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Noisy-storage Model
The noisy-storage model refers to a cryptographic model employed in quantum cryptography. It assumes that the quantum memory device of an attacker (Adversary (cryptography), adversary) trying to break the protocol is imperfect (noisy). The main goal of this model is to enable the secure implementation of two-party cryptographic primitives, such as bit commitment, oblivious transfer and Smart Card#Applications, secure identification. Motivation Quantum communication has proven to be extremely useful when it comes to distributing encryption keys. It allows two distant parties Alice and Bob to expand a small initial secret key into an arbitrarily long secret key by sending qubits (quantum bits) to each other. Most importantly, it can be shown that any eavesdropper trying to listen into their communication cannot intercept any information about the long key. This is known as quantum key distribution (QKD). Yet, it has been shown that even quantum communication does not allow the secur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Cryptography
Quantum cryptography is the science of exploiting quantum mechanical properties to perform cryptographic tasks. The best known example of quantum cryptography is quantum key distribution which offers an information-theoretically secure solution to the key exchange problem. The advantage of quantum cryptography lies in the fact that it allows the completion of various cryptographic tasks that are proven or conjectured to be impossible using only classical (i.e. non-quantum) communication. For example, it is impossible to copy data encoded in a quantum state. If one attempts to read the encoded data, the quantum state will be changed due to wave function collapse (no-cloning theorem). This could be used to detect eavesdropping in quantum key distribution (QKD). History In the early 1970s, Stephen Wiesner, then at Columbia University in New York, introduced the concept of quantum conjugate coding. His seminal paper titled "Conjugate Coding" was rejected by the IEEE Information T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Communication
Quantum information science is an interdisciplinary field that seeks to understand the analysis, processing, and transmission of information using quantum mechanics principles. It combines the study of Information science with quantum mechanics, quantum effects in physics. It includes theoretical issues in computational models and more experimental topics in quantum physics, including what can and cannot be done with quantum information. The term quantum information theory is also used, but it fails to encompass experimental research, and can be confused with a subfield of quantum information science that addresses the processing of quantum information. Scientific and engineering studies To understand quantum teleportation, quantum entanglement and the manufacturing of quantum computer hardware requires a thorough understanding of quantum physics and engineering. Since 2010s, there has been remarkable progress in manufacturing quantum computers, with companies like Google and IBM in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
BB84
BB84 is a quantum key distribution scheme developed by Charles Bennett and Gilles Brassard in 1984. It is the first quantum cryptography protocol. The protocol is provably secure, relying on two conditions: (1) the quantum property that information gain is only possible at the expense of disturbing the signal if the two states one is trying to distinguish are not orthogonal (see no-cloning theorem); and (2) the existence of an authenticated public classical channel. It is usually explained as a method of securely communicating a private key from one party to another for use in one-time pad encryption.''Quantum Computing and Quantum Information'', Michael Nielsen and Isaac Chuang, Cambridge University Press 2000 Description In the BB84 scheme, Alice wishes to send a private key to Bob. She begins with two strings of bits, a and b, each n bits long. She then encodes these two strings as a tensor product of n qubits: :, \psi\rangle = \bigotimes_^, \psi_\rangle, where a_i and b_i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mutually Unbiased Bases
In quantum information theory, mutually unbiased bases in Hilbert space C''d'' are two orthonormal bases \ and \ such that the square of the magnitude of the inner product between any basis states , e_j\rangle and , f_k\rangle equals the inverse of the dimension ''d'': : , \langle e_j, f_k \rangle, ^2 = \frac, \quad \forall j,k \in \. These bases are ''unbiased'' in the following sense: if a system is prepared in a state belonging to one of the bases, then all outcomes of the measurement with respect to the other basis are predicted to occur with equal probability. Overview The notion of mutually unbiased bases was first introduced by Schwinger in 1960, and the first person to consider applications of mutually unbiased bases was Ivanovic in the problem of quantum state determination. Another area where mutually unbiased bases can be applied is quantum key distribution, more specifically in secure quantum key exchange.M. Planat et al, A Survey of Finite Algebraic Geometrical ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Identity Channel
In quantum information theory, the identity channel is a noise-free quantum channel In quantum information theory, a quantum channel is a communication channel which can transmit quantum information, as well as classical information. An example of quantum information is the state of a qubit. An example of classical information i .... That is, the channel outputs exactly what was put in.. The identity channel is commonly denoted as I, \mathsf or \mathbb. References Information theory Mathematical analysis {{physics-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Depolarizing Channel
A quantum depolarizing channel is a model for quantum noise in quantum systems. The d-dimensional depolarizing channel can be viewed as a completely positive trace-preserving map \Delta_\lambda, depending on one parameter \lambda, which maps a state \rho onto a linear combination of itself and the maximally mixed state, :\Delta_\lambda(\rho)=(1-\lambda)\rho+\fracI. The condition of complete positivity requires \lambda to satisfy the bounds :0\le\lambda\le 1+\frac. Qubit Channel The single qubit depolarizing channel has operator-sum representation on a density matrix \rho given by :\Delta_\lambda(\rho) = \sum_^ K_i \rho K_i^\dagger, where K_i are the Kraus operators given by :K_0 = \sqrt I, K_1 = \sqrt X, K_2 = \sqrt Y, K_3 = \sqrt Z and \ are the Pauli matrices. The trace preserving condition is satisfied by the fact that \sum_K_i ^\dagger K_i = I. Geometrically the depolarizing channel \Delta_\lambda can be interpreted as a uniform contraction of the Bloch sphere, parameteri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Error-correcting
In information theory and coding theory with applications in computer science and telecommunication, error detection and correction (EDAC) or error control are techniques that enable reliable delivery of digital data over unreliable communication channels. Many communication channels are subject to channel noise, and thus errors may be introduced during transmission from the source to a receiver. Error detection techniques allow detecting such errors, while error correction enables reconstruction of the original data in many cases. Definitions ''Error detection'' is the detection of errors caused by noise or other impairments during transmission from the transmitter to the receiver. ''Error correction'' is the detection of errors and reconstruction of the original, error-free data. History In classical antiquity, copyists of the Hebrew Bible were paid for their work according to the number of stichs (lines of verse). As the prose books of the Bible were hardly ever wr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum State
In quantum physics, a quantum state is a mathematical entity that provides a probability distribution for the outcomes of each possible measurement on a system. Knowledge of the quantum state together with the rules for the system's evolution in time exhausts all that can be predicted about the system's behavior. A mixture of quantum states is again a quantum state. Quantum states that cannot be written as a mixture of other states are called pure quantum states, while all other states are called mixed quantum states. A pure quantum state can be represented by a ray in a Hilbert space over the complex numbers, while mixed states are represented by density matrices, which are positive semidefinite operators that act on Hilbert spaces. Pure states are also known as state vectors or wave functions, the latter term applying particularly when they are represented as functions of position or momentum. For example, when dealing with the energy spectrum of the electron in a hydrogen at ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Channel
In quantum information theory, a quantum channel is a communication channel which can transmit quantum information, as well as classical information. An example of quantum information is the state of a qubit. An example of classical information is a text document transmitted over the Internet. More formally, quantum channels are completely positive (CP) trace-preserving maps between spaces of operators. In other words, a quantum channel is just a quantum operation viewed not merely as the reduced dynamics of a system but as a pipeline intended to carry quantum information. (Some authors use the term "quantum operation" to also include trace-decreasing maps while reserving "quantum channel" for strictly trace-preserving maps.) Memoryless quantum channel We will assume for the moment that all state spaces of the systems considered, classical or quantum, are finite-dimensional. The memoryless in the section title carries the same meaning as in classical information theory: the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Information
Quantum information is the information of the state of a quantum system. It is the basic entity of study in quantum information theory, and can be manipulated using quantum information processing techniques. Quantum information refers to both the technical definition in terms of Von Neumann entropy and the general computational term. It is an interdisciplinary field that involves quantum mechanics, computer science, information theory, philosophy and cryptography among other fields. Its study is also relevant to disciplines such as cognitive science, psychology and neuroscience. Its main focus is in extracting information from matter at the microscopic scale. Observation in science is one of the most important ways of acquiring information and measurement is required in order to quantify the observation, making this crucial to the scientific method. In quantum mechanics, due to the uncertainty principle, non-commuting observables cannot be precisely measured simultaneously, as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Key Distribution
Quantum key distribution (QKD) is a secure communication method which implements a cryptographic protocol involving components of quantum mechanics. It enables two parties to produce a shared random secret key known only to them, which can then be used to encrypt and decrypt messages. It is often incorrectly called quantum cryptography, as it is the best-known example of a quantum cryptographic task. An important and unique property of quantum key distribution is the ability of the two communicating users to detect the presence of any third party trying to gain knowledge of the key. This results from a fundamental aspect of quantum mechanics: the process of measuring a quantum system in general disturbs the system. A third party trying to eavesdrop on the key must in some way measure it, thus introducing detectable anomalies. By using quantum superpositions or quantum entanglement and transmitting information in quantum states, a communication system can be implemented that detect ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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