scholarly journals Reality, Indeterminacy, Probability, and Information in Quantum Theory

Entropy ◽  
2020 ◽  
Vol 22 (7) ◽  
pp. 747
Author(s):  
Arkady Plotnitsky
Keyword(s):  
Information Theory ◽  
Quantum Mechanics ◽  
Quantum Theory ◽  
Quantum Information ◽  
Quantum Correlations ◽  
Quantum Information Theory ◽  
Quantum Phenomena

Following the view of several leading quantum-information theorists, this paper argues that quantum phenomena, including those exhibiting quantum correlations (one of their most enigmatic features), and quantum mechanics may be best understood in quantum-informational terms. It also argues that this understanding is implicit already in the work of some among the founding figures of quantum mechanics, in particular W. Heisenberg and N. Bohr, half a century before quantum information theory emerged and confirmed, and gave a deeper meaning to, to their insights. These insights, I further argue, still help this understanding, which is the main reason for considering them here. My argument is grounded in a particular interpretation of quantum phenomena and quantum mechanics, in part arising from these insights as well. This interpretation is based on the concept of reality without realism, RWR (which places the reality considered beyond representation or even conception), introduced by this author previously, in turn, following Heisenberg and Bohr, and in response to quantum information theory.

Quantum information theory

2009 ◽  
Author(s):  
Stephen Barnett
Keyword(s):  
Information Theory ◽  
Quantum Mechanics ◽  
Quantum Information ◽  
Quantum Information Theory ◽  
Quantum Circuits ◽  
Classical Counterpart ◽  
Theory Of Information ◽  
The Many

The astute reader might have formed the impression that quantum in formation science is a rather qualitative discipline because we have not, as yet, explained how to quantify quantum information. There are three good reasons for leaving this important question until the final chapter. Firstly, quantum information theory is technically demanding and to treat it at an earlier stage might have suggested that our subject was more complicated than it is. Secondly, there is the fact that many of the ideas in the field, such as teleportation and quantum circuits, are unfamiliar and it was important to present these as simply as possible. Finally, and most importantly, the theory of quantum information is not yet fully developed. It has not yet reached, in particular, the level of completeness of its classical counterpart. For this reason we can answer only some of the many questions we would like a quantum theory of information to address. Having said this, we can say that however, there are beautiful and useful mathematical results and it seems certain that these will continue to form an important part of the theory as it develops. We noted in the introduction to Chapter 1 that ‘quantum mechanics is a probabilistic theory and so it was inevitable that a quantum information theory would be developed’. A presentation of at least the beginnings of a quantitative theory is the objective of this final chapter. The entropy or information derived from a given probability distribution is, as we have seen, a convenient measure of the uncertainty associated with the distribution. If many of the probabilities are large, so that many of the possible events are comparably likely, then the entropy will be large. If one probability is close to unity, however, then the entropy will be small. It is convenient to introduce entropy in quantum mechanics as a measure of the uncertainty, or lack of knowledge, of the form of the state vector. If we know that our system is in a particular pure state then the associated uncertainty or entropy should be zero. For mixed states, however, it will take a non-zero value.

scholarly journals ENTANGLEMENT SHARING: FROM QUBITS TO GAUSSIAN STATES

2006 ◽  
Vol 04 (03) ◽  
pp. 383-393 ◽  
Author(s):  
GERARDO ADESSO ◽  
FABRIZIO ILLUMINATI
Keyword(s):  
Information Theory ◽  
Quantum Information ◽  
Quantum Correlations ◽  
Quantum Information Theory ◽  
Continuous Variable ◽  
Quantum Systems ◽  
Tripartite Entanglement ◽  
Gaussian States ◽  
Trade Off ◽  
Entanglement Sharing

It is a central trait of quantum information theory that there exist limitations to the free sharing of quantum correlations among multiple parties. Such monogamy constraints have been introduced in a landmark paper by Coffman, Kundu and Wootters, who derived a quantitative inequality expressing a trade-off between the couplewise and the genuine tripartite entanglement for states of three qubits. Since then, a lot of efforts have been devoted to the investigation of distributed entanglement in multipartite quantum systems. In this paper we report, in a unifying framework, a bird's eye view of the most relevant results that have been established so far on entanglement sharing in quantum systems. We will take off from the domain of N qubits, graze qudits, and finally land in the almost unexplored territory of multimode Gaussian states of continuous variable systems.

Elements of quantum theory

2009 ◽  
Author(s):  
Stephen Barnett
Keyword(s):  
Quantum Theory ◽  
Quantum Information ◽  
Quantum Physics ◽  
Superposition Principle ◽  
Dynamical Evolution ◽  
Intimate Relationship ◽  
Quantum Information Theory ◽  
Classical Domain ◽  
Interpretation Of Quantum Theory ◽  
Quantum Phenomena

We have seen that there is an intimate relationship between probability and information. The values we assign to probabilities depend on the information available, and information is a function of probabilities. This connection makes it inevitable that information will be an important concept in any statistical theory, including thermodynamics and, of course, quantum physics. The probabilistic interpretation of quantum theory has probability amplitudes rather than probabilities as the fundamental quantities. This feature, together with the associated superposition principle, is responsible for intrinsically quantum phenomena and gives quantum information theory its distinctive flavour. We shall see that the quantum rules for dynamical evolution and measurement, together with the existence of entangled states, have important implications for quantum information. They also make it possible to perform tasks which are either impractical or impossible within the classical domain. In describing these we shall make extensive use of simple but fundamental ideas in quantum theory. This chapter introduces the mathematical description of quantum physics and the concepts which will be employed in our study of quantum information.

Destruction ab Toto: Nothing from Something

2018 ◽  
Author(s):  
Vlatko Vedral
Keyword(s):  
Information Theory ◽  
Quantum Theory ◽  
Quantum Information ◽  
Quantum Teleportation ◽  
Quantum Information Theory ◽  
Boolean Logic ◽  
Biological Information ◽  
New Order ◽  
Financial Speculation ◽  
Theory Of Information

The main view promoted by this book is that underlying many different aspects of reality is some form of information processing. The theory of information started rather innocently, as the result of a very specific question that Shannon considered, which was how to maximize the capacity of communication between two users. Shannon showed that all we need is to associate a probability to an event, and defined a metric that allowed you to quantify the information content of that event. Interestingly, because of its simplicity and intuitiveness, Shannon’s views have been successfully applied to many other problems. We can view biological information through Shannon’s theory as a communication in time (where the objective of natural selection is to propagate the gene pool into the future). But it is not only that communications and biology are trying to optimize information. In physics, systems arrange themselves so that entropy is maximized, and this entropy is quantified in the same way as Shannon’s information. We encounter the same form of information in other phenomena. Financial speculation is also governed by the same concept of entropy, and optimizing your profit is the same problem as optimizing your channel capacity. In social theory, society is governed by its interconnectedness or correlation and this correlation itself is quantified by Shannon’s entropy. Underlying all these phenomena was the classical Boolean logic where events had clear outcomes, either yes or no, on or off, and so on. In our most accurate description of reality, given by quantum theory, we know that bits of information are an approximation to a much more precise concept of qubits. Qubits, unlike bits, can exist in a multitude of states, any combination of yes and no, on and off. Shannon’s information theory has been extended to account for quantum theory and the resulting framework, quantum information theory, has already shown a number of advantages. The greater power of quantum information theory is manifested in more secure cryptographic protocols, a completely new order of computing, quantum teleportation, and a number of other applications that were simply not possible according to Shannon’s view.

QUANTUM INFORMATION — WHAT PRICE REALISM?

2005 ◽  
Vol 03 (01) ◽  
pp. 165-170
Author(s):  
AMIT HAGAR
Keyword(s):  
Information Theory ◽  
Quantum Mechanics ◽  
Quantum Information ◽  
Measurement Problem ◽  
Quantum Information Theory ◽  
Conceptual Problem

Recent suggestions to supply quantum mechanics (QM) with realistic foundations by reformulating it in light of quantum information theory (QIT) are examined and are found wanting by pointing to a basic conceptual problem that QIT itself ignores, namely, the measurement problem. Since one cannot ignore the measurement problem and at the same time pretend to be a realist, as they stand, the suggestions to reformulate QM in light of QIT are nothing but instrumentalism in disguise.

Sign in / Sign up

Export Citation Format

Share Document