quantum collapse rule so that it looks almost precisely identical to Bayes rule for updating probabil…
We address characterization of many-body superradiant systems and establish a fundamental connection between quantum criticality and the possibility of locally estimating the coupling constant, i.e extracting its value by probing only a portion of the whole system. In particular, we consider Dicke-like superradiant systems made of an ensmble of two-level atoms interacting with a single-mode radiation field at zero effective temperature, and address estimation of the coupling by measurements performed only on radiation. At first, we obtain analytically the Quantum Fisher Information (QFI) and s…
Quantum non-locality has been an extremely fruitful subject of research, leading the scientific revolution towards quantum information science, in particular to device-independent quantum information processing. We argue that time is ripe to work on another basic problem in the foundations of quantum physics, the quantum measurement problem, that should produce good physics both in theoretical, mathematical, experimental and applied physics. We briefly review how quantum non-locality contributed to physics (including some outstanding open problems) and suggest ways in which questions around Ma…
In 1935, Albert Einstein and two colleagues, Boris Podolsky and Nathan Rosen (EPR) developed a thought experiment to demonstrate what they felt was a lack of completeness in quantum mechanics. EPR also postulated the existence of more fundamental theory where physical reality of any system would be completely describe by the variables/states of that fundamental theory. This variable is commonly called hidden variable and the theory is called hidden variable theory (HVT). In 1964, John Bell proposed an empirically verifiable criterion to test for the existence of these HVTs. He derived an inequ…
This paper summarizes the basics of the notion of quantum discord and how it relates to other types of correlations in quantum physics. We take the fundamental information theoretic approach and illustrate our exposition with a number of simple examples.
Motivated by a proposal from Greenberger [Physica Scripta T76, p.57 (1998) ] for superluminal signaling, and inspired by an experiment from Zou, Wang, and Mandel [Phys. Rev. Lett. 67, p.318 (1991) ] showing interference effects within multi-particle entanglement without coincidence detection, we propose a feasible quantum-optical scheme that purports to manifest the capacity for superluminal transfer of information between distant parties
In distributed quantum information processing, small devices composed of a single or a few qubits are networked together through shared entanglement to achieve a scalable machine. Typically, photons are utilized to generate remote entanglement between optically active matter qubits. In this paper, we consider another possibility for achieving entanglement between nodes: using mobile electron spins as mediators of the interaction between static qubits at each node. A strong interaction between electrons makes it feasible to couple the flying electron with the static electron. However, since the…
Shortcut to adiabaticity in various quantum systems has attracted much attention with the wide applications in quantum information processing and quantum control. In this paper, we concentrate on stimulated Raman shortcut-to-adiabatic passage in quantum three-level systems. To implement counter-diabatic driving but without additional coupling, we first reduce the quantum three-level systems to effective two-level problems at large intermediate-level detuning, or on resonance, apply counter-diabatic driving along with the unitary transformation, and eventually modify the pump and Stokes pulses …
Quantum information theorists have created axiomatic reconstructions of quantum mechanics (QM) that are very successful at identifying precisely what distinguishes quantum probability theory from classical and more general probability theories in terms of information-theoretic principles. Herein, we show how one such principle, Information Invariance & Continuity, at the foundation of those axiomatic reconstructions maps to "no preferred reference frame" (NPRF, aka "the relativity principle") as it pertains to the invariant measurement of Planck's constant h for Stern-Gerlach (SG) spin measure…
The study of mutual entropy (information) and capacity in classica l system was extensively done after Shannon by several authors like Kolmogor ov and Gelfand. In quantum systems, there have been several definitions of t he mutual entropy for classical input and quantum output. In 1983, the autho r defined the fully quantum mechanical mutual entropy by means of the relati ve entropy of Umegaki, and it has been used to compute the capacity of quant um channel for quantum communication process; quantum input-quantum output. Recently, a correlated state in quantum syatems, so-called quantum entan…
In this paper I apply newly-proposed information-theoretic principles to thermodynamic work extraction. I show that if it is possible to extract work deterministically from a physical system prepared in any one of a set of states, then those states must be distinguishable from one another. This result is formulated independently of scale and of particular dynamical laws; it also provides a novel connection between thermodynamics and information theory, established via the law of conservation of energy (rather than the second law of thermodynamics). Albeit compatible with these conclusions, exi…
Recently, Chau introduced an experimentally feasible qudit-based quantum-key-distribution (QKD) scheme. In that scheme, one bit of information is phase encoded in the prepared state in a $2^n$-dimensional Hilbert space in the form $(|i\rangle\pm|j\rangle)/\sqrt{2}$ with $n\ge 2$. For each qudit prepared and measured in the same two-dimensional Hilbert subspace, one bit of raw secret key is obtained in the absence of transmission error. Here we show that by modifying the basis announcement procedure, the same experimental setup can generate $n$ bits of raw key for each qudit prepared and measur…
We present here our introduction to the contributed volume "Quantum Theory: Informational Foundations and Foils", Springer Netherlands (2016). It highlights recent trends in quantum foundations and offers an overview of the contributions appearing in the book.
The education system for students in physics suffers (worldwide) from the absence of a deep course in probability and randomness. This is the real problem for students interested in quantum information theory, quantum optics, and quantum foundations. Here the primitive treatment of probability and randomness may lead to deep misunderstandings of theory and wrong interpretations of experimental results. Since during my visits (in 2013 and 2014) to IQOQI a number of students (experimenters!) asked me permanently about foundational problems of probability and randomness, especially inter-relation…
We discuss new approach to mathematical foundations of quantum theory, which is completely independent of Hilbert spaces and measure spaces. New kinematics is defined by non-linear geometry of spaces of integrals on abstract non-commutative algebras. New dynamics is defined by constrained maximisation of quantum relative entropy. We recover Hilbert space based approach (including unitary evolution and the von Neumann--Lüders rule) and measure theoretic approach to probability theory (including Bayes' rule) as special cases of our approach.
We review a recent approach to the foundations of quantum mechanics inspired by quantum information theory. The approach is based on a general framework, which allows one to address a large class of physical theories which share basic information-theoretic features. We first illustrate two very primitive features, expressed by the axioms of causality and purity-preservation, which are satisfied by both classical and quantum theory. We then discuss the axiom of purification, which expresses a strong version of the Conservation of Information and captures the core of a vast number of protocols i…
It is generally believed that physical laws, reflecting an inherent order in the universe, are ordained by nature. However, in modern physics the observer plays a central role raising questions about how an observer-centric physics can result in laws apparently worthy of a universal nature-centric physics. Over the last decade, we have found that the consistent apt quantification of algebraic and order-theoretic structures results in calculi that possess constraint equations taking the form of what are often considered to be physical laws. I review recent derivations of the formal relations am…
One of the predominant challenges when engineering future quantum information processors is that large quantum systems are notoriously hard to maintain and control accurately. It is therefore of immediate practical relevance to investigate quantum information processing with limited physical resources, for example to ask: How well can we perform information processing tasks if we only have access to a small quantum device? Can we beat fundamental limits imposed on information processing with classical resources? This book will introduce the reader to the mathematical framework required to answ…
