"A quantum state is a mathematical entity that embodies the knowledge of a quantum system."
Exploration of quantum states, such as superposition and entanglement, as well as measurements and their effects on these states.
Quantum Mechanics: The foundation of quantum physics, it is a mathematical framework that describes the behavior of particles at the atomic and subatomic level.
Wave-particle duality: The concept that particles can exhibit both wave-like and particle-like behavior.
Superposition: The property of a quantum system where it can exist in multiple states simultaneously until it is measured.
Entanglement: The phenomenon where two particles can become correlated and exhibit non-classical correlations, even when separated by large distances.
Hamiltonian: The operator that describes the energy of a quantum system.
Hilbert space: The mathematical space where quantum states exist.
Quantum State: The complete description of a quantum system.
Quantum Measurement: The process of obtaining information about a quantum state by making an observation.
Quantum Uncertainty: The property of a quantum system where certain observables cannot be measured with arbitrary precision.
Quantum Interference: The phenomenon where quantum states can interfere with each other, leading to constructive or destructive interference.
Quantum Computing: The field that explores the use of quantum mechanics in computing and information processing.
Quantum Cryptography: The field that explores secure communication using quantum mechanics.
Quantum Teleportation: The process of transmitting quantum information over a distance without physically moving the underlying particles.
Quantum Field Theory: The extension of quantum mechanics that describes the behavior of fields in space and time.
Pure states: These states represent a quantum system's complete information and are described by a single wave function.
Mixed states: These are statistical ensembles of pure states and describe partial information of a quantum system. The wave function is a probability distribution for a set of pure states.
Entangled states: These occur when two or more particles manifest an inseparable quantum correlation that cannot be explained classically.
Superposition states: These states refer to a quantum system's property of being in multiple states simultaneously.
Bell states: These maximally entangled states are two-qubit states that allow for efficient quantum communication and cryptography.
Coherent states: These are classical-like states of quantum systems that exhibit wave-like interference and have well-defined phase and amplitude.
Energy eigenstates: Quantum states whose wave function solves an energy eigenvalue equation for a Hamiltonian of the system.
Squeezed states: These states have a lower measurement uncertainty for one observable at the expense of larger uncertainty for its complementary observable.
Projective measurements: These are measurements that completely collapse a wave function onto a particular eigenstate.
Weak measurements: These are measurements that do not collapse the wave function and allow for the determination of the change in a particle's state.
POVM (positive operator valued measure): A generalization of projective measurement that computes probabilities for nonorthogonal states.
von Neumann measurements: State measurements that utilize the eigenvectors of a quantum system to make a measurement.
Qubit Measurements: Measurements that utilize the qubits elemental properties of superposition and entanglement.
"Quantum mechanics specifies the construction, evolution, and measurement of a quantum state."
"The result is a quantum mechanical prediction for the system represented by the state."
"Knowledge of the quantum state and the quantum mechanical rules for the system's evolution in time, exhausts all that can be known about a quantum system."
"Two broad categories are wave functions describing quantum systems using position or momentum variables and the more abstract vector quantum states."
"Historical, educational, and application-focused problems typically feature wave functions."
"Modern professional physics uses the abstract vector states."
"Quantum states divide into pure versus mixed states, or into coherent states and incoherent states."
"Categories with special properties include stationary states for time independence and quantum vacuum states in quantum field theory."
"Wave functions describe quantum systems using position or momentum variables."
"The more abstract vector quantum states."
"Quantum states divide into pure versus mixed states."
"Quantum states divide into coherent states and incoherent states."
"Stationary states are for time independence."
"Quantum vacuum states are in quantum field theory."
"A quantum state is a mathematical entity that embodies the knowledge of a quantum system."
"Quantum mechanics specifies the construction, evolution, and measurement of a quantum state."
"Knowledge of the quantum state and the quantum mechanical rules for the system's evolution in time, exhausts all that can be known about a quantum system."
"Wave functions describe quantum systems using position or momentum variables, while abstract vector quantum states are more abstract."
"The two broad categories are wave functions and the more abstract vector quantum states."