Entanglement of formation
The entanglement of formation is a quantity that measures the entanglement of a bipartite quantum state.
Quantum finite automaton
In quantum computing, quantum finite automata (QFA) or quantum state machines are a quantum analog of probabilistic automata or a Markov decision process. They provide a mathematical abstraction of re
Classical capacity
In quantum information theory, the classical capacity of a quantum channel is the maximum rate at which classical data can be sent over it error-free in the limit of many uses of the channel. Holevo,
Lieb–Robinson bounds
The Lieb–Robinson bound is a theoretical upper limit on the speed at which information can propagate in non-relativistic quantum systems. It demonstrates that information cannot travel instantaneously
Mutually unbiased bases
In quantum information theory, mutually unbiased bases in Hilbert space Cd are two orthonormal bases and such that the square of the magnitude of the inner product between any basis states and equals
Quantum t-design
A quantum t-design is a probability distribution over either pure quantum states or unitary operators which can duplicate properties of the probability distribution over the Haar measure for polynomia
Quantum capacity
In the theory of quantum communication, the quantum capacity is the highest rate at which quantum information can be communicated over many independent uses of a noisy quantum channel from a sender to
NLTS Conjecture
In quantum information theory, the No Low-Energy Trivial State (NLTS) conjecture is a precursor to a and posits the existence of families of Hamiltonians with all low energy states of non-trivial comp
POVM
In functional analysis and quantum measurement theory, a positive operator-valued measure (POVM) is a measure whose values are positive semi-definite operators on a Hilbert space. POVMs are a generali
Quantum steering
In physics, in the area of quantum information theory and quantum computation, quantum steering is a special kind of nonlocal correlation, which is intermediate between Bell nonlocality and quantum en
Entanglement witness
In quantum information theory, an entanglement witness is a functional which distinguishes a specific entangled state from separable ones. Entanglement witnesses can be linear or nonlinear functionals
Superoperator
In physics, a superoperator is a linear operator acting on a vector space of linear operators. Sometimes the term refers more specially to a completely positive map which also preserves or does not in
Quantum cognition
Quantum cognition is an emerging field which applies the mathematical formalism of quantum theory to model cognitive phenomena such as information processing by the human brain, language, decision mak
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
Hayden–Preskill thought experiment
In quantum information, the Hayden–Preskill thought experiment (also known as the Hayden–Preskill protocol) is a thought experiment that investigates the black hole information paradox by hypothesizin
Quantum complex network
Quantum complex networks are complex networks whose nodes are quantum computing devices. Quantum mechanics has been used to create secure quantum communications channels that are protected from hackin
Quantum depolarizing channel
A quantum depolarizing channel is a model for quantum noise in quantum systems. The -dimensional depolarizing channel can be viewed as a completely positive trace-preserving map , depending on one par
Solovay–Kitaev theorem
In quantum information and computation, the Solovay–Kitaev theorem says, roughly, that if a set of single-qubit quantum gates generates a dense subset of SU(2) then that set is guaranteed to fill SU(2
Quantum Computing Since Democritus
Quantum Computing Since Democritus is a 2013 book on quantum information science written by Scott Aaronson. It is loosely based on a course Aaronson taught at the University of Waterloo, Canada, the l
Time crystal
In condensed matter physics, a time crystal is a quantum system of particles whose lowest-energy state is one in which the particles are in repetitive motion. The system cannot lose energy to the envi
Quantum relative entropy
In quantum information theory, quantum relative entropy is a measure of distinguishability between two quantum states. It is the quantum mechanical analog of relative entropy.
Diamond norm
In quantum information, the diamond norm, also known as completely bounded trace norm, is a norm on the space of quantum operations, or more generally on any linear map that acts on complex matrices.
Schmidt decomposition
In linear algebra, the Schmidt decomposition (named after its originator Erhard Schmidt) refers to a particular way of expressing a vector in the tensor product of two inner product spaces. It has num
Choi–Jamiołkowski isomorphism
In quantum information theory and operator theory, the Choi–Jamiołkowski isomorphism refers to the correspondence between quantum channels (described by completely positive maps) and quantum states (d
Parity measurement
Parity measurement (also referred to as Operator measurement) is a procedure in Quantum information science that is used to project a state into an eigenstate of an operator and to acquire its eigenva
Nielsen's theorem
Nielsen's theorem is a result in quantum information concerning transformations between bipartite states due to Michael Nielsen. It makes use of majorization.
Path integral Monte Carlo
Path integral Monte Carlo (PIMC) is a quantum Monte Carlo method used to solve quantum statistical mechanics problems numerically within the path integral formulation. The application of Monte Carlo m
Joint quantum entropy
The joint quantum entropy generalizes the classical joint entropy to the context of quantum information theory. Intuitively, given two quantum states and , represented as density operators that are su
Greenberger–Horne–Zeilinger state
In physics, in the area of quantum information theory, a Greenberger–Horne–Zeilinger state (GHZ state) is a certain type of entangled quantum state that involves at least three subsystems (particle st
W state
The W state is an entangled quantum state of three qubits which in the bra-ket notation has the following shape and which is remarkable for representing a specific type of multipartite entanglement an
Channel-state duality
In quantum information theory, the channel-state duality refers to the correspondence between quantum channels and quantum states (described by density matrices). Phrased differently, the duality is t
Peres–Horodecki criterion
The Peres–Horodecki criterion is a necessary condition, for the joint density matrix of two quantum mechanical systems and , to be separable. It is also called the PPT criterion, for positive partial
Quantum state discrimination
The term quantum state discrimination collectively refers to quantum-informatics techniques, with the help of which, by performing a small number of measurements on a physical system , its specific qu
Holevo's theorem
Holevo's theorem is an important limitative theorem in quantum computing, an interdisciplinary field of physics and computer science. It is sometimes called Holevo's bound, since it establishes an upp
Entanglement monotone
In quantum information and quantum computation, an entanglement monotone is a function that quantifies the amount of entanglement present in a quantum state. Any entanglement monotone is a nonnegative
Bennett's laws
Bennett's laws of quantum information are: 1.
* 1 qubit 1 bit (classical), 2.
* 1 qubit 1 ebit (entanglement bit), 3.
* 1 ebit + 1 qubit 2 bits (i.e. superdense coding), 4.
* 1 ebit + 2 bits 1 qub
Typical subspace
In quantum information theory, the idea of a typical subspace plays an important role in the proofs of many coding theorems (the most prominent example being ). Its role is analogous to that of the ty
Classical shadow
In quantum computing, classical shadow is a protocol for predicting functions of a quantum state using only a logarithmic number of measurements. Given an unknown state , a tomographically complete se
Quantum mutual information
In quantum information theory, quantum mutual information, or von Neumann mutual information, after John von Neumann, is a measure of correlation between subsystems of quantum state. It is the quantum
No-hiding theorem
The no-hiding theorem states that if information is lost from a system via decoherence, then it moves to the subspace of the environment and it cannot remain in the correlation between the system and
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 tech
Coherent information
Coherent information is an used in quantum information theory. It is a property of a quantum state ρ and a quantum channel ; intuitively, it attempts to describe how much of the quantum information in
No-teleportation theorem
In quantum information theory, the no-teleportation theorem states that an arbitrary quantum state cannot be converted into a sequence of classical bits (or even an infinite number of such bits); nor
Schrödinger–HJW theorem
In quantum information theory and quantum optics, the Schrödinger–HJW theorem is a result about the realization of a mixed state of a quantum system as an ensemble of pure quantum states and the relat
Quantum memory
In quantum computing, quantum memory is the quantum-mechanical version of ordinary computer memory. Whereas ordinary memory stores information as binary states (represented by "1"s and "0"s), quantum