The degree of entanglement in an open quantum system varies according to how information in the environment is read. A measure of this contextual entanglement is introduced based on quantum trajectory unravelings of the open system dynamics. It is used to characterize the entanglement in a driven quantum system of dimension $2\times\infty$ where the entanglement is induced by the environmental interaction. A detailed mechanism for the environment-induced entanglement is given.
The fully quantized model of double qubits coupled to a common bath is solved using the quantum state diffusion (QSD) approach in the non-Markovian regime. We have established the explicit time-local non-Markovian QSD equations for the two-qubit dissipative and dephasing models. Diffusive quantum trajectories are applied to the entanglement estimation of two-qubit systems in a non-Markovian regime. In both cases, non-Markovian features of entanglement evolution are revealed through quantum diffusive unravellings in the system state space.
We present a description of finite dimensional quantum entanglement, based on a study of the space of all convex decompositions of a given density matrix. On this space we construct a system of real polynomial equations describing separable states. We further study this system using statistical mechanical methods. Finally, we apply our techniques to Werner states of two qubits and obtain a sufficient criterion for separability.
We explore the role played by the phase in an accurate description of the entanglement of bipartite systems. We first present an appropriate polar decomposition that leads to a truly Hermitian operator for the phase of a single qubit. We also examine the positive operator-valued measures that can describe the qubit phase properties. When dealing with two qubits, the relative phase seems to be a natural variable to understand entanglement. In this spirit, we propose a measure of entanglement based on this variable.
Producing and certifying entanglement between distant qubits is a highly desirable skill for quantum information technologies. Here we propose a new strategy to monitor and characterize entanglement genesis in a half parity measurement setup, that relies on the continuous readout of an energetic observable which is the half-parity observable itself. Based on a quantum-trajectory approach, we theoretically analyze the statistics of energetic fluctuations for a pair of continuously monitored qubits. We quantitatively relate these energetic fluctuations to the rate of entanglement produced betwee…
The dynamics of open quantum systems is generally described by a master equation, which describes the loss of information into the environment. By using a simple model of uncoupled emitters, we illustrate how the recovery of this information depends on the monitoring scheme applied to register the decay clicks. The dissipative dynamics, in this case, is described by pure-state stochastic trajectories and we examine different unravelings of the same master equation. More precisely, we demonstrate how registering the sequence of clicks from spontaneously emitted photons through a linear optical …
In this paper, we study how to generate entanglement by interaction-free measurement. Using Kwiat et al.'s interferometer, we construct a two-qubit quantum gate that changes a particle's trajectory according to the other particle's trajectory. We propose methods for generating the Bell state from an electron and a positron and from a pair of photons by this gate. We also show that using this gate, we can carry out the Bell measurement with the probability of 3/4 at the maximum and execute a controlled-NOT operation by the method proposed by Gottesman and Chuang with the probability of 9/16 at …
The unique and often-weird properties of quantum mechanics allow an information carrier to propagate through multiple trajectories of quantum channels simultaneously. This ultimately leads us to quantum trajectories with an indefinite causal order of quantum channels. It has been shown that indefinite causal order enables the violation of bottleneck capacity, which bounds the amount of the transferable classical and quantum information through a classical trajectory with a well-defined causal order of quantum channels. In this treatise, we investigate this beneficial property in the realm of b…
We present a general description of separable states in Quantum Mechanics. In particular, our result gives an easy proof that inseparabitity (or entanglement) is a pure quantum (noncommutative) notion. This implies that distinction between separability and inseparabitity has sense only for composite systems consisting of pure quantum subsystems. Moreover, we provide the unified characterization of pure-state entanglement and mixed-state entanglement.
Quantum trajectories are used to investigate the EPR-Bohr debate in a modern sense by examining entanglement and nonlocality. We synthesize a single "entanglement molecule" from the two scattered particles of the EPR experiment. We explicitly investigate the behavior of the entanglement molecule rather than the behaviors of the two scattered particles to gain insight into the EPR-Bohr debate. We develop the entanglement molecule's wave function in polar form and its reduced action, both of which manifest entanglement. We next apply Jacobi's theorem to the reduced action to generate the equatio…
We create entangled states of the spin and motion of a single $^{40}$Ca$^+$ ion in a linear ion trap. The motional part consists of coherent states of large separation and long coherence time. The states are created by driving the motion using counterpropagating laser beams. We theoretically study and experimentally observe the behaviour outside the Lamb-Dicke regime, where the trajectory in phase space is modified and the coherent states become squeezed. We directly observe the modification of the return time of the trajectory, and infer the squeezing. The mesoscopic entanglement is observed …
Two qubits is the simplest system where the notions of separable and entangled states and entanglement witnesses first appear. We give a three dimensional geometric description of these notions. This description however carries no quantitative information on the measure of entanglement. A four dimensional description captures also the entanglement measure. We give a neat formula for the Bell states which leads to a slick proof of the fundamental teleportation identity. We describe optimal distillation of two qubits geometrically and present a simple geometric proof of the Peres-Horodecki separ…
In this paper we present the novel qualities of entanglement of formation for general (so also infinite dimensional) quantum systems. A major benefit of our presentation is a rigorous description of entanglement of formation. In particular, we indicate how this description may be used to examine optimal decompositions. Illustrative examples showing the method of estimation of entanglement of formation are givem\n.
We provide a graphical description of the entanglement of pure-state multiparty systems based on an analogy between a bipartite purity analysis and the centroid of a collection of point masses. This description applies to quantum systems with $N$ parties, each with an arbitrary number of (discrete) states. The case of $N$ qubits is highlighted for simplicity. This geometric description illustrates some of the restrictions in the form of inequalities that apply to entanglement in multiparty systems.
We show how mapping techniques inherent to $N^{2}$-dimensional discrete phase spaces can be used to treat a wide family of spin systems which exhibits squeezing and entanglement effects. This algebraic framework is then applied to the modified Lipkin-Meshkov-Glick (LMG) model in order to obtain the time evolution of certain special parameters related to the Robertson-Schrödinger (RS) uncertainty principle and some particular proposals of entanglement measure based on collective angular-momentum generators. Our results reinforce the connection between both the squeezing and entanglement effects…
A hidden-variable model is explicitly constructed by use of a Liouvillian description for the dynamics of two coupled spin-1/2 particles. In this model, the underlying Hamiltonian trajectories play the role of deterministic hidden variables, whereas the shape of the initial probability distribution figures as a hidden variable that regulates the capacity of the model in producing correlations. We show that even though the model can very well describe the short-time entanglement dynamics of initially separated pure states, it is incapable of violating the Clauser-Horne-Shimony-Holt inequality. …
We propose a general method for introducing extensive characteristics of quantum entanglement. The method relies on polynomials of nilpotent raising operators that create entangled states acting on a reference vacuum state. By introducing the notion of tanglemeter, the logarithm of the state vector represented in a special canonical form and expressed via polynomials of nilpotent variables, we show how this description provides a simple criterion for entanglement as well as a universal method for constructing the invariants characterizing entanglement. We compare the existing measures and clas…
The wave packet approach to neutrino oscillations provides an enlightening description of quantum decoherence induced, during propagation, by localization effects. Within this approach, we show that a deeper insight into the dynamical aspects of particle mixing can be obtained if one investigates the behavior of quantum correlations associated to flavor oscillations. By identifying the neutrino three-flavor modes with (suitably defined) three-qubit modes, the exploitation of tools of quantum information theory for mixed states allows a detailed analysis of the dynamical behavior of flavor enta…
We present a quantum information theory that allows for a consistent description of entanglement. It parallels classical (Shannon) information theory but is based entirely on density matrices (rather than probability distributions) for the description of quantum ensembles. We find that quantum conditional entropies can be negative for entangled systems, which leads to a violation of well-known bounds in Shannon information theory. Such a unified information-theoretic description of classical correlation and quantum entanglement clarifies the link between them: the latter can be viewed as ``sup…
In this paper we derive an effective master equation and quantum trajectory equation for multiple qubits in a single resonator and in the large resonator decay limit. We show that homodyne measurement of the resonator transmission is a weak measurement of the collective qubit inversion. As an example of this result, we focus on the case of two qubits and show how this measurement can be used to generate an entangled state from an initially separable state. This is realized without relying on an entangling Hamiltonian. We show that, for {\em current} experimental values of both the decoherence …
Many protocols and experiments in quantum information science are described in terms of simple measurements on qubits. However, in a real implementation, the exact description is more difficult, and more complicated observables are used. The question arises whether a claim of entanglement in the simplified description still holds, if the difference between the realistic and simplified models is taken into account. We show that a positive entanglement statement remains valid if a certain positive linear map connecting the two descriptions--a so-called squashing operation--exists; then lower bou…
Within the Wigner-PDC picture of photon entanglement, detection "errors" are not independent (though they may look, on average), nor can they be controlled by means of a technological improvement on the detectors. Those two elements make possible the interpretation of experimental evidence without the need to exclude local realism: for that reason, we propose the abandonment of the usual (photon, particle-based) description of (PDC-generated) light states, in favour of an also quantum, but field-theoretical description (QED), a description that finds a one-to-one equivalent in the Wigner-PDC a…
We use quantum diffusive trajectories to prove that the time evolution of two-qubit entanglement under spontaneous emission can be fully characterized by optimal continuous monitoring. We analytically determine this optimal unraveling and derive a deterministic evolution equation for the system's concurrence. Furthermore, we propose an experiment to monitor the entanglement dynamics in bipartite two-level systems and to determine the disentanglement time from a single trajectory.
It is argued that recent experiments testing Multisimultaneity prove that quantum entanglement occurs without the flow of time. Bohm's theory cannot be considered a real temporal description.
It is well established that an entanglement encoded in the Bell states of a two-qubit system with correlated spins exhibits completely different evolution properties than that encoded in states with the anti-correlated spins. A complete and abrupt loss of the entanglement, called the entanglement sudden death, can be found to occur for the spin correlated states, but the entanglement evolves without any discontinuity or decays asymptotically for the spin anti-correlated states. We consider the evolution of an initial entanglement encoded in the spin anti-correlated states and demonstrate that …
We propose a general formalism for analytical description of multiatomic ensembles interacting with a single mode quantized cavity field under the assumption that most atoms remain un-excited on average. By combining the obtained formalism with the nilpotent technique for the description of multipartite entanglement we are able to overview in a unified fashion different probabilistic control scenarios of entanglement among atoms or examine atomic ensembles. We then apply the proposed control schemes to the creation of multiatom states useful for quantum information.
Comprehending the connections between the geometric, topological, and dynamical structures of integrable quantum systems with quantum phenomena exploitable in quantum information tasks, such as quantum entanglement, is a major problem in geometric information science. In this work we investigate these issues in a physical system of $\mathcal{N}$ interacting spin-$\mathtt{s}$ under long-range Ising model. We discover the relevant dynamics, identify the corresponding quantum phase space and we derive the associated Fubini-Study metric. Through the application of the Gauss-Bonnet theorem and the …
In order to study the temporal coherence of a single-mode dye-cavity photon condensate, a model is developed for the dynamics which treats the condensate mode on a quantum-mechanical level. The effects of driving-dissipation and Kerr interactions on the number fluctuations are studied analytically and numerically, including the finding of a long-$τ$ antibunching effect. Depending on the interaction strength, we quantitatively observe an exponential Schawlow-Townes-like decay or Gaussian Henry-like decay of phase correlations. The adequacy of a heuristic phasor model originating from laser phys…
Closed timelike curves are striking predictions of general relativity allowing for time-travel. They are afflicted by notorious causality issues (e.g. grandfather's paradox). Quantum models where a qubit travels back in time solve these problems, at the cost of violating quantum theory's linearity - leading e.g. to universal quantum cloning. Interestingly, linearity is violated even by open timelike curves (OTCs), where the qubit does not interact with its past copy, but is initially entangled with another qubit. Non-linear dynamics is needed to avoid violating entanglement monogamy. Here we p…
We present a comprehensive implementation of the quantum trajectory theory for the description of the entanglement dynamics in a Markovian open quantum system made of two qubits. We introduce the average concurrence to characterize the entanglement in the system and derive a deterministic evolution equation for it that depends on the ways information is read from the environment. This builded in flexibility of the method is used to address two actual issues in quantum information: entanglement protection and entanglement estimation. We identify general physical situations in which an entanglem…
The entanglement measure for multiqudits is proposed. This measure calculates the partial entanglement distributed by subsystems and the complete entanglement of the total system. This shows that we need to measure the subsystem entanglements to explain the full description for multiqudit entanglement. Furthermore, we extend the entanglement measure to mixed multiqubits and the higher dimension Hilbert spaces.
We develop a novel approach aimed at solving the equations of motion of open quantum many-body systems. It is based on a combination of generalized wave function trajectories and matrix product states. We introduce an adaptive quantum stochastic propagator, which minimizes the expected entanglement in the many-body quantum state, thus minimizing the computational cost of the matrix product state representation of each trajectory. We illustrate this approach on the example of a one-dimensional open Brownian circuit. We show that this model displays an entanglement phase transition between area …
Using the trajectory conception of state we give a simple demonstration that the quantum state of a many-body system may be expressed as a set of states in three-dimensional space, one associated with each particle. It follows that the many-body wavefunction may be derived from a set of waves in 3-space. Entanglement is represented in the trajectory picture by the mutual dependence of the 3-states on the trajectory labels.
We show using a numerical approach that gives necessary and sufficient conditions for the existence of local realism, that the bound entangled state presented in Bennett et. al. Phys. Rev. Lett. 82, 5385 (1999) admits a local and realistic description. We also find the lowest possible amount of some appropriate entangled state that must be ad-mixed to the bound entangled state so that the resulting density operator has no local and realistic description and as such can be useful in quantum communication and quantum computation.
Quantum nonlocality can be revealed "via local contextuality" in qudit-qudit entangled systems with $d > 2$, that is, through the violation of inequalities containing Alice-Bob correlations that admit a local description, and Alice-Alice correlations (between the results of sequences of measurements on Alice's subsystem) that admit a local (but contextual) description. A fundamental question to understand the respective roles of entanglement and local contextuality is whether nonlocality via local contextuality exists when the parties have only qubit-qubit entanglement. Here we respond affirma…
We propose a scheme to realize entanglement swapping via superradiance, entangling two distant cavities without a direct interaction. The successful Bell-state-measurement outcomes are performed naturally by the electromagnetic reservoir, and we show how, using a quantum trajectory method, the non-local properties of the state obtained after the swapping procedure can be verified by the steering inequality. Furthermore, we discuss how the unsuccessful measurement outcomes can be used in an experiment of delayed-choice entanglement swapping. An extension of testing the quantum steering inequali…
It has been accepted that the polarization of the photon in vector beams is entangled with its momentum. Here a quantum description is advanced for the polarization that shows entanglement with the momentum. This is done by showing that the Jones vector at each value of the momentum plays the role of the polarization wavefunction in the sense that the Pauli matrices represent the Cartesian components of the polarization in the local reference system with respect to which the Jones vector is defined. The unit vector that the constraint of transversality condition requires to specify the local r…
We present an entanglement criterion for multiqubits by using the quantum correlation tensors which rely on the expectation values of the Pauli operators for a multiqubit state. Our criterion explains not only the total entanglement of the system but also the partial entanglement in subsystems. It shows that we have to consider the subsystem entanglements in order to obtain the full description for multiqubit entanglements. Furthermore, we offer an extension of the entanglement to multiqudits.
We present an analysis of the entangling quantum kicked top focusing on the few qubit case and the initial condition dependence of the time-averaged entanglement $S_Q$ for spin-coherent states. We show a very strong connection between the classical phase space and the initial condition dependence of $S_Q$ even for the extreme case of two spin-$1/2$ qubits. This correlation is not related directly to chaos in the classical dynamics. We introduce a measure of the behavior of a classical trajectory which correlates far better with the entanglement and show that the maps of classical and quantum i…
We address the question of description of qubit system in a formalism based on the nilpotent commuting variables. In this formalism qubits exhibit properties of composite objects being subject of the Pauli exclusion principle, but otherwise behaving boson-like. They are not fundamental particles. In such an approach the classical limit yields the nilpotent mechanics. Using the space of $η$-wavefunctions, generalized Schrödinger equation etc. we study properties of pure qubit systems and also properties of some composed, hybrid models: fermion-qubit, boson-qubit. The fermion-qubit system can be…
A possible causal solution to the problem of providing a spacetime description of the transmission of signals in quantum entangled states is described using a `bimetric' spacetime structure, in which the quantum entanglement measurements alter the structure of spacetime. Possible experimental tests to verify the suggested spacetime interpretation of quantum entangled states are proposed.
We apply the Wigner formalism of quantum optics to study the role of the zeropoint field fluctuations in entanglement swapping produced via parametric down conversion. It is shown that the generation of mode entanglement between two initially non interacting photons is related to the quadruple correlation properties of the electromagnetic field, through the stochastic properties of the vacuum. The relationship between the process of transferring entanglement and the different zeropoint inputs at the nonlinear crystal and the Bell-state analyser is emphasized.
We discuss the application of the static path plus random phase approximation (SPA+RPA) and the ensuing mean field+RPA treatment to the evaluation of entanglement in composite quantum systems at finite temperature. These methods involve just local diagonalizations and the determination of the generalized collective vibrational frequencies. As illustration, we evaluate the pairwise entanglement in a fully connected XXZ chain of $n$ spins at finite temperature in a transverse magnetic field $b$. It is shown that already the mean field+RPA provides an accurate analytic description of the concurre…
The density matrix of composite spin system is discussed in relation to the adjoint representation of unitary group U(n). The entanglement structure is introduced as an additional ingredient to the description of the linear space carrying the adjoint representation. Positive maps of density operator are related to random matrices. The tomographic probability description of quantum states is used to formulate the problem of separability and entanglement as the condition for joint probability distribution of several random variables represented as the convex sum of products of probabilities of r…
Atom-field entanglement is shown to play a crucial role for the onset of spatial self-organization of ultracold atoms in an optical lattice within a high-Q cavity. Like particles on a seesaw, the atoms feel a different potential depending on their spatial distribution. The system possesses two stable configurations, where all atoms occupy either only even or only odd lattice sites. While for a classical cavity field description a distribution balanced between even and odd sites is a stationary equilibrium state at zero temperature, the possibility of atom-field entanglement in a quantum field …
We examine the thermal pairwise entanglement in a symmetric system of $n$ spins fully connected through anisotropic $XYZ$-type couplings embedded in a transverse magnetic field. We consider both the exact evaluation together with that obtained with the static path + random phase approximation (RPA) and the ensuing mean field + RPA. The latter is shown to provide an accurate analytic description of both the parallel and antiparallel thermal concurrence in large systems. We also analyze the limit temperature for pairwise entanglement, which is shown to increase for large fields and to decrease l…
We present a novel, universal description of quantum entanglement using group theory and generalized characteristic functions. It leads to new reformulations of the separability problem, and the positivity of partial transpose (PPT) criterion. The latter turns out to be intimately related to a certain reality condition for group representations. Within our formalism, we also show a connection between existence of entanglement and group non-commutativity.
We describe and examine entanglement between different degrees of freedom in multiphoton states based on the permutation properties. From the state description, the entanglement comes from the permutation asymmetry. According to the different permutation properties, the multiphoton states can be divided into several parts. It will help to deal with the multiphoton interference, which can be used as the measurement of the entanglement.
