In quantum physics, entanglement depth characterizes the strength of multiparticle entanglement. An entanglement depth 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 particles. It has been used to characterize the quantum states created in experiments with cold gases.
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. [1]
Later it was formalized in terms of convex sets of quantum states, independent of spin squeezing as follows. [2] Let us consider a pure state that is the tensor product of multi-particle quantum states
The pure state is said to be -producible if all are states of at most particles. A mixed state is called -producible, if it is a mixture of pure states that are all at most -producible. The -producible mixed states form a convex set.
A quantum state contains at least multiparticle entanglement of particles, if it is not -producible. A -particle state with -entanglement is called genuine multipartite entangled.
Finally, a quantum state has an entanglement depth , if it is -producible, but not -producible.
It was possible to detect the entanglement depth close to states different from spin-squeezed states. Since there is not a general method to detect multipartite entanglement, these methods had to be tailored to experiments with various relevant quantum states.
Thus, entanglement criteria has been developed to detect entanglement close to symmetric Dicke states with [3] [4] They are very different from spin-squeezed states, since they do not have a large spin polarization. They can provide Heisenberg limited metrology, while they are more robust to particle loss than Greenberger-Horne-Zeilinger (GHZ) states.
There are also criteria for detecting the entanglement depth in planar-squeezed states. [5] Planar squeezed states are quantum states that can be used to estimate a rotation angle that is not expected to be small. [6]
Finally, multipartite entanglement can be detected based on the metrological usefulness of the quantum state. [7] [8] The criteria applied are based on bounds on the quantum Fisher information.
The entanglement criterion in Ref. [1] has been used in many experiments with cold gases in spin-squeezed states. [9] [10] [11] [12] [13]
There have also been experiments in cold gases for detecting multipartite entanglement in symmetric Dicke states. [3] [14]
There have been also experiments with Dicke states that detected entanglement based on metrological usefulness in cold gases [15] and in photons. [16]
Quantum teleportation is a technique for transferring quantum information from a sender at one location to a receiver some distance away. While teleportation is commonly portrayed in science fiction as a means to transfer physical objects from one location to the next, quantum teleportation only transfers quantum information. The sender does not have to know the particular quantum state being transferred. Moreover, the location of the recipient can be unknown, but to complete the quantum teleportation, classical information needs to be sent from sender to receiver. Because classical information needs to be sent, quantum teleportation cannot occur faster than the speed of light.
Quantum entanglement is the phenomenon of a group of particles being generated, interacting, or sharing spatial proximity in such a way that the quantum state of each particle of the group cannot be described independently of the state of the others, including when the particles are separated by a large distance. The topic of quantum entanglement is at the heart of the disparity between classical and quantum physics: entanglement is a primary feature of quantum mechanics not present in classical mechanics.
In physics, a squeezed coherent state is a quantum state that is usually described by two non-commuting observables having continuous spectra of eigenvalues. Examples are position and momentum of a particle, and the (dimension-less) electric field in the amplitude and in the mode of a light wave. The product of the standard deviations of two such operators obeys the uncertainty principle:
In the interpretation of quantum mechanics, a local hidden-variable theory is a hidden-variable theory that satisfies the principle of locality. These models attempt to account for the probabilistic features of quantum mechanics via the mechanism of underlying, but inaccessible variables, with the additional requirement that distant events be statistically independent.
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 as being due to entanglement.
LOCC, or local operations and classical communication, is a method in quantum information theory where a local (product) operation is performed on part of the system, and where the result of that operation is "communicated" classically to another part where usually another local operation is performed conditioned on the information received.
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 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.
The W state is an entangled quantum state of three qubits which in the bra-ket notation has the following shape
In quantum computing, a graph state is a special type of multi-qubit state that can be represented by a graph. Each qubit is represented by a vertex of the graph, and there is an edge between every interacting pair of qubits. In particular, they are a convenient way of representing certain types of entangled states.
In quantum optics, a NOON state or N00N state is a quantum-mechanical many-body entangled state:
In theoretical physics, quantum nonlocality refers to the phenomenon by which the measurement statistics of a multipartite quantum system do not allow an interpretation with local realism. Quantum nonlocality has been experimentally verified under a variety of physical assumptions.
In quantum information and quantum computing, a cluster state is a type of highly entangled state of multiple qubits. Cluster states are generated in lattices of qubits with Ising type interactions. A cluster C is a connected subset of a d-dimensional lattice, and a cluster state is a pure state of the qubits located on C. They are different from other types of entangled states such as GHZ states or W states in that it is more difficult to eliminate quantum entanglement in the case of cluster states. Another way of thinking of cluster states is as a particular instance of graph states, where the underlying graph is a connected subset of a d-dimensional lattice. Cluster states are especially useful in the context of the one-way quantum computer. For a comprehensible introduction to the topic see.
In the case of systems composed of subsystems, the classification of quantum-entangledstates is richer than in the bipartite case. Indeed, in multipartite entanglement apart from fully separable states and fully entangled states, there also exists the notion of partially separable states.
In quantum mechanics, the cat state, named after Schrödinger's cat, refers to a quantum state composed of a superposition of two other states of flagrantly contradictory aspects. Generalizing Schrödinger's thought experiment, any other quantum superposition of two macroscopically distinct states is also referred to as a cat state. A cat state could be of one or more modes or particles, therefore it is not necessarily an entangled state. Such cat states have been experimentally realized in various ways and at various scales.
Spin squeezing is a quantum process that decreases the variance of one of the angular momentum components in an ensemble of particles with a spin. The quantum states obtained are called spin squeezed states. Such states have been proposed for quantum metrology, to allow a better precision for estimating a rotation angle than classical interferometers. However a wide body of work contradicts this analysis. In particular, these works show that the estimation precision obtainable for any quantum state can be expressed solely in terms of the state response to the signal. As squeezing does not increase the state response to the signal, it cannot fundamentally improve the measurement precision.
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 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. The quantum Fisher information of a state with respect to the observable is defined as
In quantum physics, the "monogamy" of quantum entanglement refers to the fundamental property that it cannot be freely shared between arbitrarily many parties.
Permutationally invariant quantum state tomography is a method for the partial determination of the state of a quantum system consisting of many subsystems.
In quantum metrology in a multiparticle system, the quantum metrological gain for a quantum state is defined as the sensitivity of phase estimation achieved by that state divided by the maximal sensitivity achieved by separable states, i.e., states without quantum entanglement. In practice, the best separable state is 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.
In quantum optics and quantum information, a Dicke state is a quantum state that is the simultaneous eigenstate of the operators and It has been defined by Robert H. Dicke in connection to spontaneous radiation processes taking place in an ensemble of two-state atoms. Dicke states have recenly been realized with photons with up to six particles and cold atoms of more than thousands of particles. They are highly entangled, and in quantum metrology they lead to the maximal Heisenberg scaling of the precision of parameter estimation.
