Narrow Results

We investigate the time evolutions of purity, coherence and entanglement in two superconducting qubits coupled through Josephson junctions. The system is modeled by coupling strength, energy, Josephson energy and phase difference. Meanwhile, the structure is under the action of thermal field and classical Ornstein–Uhlenbeck (OU) noise. According to our findings, quantum correlations are notably developed governed by the system parameters. Purity and entanglement generally increase for the energetic qubit regimes. The state’s entanglement and purity degrade with increased coupling strength and temperature. On the other hand, the optimal preservation of quantum correlations reqires the adjustment to intermediate Josephson energies ($E_j=0.5$) and phase differences ($\varphi =\pi ∕4$). The coherence measurement shows completely opposite traits compared to the entanglement and purity in the system. These results reveal that quantum states need proper parametrization for the considered state while providing optimization for the higher performance of superconducting qubits in quantum information processing.

We numerically estimate the superposition of the HOMFLY-PT polynomial of an open two-component link, define its spread, and describe how this quantity may be employed to quantify the degree of entanglement of confined two component open links.

A new framework is formulated to study entanglement dynamics in many-body quantum systems along with an associated geometric description. In this formulation, called the Quantum Correlation Transfer Function (QCTF), the system’s wave function or density matrix is transformed into a new space of complex functions with isolated singularities. Accordingly, entanglement dynamics is encoded in specific residues of the QCTF, and importantly, the explicit evaluation of the system’s time dependence is avoided. Notably, the QCTF formulation allows for various algebraic simplifications and approximations to address the normally encountered complications due to the exponential growth of the many-body Hilbert space with the number of bodies. These simplifications are facilitated by considering the patterns, in lieu of the elements, lying within the system’s state. Consequently, a main finding of this paper is the exterior (Grassmannian) algebraic expression of many-body entanglement as the collective areas of regions in the Hilbert space spanned by pairs of projections of the wave function onto an arbitrary basis. This latter geometric measure is shown to be equivalent to the second-order Rényi entropy. Additionally, the geometric description of the QCTF shows that characterizing features of the reduced density matrix can be related to experimentally observable quantities. The QCTF-based geometric description offers the prospect of theoretically revealing aspects of many-body entanglement, by drawing on the vast scope of methods from geometry.

Fix distinct primes $p$ and $q$ and let $E$ be an elliptic curve defined over a number field $K$. The $(p,q)$-entanglement type of $E$ over $K$ is the isomorphism class of the group $\mathrm{\text{Gal}}(K(E[p])\cap K(E[q])/K)$. The size of this group measures the extent to which the image of the mod $pq$ Galois representation attached to $E$ fails to be a direct product of the mod $p$ and mod $q$ images. In this paper, we study how the $(p,q)$-entanglement group varies over different base fields. We prove that for each prime $\ell$ dividing the greatest common divisor of the size of the mod $p$ and $q$ images, there are infinitely many fields $L/K$ such that the entanglement over $L$ is cyclic of order $\ell$. We also classify all possible $(2,q)$-entanglement types that can occur as the base field $L$ varies.

Given a pure state |ψ_N>∈ℋ_N of a quantum system composed of n qubits, where ℋ_N is the Hilbert space of dimension N=2ⁿ, this paper answers two questions: what conditions should the amplitudes in |ψ_N> satisfy for this state to be separable (i) into a tensor product of n qubit states |ψ₂>₀⊗ |ψ₂>₁ ⊗⋯⊗ |ψ₂>_n-1, and (ii), into a tensor product of two subsystems states |ψ_P> ⊗ |ψ_Q> with P=2^p and Q=2^q such that p+q=n? For both questions, necessary and sufficient conditions are proved, thus characterizing at the same time families of separable and entangled states of n qubit systems. A number of more refined questions about separability in n qubit systems can be studied on the basis of these results.

Criteria for distillability, and the property of having a positive partial transpose, are introduced for states of general bipartite quantum systems. The framework is sufficiently general to include systems with an infinite number of degrees-of-freedom, including quantum fields. We show that a large number of states in relativistic quantum field theory, including the vacuum state and thermal equilibrium states, are distillable over subsystems separated by arbitrary spacelike distances. These results apply to any quantum field model. It will also be shown that these results can be generalized to quantum fields in curved spacetime, leading to the conclusion that there is a large number of quantum field states which are distillable over subsystems separated by an event horizon.

We consider an infinite spin chain as a bipartite system consisting of the left and right half-chains and analyze entanglement properties of pure states with respect to this splitting. In this context, we show that the amount of entanglement contained in a given state is deeply related to the von Neumann type of the observable algebras associated to the half-chains. Only the type I case belongs to the usual entanglement theory which deals with density operators on tensor product Hilbert spaces, and only in this situation separable normal states exist. In all other cases, the corresponding state is infinitely entangled in the sense that one copy of the system in such a state is sufficient to distill an infinite amount of maximally entangled qubit pairs. We apply this results to the critical XY model and show that its unique ground state φ_S provides a particular example for this type of entanglement.

In this expository note, we explain facial structures for the convex cones consisting of positive linear maps, completely positive linear maps, and decomposable positive linear maps between matrix algebras, respectively. These will be applied to study the notions of entangled edge states with positive partial transposes and optimality of entanglement witnesses.

Motivated by the notions of $k$-extendability and complete extendability of the state of a finite level quantum system as described by Doherty et al. [Complete family of separability criteria, Phys. Rev. A69 (2004) 022308], we introduce parallel definitions in the context of Gaussian states and using only properties of their covariance matrices, derive necessary and sufficient conditions for their complete extendability. It turns out that the complete extendability property is equivalent to the separability property of a bipartite Gaussian state.

Following the proof of quantum de Finetti theorem as outlined in Hudson and Moody [Locally normal symmetric states and an analogue of de Finetti’s theorem, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 33(4) (1975/76) 343–351], we show that separability is equivalent to complete extendability for a state in a bipartite Hilbert space where at least one of which is of dimension greater than 2. This, in particular, extends the result of Fannes, Lewis, and Verbeure [Symmetric states of composite systems, Lett. Math. Phys.15(3) (1988) 255–260] to the case of an infinite dimensional Hilbert space whose C* algebra of all bounded operators is not separable.

We consider the entanglement evolution of two qubits embedded into disordered multiconnected environment. We model the environment and its interaction with qubits by large random matrices allowing for a possibility to describe environments of meso- and even nanosize. We obtain general formulas for the time dependent reduced density matrix of the qubits corresponding to several cases of the qubit-environment interaction and initial condition. We then work out an analog of the Born–Markov approximation to find the evolution of the widely used entanglement quantifiers: the concurrence, the negativity and the quantum discord. We show that even in this approximation the time evolution of the reduced density matrix can be non-Markovian, thereby describing certain memory effects due to the backaction of the environment on qubits. In particular, we find the vanishing of the entanglement (Entanglement Sudden Death) at finite moments and its revivals (Entanglement Sudden Birth). Our results, partly known and partly new, can be viewed as a manifestation of the universality of certain properties of decoherent qubit evolution which have been found previously in various versions of bosonic macroscopic environment.

We study the interaction of two entangled two-energy-level atoms interacts with a single-mode and two-photon cavity field. The atom state is detected after exiting the cavity, and it is found that the nonclassical properties of the field states depend strongly on the entanglement degree between the two atoms. Meanwhile it is shown that squeezing of field and photon antibunching can be greatly enhanced via selective atomic measurements.

We study ground state pairwise entanglement within one-dimensional spin-1/2 antiferromagnetic J₁–J₂ model with competing interactions. Contrary to some claims we found that frustration does not increase entanglement. Concurrence of nearest and next nearest neighbors are found to show abrupt change at phase transition points. We also show that the concurrence can be used to classify the phase diagram of the model in anisotropy–frustration plane.

A complementarity relation is shown between the visibility of interference and bipartite entanglement in a two qubit interferometric system when the parameters of the quantum operation change for a given input state. The entanglement measure is a decreasing function of the visibility of interference. The implications for quantum computation are briefly discussed.

In this paper, we study the quantum entanglement of three two-level atoms under the action of Fock state of a single-mode quantized radiation field. Milburn model is considered. Concurrence of the two atoms is given explicitly. As is expected, because of the intrinsic decoherence, Concurrence comes to a stationary value. A rule is summarized between this value and entanglement sudden death. As for the potential measurement of multi-particle entanglement, spin squeezing parameter is calculated.

The dynamics of entropy exchange and correlation in u(2) algebraic model for two stretches of H₂O and SO₂ is studied in terms of the linear entropy with diagonal approximation, where various initial states are respectively taken to be the product of thermal states and squeezed states on each mode. It is shown that with a suitable parameter in initial states, the entropies in each stretch are positively correlated or anticorrelated, which depend on initial states and a molecule. The entropy correlation is also studied in terms of a correlation index. It is demonstrated that the correlation index and the sum of linear entropies in each stretch are identical in oscillation. The differences in the linear entropy in each stretch and the correlation index of the thermal states and the squeezed states between H₂O and SO₂ are noticed. These may be useful for quantum computing and quantum information processing based on two stretching modes in both molecules.

Based on the general unitary operations of two-qubit system, we investigate the dynamics of information swapping between two qubits. We briefly describe the general behavior of entanglement entropy and the purity taking into account two classes of initially states, either product state or entangled state. Using the phenomenon of information swapping, we suggest a theoretical protocol to transform the coded information from sender to the receiver.

In this paper, we present a simulator for two-particle quantum walks on the line and one-particle on a two-dimensional squared lattice. It can be used to investigate the equivalence between the two cases (one- and two-particle walks) for various boundary conditions (open, circular, reflecting, absorbing and their combinations). For the case of a single walker on a two-dimensional lattice, the simulator can also implement the Möbius strip. Furthermore, other topologies for the walker are also simulated by the proposed tool, like certain types of planar graphs with degree up to 4, by considering missing links over the lattice. The main purpose of the simulator is to study the genuinely quantum effects on the global properties of the two-particle joint probability distribution on the entanglement between the walkers/axis. For that purpose, the simulator is designed to compute various quantities such as: the entanglement and classical correlations, (classical and quantum) mutual information, the average distance between the two walkers, different hitting times and quantum discord. These quantities are of vital importance in designing possible algorithmic applications of quantum walks, namely in search, 3-SAT problems, etc. The simulator can also implement the static partial measurements of particle(s) positions and dynamic breaking of the links between certain nodes, both of which can be used to investigate the effects of decoherence on the walker(s). Finally, the simulator can be used to investigate the dynamic Anderson-like particle localization by varying the coin operators of certain nodes on the line/lattice. We also present some illustrative and relevant examples of one- and two-particle quantum walks in various scenarios. The tool was implemented in C and is available on-line at http://qwsim.weebly.com/.

Properties of one-dimensional discrete-time quantum walks (DTQWs) are sensitive to the presence of inhomogeneities in the substrate, which can be generated by defining position-dependent coin operators. Deterministic aperiodic sequences of two or more symbols provide ideal environments where these properties can be explored in a controlled way. Based on an exhaustive numerical study, this work discusses a two-coin model resulting from the construction rules that lead to the usual fractal Cantor set. Although the fraction of the less frequent coin $\to 0$ as the size of the chain is increased, it leaves peculiar properties in the walker dynamics. They are characterized by the wave function, from which results for the probability distribution and its variance, as well as the entanglement entropy, were obtained. A number of results for different choices of the two coins are presented. The entanglement entropy has shown to be very sensitive to uncovering subtle quantum effects present in the model.

Entanglement exhibits a unique property of quantum theory that is unseen in classical counterparts. The experimental confirmation of Bell’s inequalities has surprised many people and revived interest and debate regarding the exact nature of quantum theory, including the wave-particle duality. On the other hand, rapid advancements in computing technology in recent years have provided a new tool for investigating the nature of quantum theory. In this paper, numerical simulation is used to visualize the nonlocality implied in quantum entanglement. In particular, a Gedanken experiment of a discrete approximation of a continuous quantum space is provided, similar to the case of the dual nature of particle/wave in the double-slit experiment. The results are expected to provide a different angle for a deeper understanding of the mysterious nature of quantum correlations.

The aim of quantum key distribution protocols is to establish a secret key among two parties with high security confidence. Such algorithms generally require a quantum channel and an authenticated classical channel. This paper presents a totally new perception of communication in such protocols. The quantum communication alone satisfies all needs of array communication between the two parties. Even so, the quantum communication channel does not need to be protected or authenticated whatsoever. As such, our algorithm is a purely quantum key distribution algorithm. The only certain identification of the two parties is through public keys.