Quantum information processing is the emerging field that defines and realizes computing devices that make use of quantum mechanical principles such as the superposition principle, entanglement, and interference. Until recently the common notion of computing was based on classical mechanics and did not take into account all the possibilities that physically realizable computing devices offer in principle. The field gained momentum after Shor developed an efficient algorithm for factoring numbers, demonstrating the potential computing powers that quantum computing devices can unleash. In this review the information counterpart of computing is studied. It was realized early on by Holevo that quantum bits, the quantum mechanical counterpart of classical bits, cannot be used for efficient transformation of information in the sense that arbitrary $k$-bit messages cannot be compressed into messages of $k\ensuremath{-}1$ qubits. The abstract form of the distributed computing setting is called communication complexity. It studies the amount of information, in terms of bits or in our case qubits, that two spatially separated computing devices need to exchange in order to perform some computational task. Surprisingly, quantum mechanics can be used to obtain dramatic advantages for such tasks. The area of quantum communication complexity is reviewed and it is shown how it connects the foundational physics questions regarding nonlocality with those of communication complexity studied in theoretical computer science. The first examples exhibiting the advantage of the use of qubits in distributed information-processing tasks were based on nonlocality tests. However, by now the field has produced strong and interesting quantum protocols and algorithms of its own that demonstrate that entanglement, although it cannot be used to replace communication, can be used to reduce the communication exponentially. In turn, these new advances yield a new outlook on the foundations of physics and could even yield new proposals for experiments that test the foundations of physics.
Quantum information processing is the emerging field that defines and realizes computing devices that make use of quantum mechanical principles such as the superposition principle, entanglement, and interference. Until recently the common notion of computing was based on classical mechanics and did not take into account all the possibilities that physically realizable computing devices offer in principle. The field gained momentum after Shor developed an efficient algorithm for factoring numbers, demonstrating the potential computing powers that quantum computing devices can unleash. In this review the information counterpart of computing is studied. It was realized early on by Holevo that quantum bits, the quantum mechanical counterpart of classical bits, cannot be used for efficient transformation of information in the sense that arbitrary k-bit messages cannot be compressed into messages of k\ensuremath−1 qubits. The abstract form of the distributed computing setting is called communication complexity. It studies the amount of information, in terms of bits or in our case qubits, that two spatially separated computing devices need to exchange in order to perform some computational task. Surprisingly, quantum mechanics can be used to obtain dramatic advantages for such tasks. The area of quantum communication complexity is reviewed and it is shown how it connects the foundational physics questions regarding nonlocality with those of communication complexity studied in theoretical computer science. The first examples exhibiting the advantage of the use of qubits in distributed information-processing tasks were based on nonlocality tests. However, by now the field has produced strong and interesting quantum protocols and algorithms of its own that demonstrate that entanglement, although it cannot be used to replace communication, can be used to reduce the communication exponentially. In turn, these new advances yield a new outlook on the foundations of physics and could even yield new proposals for experiments that test the foundations of physics.
The theoretical, experimental and technological areas covering the use of quantum mechanics for communication and computation.Quantum information processing includes investigations in quantum information theory, quantum communication, quantum computation, quantum algorithms and their complexity, and quantum control.The science of quantum information processing is a highly interdisciplinary field.In the context of mathematics it is stimulating research in pure mathematics (e.g.coding theory, *algebras, quantum topology) as well as requiring and providing many opportunities for applied mathematics.The science of quantum information processing emerged from the recognition that usable notions of information need to be physically implementable.In the 1960s and 1970s researchers such as R. Landauer, C. Bennett, C. Helstrom and A. Holevo realized that the laws of physics give rise to fundamental constraints on the ability to implement and manipulate information.Landauer repeatedly stated that "information is physical", providing impetus to the idea that it should be possible to found theories of information on the laws of physics.This is in contrast to the introspective approach which led to the basic definitions of computer science and information theory as formulated by A. Church, A. Turing, C. Shannon and others in the first half of the 20th century.Early work in studying the physical foundations of information focused on the effects of energy limitations and the need for dissipating heat in computation and communication.Beginning with S. Wiesner's work on applications of quantum mechanics to cryptography in the late 1960s, it was realized that there may be intrinsic advantages to using quantum physics in information processing.Quantum cryptography and quantum communication in general were soon established as interesting and non-trivial extensions of classical communication based on bits.That quantum mechanics may be used to improve the efficiency of algorithms was first realized when attempts at simulating quantum mechanical systems resulted in exponentially complex algorithms compared to the physical resources associated with the system simulated.In the 1980s, P. Benioff and R. Feynman introduced the idea of a quantum computer for efficiently implementing quantum physics simulations.Models of quantum computers were developed by D. Deutsch, leading to the formulation of artificial problems that could be solved more efficiently by quantum than by classical computers.The advantages of quantum computers became widely recognized when P.
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 discuss how the distribution of quantum information through quantum cloning processes can be useful in quantum computing. Regarding entanglement characterisation, some results are obtained relating two problems, that of additivity of the relative entropy of entanglement, and that of identifying different types of tripartite entanglement in the asymptotic regime of manipulations of many copies of a given state. The thesis ends with a description of an information processing task in which a single qubit substitutes for an arbitrarily large amount of classical communication. This result is interpreted in different ways: as a gap between quantum and classical computation space complexity; as a bound on the amount of classical communication necessary to simulate entanglement; and as a basic result on hidden-variable theories for quantum mechanics. I also show that the advantage of quantum over classical communication can be established in a feasible experiment.
Abstract. Quantum information processing is at the crossroads of physics, mathematics and computer science. It is concerned with that we can and cannot do with quantum information that goes beyond the abilities of classical information processing devices. Communication complexity is an area of classical computer science that aims at quantifying the amount of communication necessary to solve distributed computational problems. Quantum communication complexity uses quantum mechanics to reduce the amount of communication that would be classically required. Pseudo-telepathy is a surprising application of quantum information processing to communication complexity. Thanks to entanglement, perhaps the most nonclassical manifestation of quantum mechanics, two or more quantum players can accomplish a distributed task with no need for communication whatsoever, which would be an impossible feat for classical players. After a detailed overview of the principle and purpose of pseudo-telepathy, we present a survey of recent and no-so-recent work on the subject. In particular, we describe and analyse all the pseudo-telepathy games currently known to the authors. 1.
Can quantum communication be more efficient than its classical counterpart? Holevo's theorem rules out the possibility of communicating more than n bits of classical information by the transmission of n quantum bits --- unless the two parties are entangled, in which case twice as many classical bits can be communicated but no more. In apparent contradiction, there are distributed computational tasks for which quantum communication cannot be simulated efficiently by classical means. In extreme cases, the effect of transmitting quantum bits cannot be achieved classically short of transmitting an exponentially larger number of bits. In a similar vein, can entanglement be used to save on classical communication? It is well known that entanglement on its own is useless for the transmission of information. Yet, there are distributed tasks that cannot be accomplished at all in a classical world when communication is not allowed, but that become possible if the non-communicating parties share prior entanglement. This leads to the question of how expensive it is, in terms of classical communication, to provide an exact simulation of the spooky power of entanglement.
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.
In order to provide novel techniques for processing, storing, and transmitting information, the multidisciplinary field of quantum information science (QIS) integrates ideas from quantum physics [ 4 ] with information science. However, due to a number of events, including Peter Shor’s invention of quantum algorithms and the rise in interest in quantum computing, the history of QIS started to expand quickly in the early to middle 1990s. Peter Shor, a physicist and mathematician, developed the first quantum algorithm that could factor big numbers exponentially more rapidly than any classical algorithm in 1994. This finding triggered strong interest in quantum computing’s potential to tackle issues that are currently unsolvable for classical computers. Since then, QIS has advanced due to the development of novel quantum algorithms and enhancements in the hardware used for quantum computing. Understanding complex quantum phenomena like entanglement and superposition and developing novel strategies for utilizing them for information processing and communication are the core goals of QIS. Quantum bits (qubits) can exist in superpositions of 0 and 1 simultaneously, which enables far more efficient computation than classical bits, which can only be in one state or the other at a given time. Superposition is a key concept in quantum computing. In addition to superposition, entanglement, coherence, and quantum algorithms are other important QIS concepts. Entanglement is a key feature of quantum mechanics and has been observed experimentally in a wide range of physical systems, including photons, atoms, and superconducting qubits. Two particles can get entangled with one another through a phenomenon called entanglement in which their quantum states exhibit a high correlation. This indicates that even if two particles are separated by a considerable distance, modifying the state of one can change the state of the other. No matter how far away two separate particles are from one another when they are entangled, measuring the state of one particle immediately gives the state of another particle. It plays a central role in many quantum technologies, including quantum computing for solving complex problems that take classical computers a long time to solve, quantum cryptography for secure communications, quantum sensing for quantum properties of particles to enable more precise measurements, and quantum networking to improve communication and processing speed over both short and long distances. Quantum metrology methods use the principles of quantum mechanics to improve the accuracy of measurements in fields like gravity sensors, timekeeping, and frequency standards. Some of the benefits of QIS are enhanced computing power, improved communication, advanced cryptography, more precise scientific measurements, and better logistics optimization.