311,681 research outputs found
Matter as Information. Quantum Information as Matter
Quantum information is discussed as the universal substance of the world. It is interpreted as that generalization of classical information, which includes both finite and transfinite ordinal numbers. On the other hand, any wave function and thus any state of any quantum system is just one value of quantum information. Information and its generalization as quantum information are considered as quantities of elementary choices. Their units are correspondingly a bit and a qubit. The course of time is what generates choices by itself, thus quantum information and any item in the world in final analysis. The course of time generates necessarily choices so: The future is absolutely unorderable in principle while the past is always well-ordered and thus unchangeable. The present as the mediation between them needs the well-ordered theorem equivalent to the axiom of choice. The latter guarantees the choice even among the elements of an infinite set, which is the case of quantum information. The concrete and abstract objects share information as their common base, which is quantum as to the formers and classical as to the latter. The general quantities of matter in physics, mass and energy can be considered as particular cases of quantum information. The link between choice and abstraction in set theory allows of âHumeâs principleâ to be interpreted in terms of quantum mechanics as equivalence of âmanyâ and âmuchâ underlying quantum information. Quantum information as the universal substance of the world calls for the unity of physics and mathematics rather than that of the concrete and abstract objects and thus for a form of quantum neo-Pythagoreanism in final analysis
Philosophical Aspects of Quantum Information Theory
Quantum information theory represents a rich subject of discussion for those
interested in the philosphical and foundational issues surrounding quantum
mechanics for a simple reason: one can cast its central concerns in terms of a
long-familiar question: How does the quantum world differ from the classical
one? Moreover, deployment of the concepts of information and computation in
novel contexts hints at new (or better) means of understanding quantum
mechanics, and perhaps even invites re-assessment of traditional material
conceptions of the basic nature of the physical world. In this paper I review
some of these philosophical aspects of quantum information theory, begining
with an elementary survey of the theory, seeking to highlight some of the
principles and heuristics involved. We move on to a discussion of the nature
and definition of quantum information and deploy the findings in discussing the
puzzles surrounding teleportation. The final two sections discuss,
respectively, what one might learn from the development of quantum computation
(both about the nature of quantum systems and about the nature of computation)
and consider the impact of quantum information theory on the traditional
foundational questions of quantum mechanics (treating of the views of
Zeilinger, Bub and Fuchs, amongst others).Comment: LaTeX; 55pp; 3 figs. Forthcoming in Rickles (ed.) The Ashgate
Companion to the New Philosophy of Physic
Quantum probabilities as Bayesian probabilities
In the Bayesian approach to probability theory, probability quantifies a
degree of belief for a single trial, without any a priori connection to
limiting frequencies. In this paper we show that, despite being prescribed by a
fundamental law, probabilities for individual quantum systems can be understood
within the Bayesian approach. We argue that the distinction between classical
and quantum probabilities lies not in their definition, but in the nature of
the information they encode. In the classical world, maximal information about
a physical system is complete in the sense of providing definite answers for
all possible questions that can be asked of the system. In the quantum world,
maximal information is not complete and cannot be completed. Using this
distinction, we show that any Bayesian probability assignment in quantum
mechanics must have the form of the quantum probability rule, that maximal
information about a quantum system leads to a unique quantum-state assignment,
and that quantum theory provides a stronger connection between probability and
measured frequency than can be justified classically. Finally we give a
Bayesian formulation of quantum-state tomography.Comment: 6 pages, Latex, final versio
Why the Tsirelson bound?
Wheeler's question 'why the quantum' has two aspects: why is the world
quantum and not classical, and why is it quantum rather than superquantum,
i.e., why the Tsirelson bound for quantum correlations? I discuss a remarkable
answer to this question proposed by Pawlowski et al (2009), who provide an
information-theoretic derivation of the Tsirelson bound from a principle they
call 'information causality.'Comment: 17 page
Entropy in general physical theories
Information plays an important role in our understanding of the physical
world. We hence propose an entropic measure of information for any physical
theory that admits systems, states and measurements. In the quantum and
classical world, our measure reduces to the von Neumann and Shannon entropy
respectively. It can even be used in a quantum or classical setting where we
are only allowed to perform a limited set of operations. In a world that admits
superstrong correlations in the form of non-local boxes, our measure can be
used to analyze protocols such as superstrong random access encodings and the
violation of `information causality'. However, we also show that in such a
world no entropic measure can exhibit all properties we commonly accept in a
quantum setting. For example, there exists no`reasonable' measure of
conditional entropy that is subadditive. Finally, we prove a coding theorem for
some theories that is analogous to the quantum and classical setting, providing
us with an appealing operational interpretation.Comment: 20 pages, revtex, 7 figures, v2: Coding theorem revised, published
versio
Quantum information with continuous variables
Quantum information is a rapidly advancing area of interdisciplinary
research. It may lead to real-world applications for communication and
computation unavailable without the exploitation of quantum properties such as
nonorthogonality or entanglement. We review the progress in quantum information
based on continuous quantum variables, with emphasis on quantum optical
implementations in terms of the quadrature amplitudes of the electromagnetic
field.Comment: accepted for publication in Reviews of Modern Physic
Experimental Test of Quantum No-Hiding Theorem
Linearity and unitarity are two fundamental tenets of quantum theory. Any
consequence that follows from these must be respected in the quantum world. The
no-cloning theorem and the no-deleting theorem are the consequences of the
linearity and the unitarity. Together with the stronger no-cloning theorem they
provide permanence to quantum information, thus, suggesting that in the quantum
world information can neither be created nor be destroyed. In this sense
quantum information is robust, but at the same time it is also fragile because
any interaction with the environment may lead to loss of information. Recently,
another fundamental theorem was proved, namely, the no-hiding theorem that
addresses precisely the issue of information loss. It says that if any physical
process leads to bleaching of quantum information from the original system,
then it must reside in the rest of the universe with no information being
hidden in the correlation between these two subsystems. This has applications
in quantum teleportation, state randomization, private quantum channels,
thermalization and black hole evaporation. Here, we report experimental test of
the no-hiding theorem with the technique of nuclear magnetic resonance (NMR).
We use the quantum state randomization of a qubit as one example of the
bleaching process and show that the missing information can be fully recovered
up to local unitary transformations in the ancilla qubits. Since NMR offers a
way to test fundamental predictions of quantum theory using coherent control of
quantum mechanical nuclear spin states, our experiment is a step forward in
this direction.Comment: 12 pages, 6 Figs. Jharana Rani Samal, Deceased on her 27th birthday
12th Nov. 2009. The experimental work of this paper was completely carried
out by the first author. We dedicate this paper to the memory of the
brilliant soul of Ms. Jharana Rani Samal
- âŠ