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Quantum Conditional Entropy
The conditional quantum entropy is an entropy measure used in quantum information theory. It is a generalization of the conditional entropy of classical information theory. For a bipartite state \rho^, the conditional entropy is written S(A, B)_\rho, or H(A, B)_\rho, depending on the notation being used for the von Neumann entropy. The quantum conditional entropy was defined in terms of a conditional density operator \rho_ by Nicolas Cerf and Chris Adami, who showed that quantum conditional entropies can be negative, something that is forbidden in classical physics. The negativity of quantum conditional entropy is a sufficient criterion for quantum non-separability. In what follows, we use the notation S(\cdot) for the von Neumann entropy, which will simply be called "entropy". Definition Given a bipartite quantum state \rho^, the entropy of the joint system AB is S(AB)_\rho \ \stackrel\ S(\rho^), and the entropies of the subsystems are S(A)_\rho \ \stackrel\ S(\rho^ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Entropy Measure
Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynamics, where it was first recognized, to the microscopic description of nature in statistical physics, and to the principles of information theory. It has found far-ranging applications in chemistry and physics, in biological systems and their relation to life, in cosmology, economics, sociology, Atmospheric science, weather science, climate change, and information systems including the transmission of information in telecommunication. The thermodynamic concept was referred to by Scottish scientist and engineer William Rankine in 1850 with the names ''thermodynamic function'' and ''heat-potential''. In 1865, German physicist Rudolf Clausius, one of the leading founders of the field of thermodynamics, defined it as the quotient of an infinite ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Separable State
In quantum mechanics, separable states are quantum states belonging to a composite space that can be factored into individual states belonging to separate subspaces. A state is said to be entangled if it is not separable. In general, determining if a state is separable is not straightforward and the problem is classed as NP-hard. Separability of bipartite systems Consider first composite states with two degrees of freedom, referred to as ''bipartite states''. By a postulate of quantum mechanics these can be described as vectors in the tensor product space H_1\otimes H_2. In this discussion we will focus on the case of the Hilbert spaces H_1 and H_2 being finite-dimensional. Pure states Let \_^n\subset H_1 and \_^m \subset H_2 be orthonormal bases for H_1 and H_2, respectively. A basis for H_1 \otimes H_2 is then \, or in more compact notation \. From the very definition of the tensor product, any vector of norm 1, i.e. a pure state of the composite system, can be written a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Andreas Winter
Andreas J. Winter (born 14 June 1971, Mühldorf, Germany) is a German mathematician and mathematical physicist at the Universitat Autònoma de Barcelona (UAB) in Spain. He received his Ph.D. in 1999 under Rudolf Ahlswede and Friedrich Götze at the Universität Bielefeld in Germany before moving to the University of Bristol and then to the Centre for Quantum Technologies (CQT) at the National University of Singapore. In 2013 he was appointed ICREA Research Professor at UAB. Winter's research is focused in the field of quantum information theory. Some of his main contributions concern the understanding of quantum communication protocols, the coding theory for quantum channels, and the theory of quantum entanglement. Together with Michał Horodecki and Jonathan Oppenheim, he discovered quantum state-merging and used this primitive to show that quantum information could be negative. Together with Marcin Pawlowski, Tomasz Paterek, Dagomir Kaszlikowski, and Valerio Scarani, he disc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jonathan Oppenheim
Jonathan Oppenheim is a professor of physics at University College London. He is an expert in quantum information theory and quantum gravity. Work Oppenheim proved the third law of thermodynamics (first conjectured by Walther Nernst in 1912) with Lluis Masanes. Together with Michał Horodecki and Andreas Winter, he discovered quantum state-merging and used this primitive to show that quantum information could be negative. More recently he and collaborators have developed a resource theory for thermodynamics on the nano and quantum scale. His Ph.D. under Bill Unruh at the University of British Columbia was on Quantum time. In 2004 he was a postdoctoral researcher under Jacob Bekenstein and a Royal Society University Fellow in Cambridge before moving to University College London. Edible ballot society As a student, Oppenheim was involved in the Edible Ballot Society which satirically advanced eating ballots to highlight the democracy gap in electoral politics. He was a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Michał Horodecki
Michał Horodecki (born 1973) is a Polish physicist at the University of Gdańsk working in the field of quantum information theory, notable for his work on entanglement theory. He co-discovered the Peres-Horodecki criterion for testing whether a state is entangled, and used it to find bound entanglement together with his brother Paweł Horodecki and father Ryszard Horodecki. He co-discovered with Jonathan Oppenheim, Paweł Horodecki and Karol Horodecki that secret key can be drawn from some bound entangled states. Together with Fernando Brandao he proved that every one-dimensional quantum state with a finite correlation length obeys an area law for entanglement entropy. Together with Jonathan Oppenheim and Andreas Winter, he discovered quantum state-merging In quantum information theory, quantum state merging is the transfer of a quantum state when the receiver already has part of the state. The process optimally transfers partial information using entanglement and classical c ... [...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 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] |
Mixed State (physics)
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 hydrog ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Physical Review A
''Physical Review A'' (also known as PRA) is a monthly peer-reviewed scientific journal published by the American Physical Society covering atomic, molecular, and optical physics and quantum information. the editor was Jan M. Rost (Max Planck Institute for the Physics of Complex Systems). History In 1893, the ''Physical Review'' was established at Cornell University. It was taken over by the American Physical Society (formed in 1899) in 1913. In 1970, ''Physical Review'' was subdivided into ''Physical Review A'', ''B'', ''C'', and ''D''. At that time section ''A'' was subtitled ''Physical Review A: General Physics''. In 1990 a process was started to split this journal into two, resulting in the creation of ''Physical Review E'' in 1993. Hence, in 1993, ''Physical Review A'' changed its statement of scope to ''Atomic, Molecular and Optical Physics.'' In January 2007, the section of ''Physical Review E'' that published papers on classical optics was merged into ''Physical Review ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Information Theory
Quantum information is the information of the quantum state, 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 Observable, observables cannot be precisely mea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Physical Review Letters
''Physical Review Letters'' (''PRL''), established in 1958, is a peer-reviewed, scientific journal that is published 52 times per year by the American Physical Society. As also confirmed by various measurement standards, which include the ''Journal Citation Reports'' impact factor and the journal ''h''-index proposed by Google Scholar, many physicists and other scientists consider ''Physical Review Letters'' to be one of the most prestigious journals in the field of physics. ''According to Google Scholar, PRL is the journal with the 9th journal h-index among all scientific journals'' ''PRL'' is published as a print journal, and is in electronic format, online and CD-ROM. Its focus is rapid dissemination of significant, or notable, results of fundamental research on all topics related to all fields of physics. This is accomplished by rapid publication of short reports, called "Letters". Papers are published and available electronically one article at a time. When published in s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chris Adami
Christoph Carl Herbert "Chris" Adami (born August 30, 1962) is a professor of Microbiology and Molecular Genetics, as well as professor of Physics and Astronomy, at Michigan State University. Education Adami was born in Brussels, Belgium, and graduated from the European School of Brussels I. He obtained a Diplom in physics from the University of Bonn and an MA and a Ph.D. in theoretical nuclear physics from Stony Brook University in 1991. Adami was a Division Prize Fellow in the lab of Steven E. Koonin at the California Institute of Technology from 1992-1995, and was subsequently on the Caltech faculty as a senior research associate. Career Before joining Michigan State University, he was a professor of Applied Life Sciences at the Keck Graduate Institute in Claremont, California. Adami is best known for his work on Avida, an artificial life simulator used to study evolutionary biology, and for applying the theory of information to physical and biological systems. Together wit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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