|
Quantum Metrological Gain
The quantum metrological gain is defined in the context of carrying out a metrological task using a quantum state of a multiparticle system. It is the sensitivity of parameter estimation using the state compared to what can be reached using separable states, i.e., states without quantum entanglement. Hence, the quantum metrological gain is given as the fraction of the sensitivity achieved by the state and the maximal sensitivity achieved by separable states. The best separable state is often the trivial fully polarized state, in which all spins point into the same direction. If the metrological gain is larger than one then the quantum state is more useful for making precise measurements than separable states. Clearly, in this case the quantum state is also entangled. Background The metrological gain is, in general, the gain in sensitivity of a quantum state compared to a product state. Metrological gains up to 100 are reported in experiments. Let us consider a unitary dynami ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Separable States
In quantum mechanics, separable states are multipartite quantum states that can be written as a convex combination of product states. Product states are multipartite quantum states that can be written as a tensor product of states in each space. The physical intuition behind these definitions is that product states have no correlation between the different degrees of freedom, while separable states might have correlations, but all such correlations can be explained as due to a classical random variable, as opposed to being due to entanglement. In the special case of pure states the definition simplifies: a pure state is separable if and only if it is a product state. 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Entangled State
Quantum entanglement is the phenomenon where the quantum state of each particle in a group cannot be described independently of the state of the others, even when the particles are separated by a large distance. The topic of quantum entanglement is at the heart of the disparity between classical physics and quantum physics: entanglement is a primary feature of quantum mechanics not present in classical mechanics. Measurements of physical properties such as position, momentum, spin, and polarization performed on entangled particles can, in some cases, be found to be perfectly correlated. For example, if a pair of entangled particles is generated such that their total spin is known to be zero, and one particle is found to have clockwise spin on a first axis, then the spin of the other particle, measured on the same axis, is found to be anticlockwise. However, this behavior gives rise to seemingly paradoxical effects: any measurement of a particle's properties results in an appar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unitarity (physics)
In quantum physics, unitarity is (or a unitary process has) the condition that the time evolution of a quantum state according to the Schrödinger equation is mathematically represented by a unitary operator. This is typically taken as an axiom or basic postulate of quantum mechanics, while generalizations of or departures from unitarity are part of speculations about theories that may go beyond quantum mechanics. A unitarity bound is any inequality that follows from the unitarity of the evolution operator, i.e. from the statement that time evolution preserves inner products in Hilbert space. Hamiltonian evolution Time evolution described by a time-independent Hamiltonian is represented by a one-parameter family of unitary operators, for which the Hamiltonian is a generator: U(t) = e^. In the Schrödinger picture, the unitary operators are taken to act upon the system's quantum state, whereas in the Heisenberg picture, the time dependence is incorporated into the observable ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Fisher Information
The quantum Fisher information is a central quantity in quantum metrology and is the quantum analogue of the classical Fisher information. It is one of the central quantities used to qualify the utility of an input state, especially in Mach–Zehnder (or, equivalently, Ramsey) interferometer-based phase or parameter estimation. It is shown that the quantum Fisher information can also be a sensitive probe of a quantum phase transition (e.g. recognizing the superradiant quantum phase transition in the Dicke model). The quantum Fisher information F_[\varrho,A] of a quantum state, state \varrho with respect to the quantum observable, observable A is defined as : F_[\varrho,A]=2\sum_ \frac \vert \langle k \vert A \vert l\rangle \vert^2, where \lambda_k and \vert k \rangle are the eigenvalues and eigenvectors of the density matrix \varrho, respectively, and the summation goes over all k and l such that \lambda_k+\lambda_l>0. When the observable generates a unitarity (physics), unita ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Cramér–Rao Bound
The quantum Cramér–Rao bound is the quantum analogue of the classical Cramér–Rao bound. It bounds the achievable precision in parameter estimation with a quantum system: (\Delta \theta)^2 \ge \frac 1 , where m is the number of independent repetitions, and F_ varrho,H/math> is the quantum Fisher information. Here, \varrho is the state of the system and H is the Hamiltonian of the system. When considering a unitary dynamics of the type \varrho(\theta)=\exp(-iH\theta)\varrho_0\exp(+iH\theta), where \varrho_0 is the initial state of the system, \theta is the parameter to be estimated based on measurements on \varrho(\theta). Simple derivation from the Heisenberg uncertainty relation Let us consider the decomposition of the density matrix to pure components as \varrho=\sum_k p_k \vert\Psi_k\rangle\langle\Psi_k\vert. The Heisenberg uncertainty relation is valid for all \vert\Psi_k\rangle (\Delta A)^2_(\Delta B)^2_\ge \frac 1 4 , \langle i ,B\rangle_, ^2. From these, emplo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Entanglement
Quantum entanglement is the phenomenon where the quantum state of each Subatomic particle, particle in a group cannot be described independently of the state of the others, even when the particles are separated by a large distance. The topic of quantum entanglement is at the heart of the disparity between classical physics and quantum physics: entanglement is a primary feature of quantum mechanics not present in classical mechanics. Measurement#Quantum mechanics, Measurements of physical properties such as position (vector), position, momentum, Spin (physics), spin, and polarization (waves), polarization performed on entangled particles can, in some cases, be found to be perfectly correlated. For example, if a pair of entangled particles is generated such that their total spin is known to be zero, and one particle is found to have clockwise spin on a first axis, then the spin of the other particle, measured on the same axis, is found to be anticlockwise. However, this behavior ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Metrology
Quantum metrology is the study of making high-resolution and highly sensitive measurements of physical parameters using quantum theory to describe the physical systems, particularly exploiting quantum entanglement and quantum Squeezed coherent state, squeezing. This field promises to develop measurement techniques that give better precision than the same measurement performed in a classical framework. Together with quantum hypothesis testing, it represents an important theoretical model at the basis of quantum sensing. Mathematical foundations A basic task of quantum metrology is estimating the parameter \theta of the unitary dynamics : \varrho(\theta)=\exp(-iH\theta)\varrho_0\exp(+iH\theta), where \varrho_0 is the initial state of the system and H is the Hamiltonian of the system. \theta is estimated based on measurements on \varrho(\theta). Typically, the system is composed of many particles, and the Hamiltonian is a sum of single-particle terms : H=\sum_k H_k, where H_k ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Entanglement Depth
In quantum physics, entanglement depth characterizes the strength of multiparticle entanglement. An entanglement depth k means that the quantum state of a particle ensemble cannot be described under the assumption that particles interacted with each other only in groups having fewer than k particles. It has been used to characterize the quantum states created in experiments with cold gases. Definition Entanglement depth appeared in the context of spin squeezing. It turned out that to achieve larger and larger spin squeezing, and thus larger and larger precision in parameter estimation, a larger and larger entanglement depth is needed. Later it was formalized in terms of convex sets of quantum states, independent of spin squeezing as follows. Let us consider a pure state that is the tensor product of multi-particle quantum states , \Psi\rangle=, \phi_1\rangle\otimes, \phi_2\rangle\otimes ... \otimes, \phi_n\rangle. The pure state , \Psi\rangle is said to be k-producibl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Information Science
Quantum information science is a field that combines the principles of quantum mechanics with information theory to study the processing, analysis, and transmission of information. It covers both theoretical and experimental aspects of quantum physics, including the limits of what can be achieved with quantum information. The term quantum information theory is sometimes used, but it does not include experimental research and can be confused with a subfield of quantum information science that deals with the processing of quantum information. Scientific and engineering studies Quantum teleportation, Quantum entanglement, entanglement and the manufacturing of quantum computers depend on a comprehensive understanding of quantum physics and engineering. Google and IBM have invested significantly in quantum computer hardware research, leading to significant progress in manufacturing quantum computers since the 2010s. Currently, it is possible to create a quantum computer with over 100 qub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
