Even though quantum mechanics allows a state to pack a lot of information (via arbitrary superposition of basis states), not all information contained in a quantum state is retrievable from measurements. This seems to be a limitation at first, but can also offer some advantages over classical ways to store and transmit information.
The concept of information is not different in quantum theory from its counterpart in classical physics: a sui generis quantum information concept is not needed. However, the quantum world is radically different from its classical counterpart. This difference in structure of the material world has important consequences for the amounts of information that can be stored in physical systems and for the possibilities of information transfer. In many cases, overlap between quantum states (non-orthogonality of states) blurs distinctions and impedes efficient information transfer. However, the other typical quantum feature, entanglement, makes new and seemingly mysterious ways of transporting information possible. In this article, we suggest an interpretational scheme of quantum mechanics in terms of perspectival physical properties that may provide an intelligible account of these novel quantum possibilities, while staying close to the mathematical formalism of quantum mechanics.
Quantum information stands apart from classical information, rooted in the principles of quantum mechanics and quantum information theory. Quantum states serve as the fundamental unit of quantum information, whose evolution is governed by the laws of quantum mechanics. While some philosophers, such as A. Duwell have argued that there is no quantum information, which is not a new concept and can be described using Shannon information theory, others, like C. M. Caves and C. A. Fuchs have proposed that quantum information represents classical information stored within quantum systems. However, this chapter argues that quantum information exists and is different from classical information from the perspectives of how information exists and how it is transmitted. Quantum information, unlike classical information, can be categorized into two kinds: Ontological quantum information and epistemological quantum information, where the former reflects the inherent state of microscopic particles, which is independent of observation, and the latter describes how we perceive their state through measurements. Finally, this chapter explores the connection between quantum information and quantum reality. Quantum reality refers to the show of the self-identity of quantum entities. Quantum information, on the other hand, is the show of the states and correlative ways of quantum entities, and it coexists with quantum reality.
Abstract Information is often considered classical in a definite state rather than in a superposition of states. It seems rather strange to consider information in superpositions. Some people would, on the basis of this argument, conclude that quantum information can never exist and we can only have access to classical information. It turns out, however, that quantum information can be quantified in the same way as classical information using Shannon's prescription. There is a unique measure (up to a constant additive or multiplicative term) of quantum information such that S (the von Neumann entropy) is purely a function of the probabilities of outcomes of measurements made on a quantum system (that is, a function of a density operator); S is a continuous function of probability; S is additive. This chapter discusses the fidelity of pure quantum states, Helstrom's discrimination, quantum data compression, entropy of observation, conditional entropy and mutual information, relative entropy, and statistical interpretation of relative entropy.
Nowadays quantum information science is in a state of theoretic completeness; much is invested to research quality physical solution for quantum computer and applications, so the field is led by physicists and information science and technology professionals. This field proved its potential and many (including us) believe it is in the right direction to go. In this paper we'll try to present and analyze the philosophy and nature of quantum information science and discuss hot topics around them. Although there is plenty of space for discussion around this field, we will concentrate on some important issues, such as quantum communication, algorithms and cryptography. Communication promises to be one of the directions where huge breakthroughs will be observed (entanglement as communication), algorithms have already shown exponential advantage (Shor's factoring) over classical counterparts and different paradigm of information processing. Cryptography seems to utilize general achievements in quantum information science and make encryption protocols very secure. Quantum computation can be understood as a generalization of classical computation: The possible states of a quantum computer are superpositions of bit strings, where the tensor factor is called a quantum bit or qubit. To evaluate the computational complexity of an algorithm, either classical or quantum, it is necessary to specify a set of elementary operations, the number of which used during the computation quantities the complexity. If we allow arbitrary permutations classically, or arbitrary unitary transformations quantum mechanically, any state can be reached from any other state in a single step. The general kind of quantum computer should be programmed to perform distinctively quantum operations such as generating two bits in a superposition state. An appropriate measurement on the final superposed state of the computer produces a probabilistic behavior of the output, and because of this quantum parallelization does not reduce the average time required for parallelizable computation completion. The development of quantum computing science and technology as well as quantum computers as thinking machines is very dependent on different achievements of modern research in fundamental and applied physics as well as novel mathematical methods and tools.
The packing lemma is a general method for one party to pack classical messages into a Hilbert space so that another party can distinguish the packed messages. The first party can prepare an ensemble of quantum states, and the other party has access to a set of projectors from which he can form a quantum measurement. If the ensemble and the projectors satisfy the conditions of the packing lemma, then it guarantees the existence of a scheme by which the second party can distinguish the classical messages that the first party prepares. The statement of the packing lemma is quite general, and this approach has a great advantage because we can use it as a primitive in many coding theorems in quantum Shannon theory. Examples of coding theorems that we can prove with the packing lemma are the Holevo–Schumacher–Westmoreland (HSW) theorem for transmission of classical information over a quantum channel and the entanglement-assisted classical capacity theorem for the transmission of classical information over an entanglement-assisted quantum channel (furthermore, Chapter 21 shows that these two protocols are sufficient to generate most known protocols in quantum Shannon theory). Combined with the covering lemma of the next chapter, the packing lemma gives a method for transmitting private classical information over a quantum channel, and this technique in turn gives a way to communicate quantum information over a quantum channel.
Although the interpretation of the concept of information is not clear, even in the classical framework, new interpretive problems have arisen with the advent of the so-called quantum information, which combine the difficulties in understanding the concept of information with the well-known foundational puzzles derived from quantum mechanics itself. The aim of this paper is to consider some arguments traditionally put forward to support the idea that quantum information is qualitatively different from classical information. The final conclusion is that there are no reasons to admit the existence of quantum information as qualitatively different from classical information: there is only one kind of information, physically neutral, which can be encoded by means of classical or quantum states.