We study operator entanglement of the quantum chaotic evolutions. This study shows that properties of the operator entanglement production are qualitatively similar to the properties reported in literature about the pure state entanglement production. This similarity establishes that the operator entanglement quantifies {\it intrinsic} entangling power of an operator. The term `intrinsic' suggests that this measure is independent of any specific choice of initial states.
We study the quantum entanglement caused by unitary operators that have classical limits that can range from the near integrable to the completely chaotic. Entanglement in the eigenstates and time-evolving arbitrary states is studied through the von Neumann entropy of the reduced density matrices. We demonstrate that classical chaos can lead to substantially enhanced entanglement. Conversely, entanglement provides a novel and useful characterization of quantum states in higher dimensional chaotic or complex systems. Information about eigenfunction localization is stored in a graded manner in t…
We establish the entangling power of a unitary operator on a general finite-dimensional bipartite quantum system with and without ancillas, and give relations between the entangling power based on the von Neumann entropy and the entangling power based on the linear entropy. Significantly, we demonstrate that the entangling power of a general controlled unitary operator acting on two equal-dimensional qudits is proportional to the corresponding operator entanglement if linear entropy is adopted as the quantity representing the degree of entanglement. We discuss the entangling power and operator…
We investigate the average bipartite entanglement, over all possible divisions of a multipartite system, as a useful measure of multipartite entanglement. We expose a connection between such measures and quantum-error-correcting codes by deriving a formula relating the weight distribution of the code to the average entanglement of encoded states. Multipartite entangling power of quantum evolutions is also investigated.
We investigate entanglement production in a class of quantum baker's maps. The dynamics of these maps is constructed using strings of qubits, providing a natural tensor-product structure for application of various entanglement measures. We find that, in general, the quantum baker's maps are good at generating entanglement, producing multipartite entanglement amongst the qubits close to that expected in random states. We investigate the evolution of several entanglement measures: the subsystem linear entropy, the concurrence to characterize entanglement between pairs of qubits, and two proposal…
Quantum gates, that play a fundamental role in quantum computation and other quantum information processes, are unitary evolution operators $\hat U$ that act on a composite system changing its entanglement. In the present contribution we study some aspects of these entanglement changes. By recourse of a Monte Carlo procedure, we compute the so called "entangling power" for several paradigmatic quantum gates and discuss results concerning the action of the CNOT gate. We pay special attention to the distribution of entanglement among the several parties involved.
We analyze the quantum entanglement properties of bosonic particles hopping over graph structures.Mode-entanglement of a graph vertex with respect the rest of the graph is generated, starting from a product state, by turning on for a finite time a tunneling along the graph edges. The maximum achieved during the dynamical evolution by this bi-partite entanglement characterizes the entangling power of a given hopping hamiltonian. We studied this entangling power as a function of the self-interaction parameters i.e., non-linearities, for all the graphs up to four vertices and for two different na…
We study when a physical operation can produce entanglement between two systems initially disentangled. The formalism we develop allows to show that one can perform certain non-local operations with unit probability by performing local measurement on states that are weakly entangled.
Not all quantum protocols require entanglement to outperform their classical alternatives. The nonclassical correlations that lead to this quantum advantage are conjectured to be captured by quantum discord. Here we demonstrate that discord can be explicitly used as a resource: certifying untrusted entangling gates without generating entanglement at any stage. We implement our protocol in the single-photon regime, and show its success in the presence of high levels of noise and imperfect gate operations. Our technique offers a practical method for benchmarking entangling gates in physical arch…
In this paper we discuss four different proposals of entangling atomic states of particles which have never interacted. The experimental realization proposed makes use of the interaction of Rydberg atoms with a micromaser cavity prepared in either a coherent state or in a superposition of the zero and one field Fock states. We consider atoms in either a three-level cascade or lambda configuration
Given a quantum gate $U$ acting on a bipartite quantum system, its maximum (average, minimum) entangling power is the maximum (average, minimum) entanglement generation with respect to certain entanglement measure when the inputs are restricted to be product states. In this paper, we mainly focus on the 'weakest' one, i.e., the minimum entangling power, among all these entangling powers. We show that, by choosing von Neumann entropy of reduced density operator or Schmidt rank as entanglement measure, even the 'weakest' entangling power is generically very close to its maximal possible entangle…
We obtain expressions for the optimal rates of one- shot entanglement manipulation under operations which generate a negligible amount of entanglement. As the optimal rates for entanglement distillation and dilution in this paradigm, we obtain the max- and min-relative entropies of entanglement, the two logarithmic robustnesses of entanglement, and smoothed versions thereof. This gives a new operational meaning to these entanglement measures. Moreover, by considering the limit of many identical copies of the shared entangled state, we partially recover the recently found reversibility of entan…
We demonstrate that non-linear entanglement witnesses can be made particularly useful for entanglement detection in hyper-entangled or multilevel states. We test this idea experimentally on the platform of linear optics using a hyper-entangled state of two photons. Instead of several simultaneous copies of two-photon entangled states, one can directly measure the witness on single copy of a hyper-entangled state. Our results indicate that hyper-entanglement can be used for quick entanglement detection and it provides a practical testbed for experiments with non-linear entanglement witnesses.
We study global entangling properties of the system of coupled kicked tops testing various hypotheses and predictions concerning entanglement in quantum chaotic systems. In order to analyze the averaged initial entanglement production rate and the averaged asymptotic entanglement different ensembles of initial product states are evolved. Two different ensembles with natural probability distribution are considered: product states of independent spin-coherent states and product states of arbitrary states. It appears that the choice of either of these ensembles results in significantly different …
We investigate the entangling capacity of dynamical operations when provided with local ancilla. A comparison is made between the entangling capacity with and without the assistance of prior entanglement. An analytic solution is found for the log-negativity entangling capacity of two-qubit gates, which equals the entanglement of the Choi matrix isomorphic to the unitary operator. Surprisingly, the availability of prior entanglement does not affect this result; a property we call resource independence of the entangling capacity. We prove several useful upper-bounds on the entangling capacity th…
We propose a scheme able to generate stationary continuous variable entanglement between an optical and a microwave cavity mode by means of their common interaction with a micro-mechanical resonator. We show that when both cavities are intensely driven one can generate bipartite entanglement between any pair of the tripartite system, and that, due to entanglement sharing, optical-microwave entanglement is efficiently generated at the expense of microwave-mechanical and opto-mechanical entanglement.
We explore the dynamics of entanglement in classically chaotic systems by considering a multiqubit system that behaves collectively as a spin system obeying the dynamics of the quantum kicked top. In the classical limit, the kicked top exhibits both regular and chaotic dynamics depending on the strength of the chaoticity parameter $κ$ in the Hamiltonian. We show that the entanglement of the multiqubit system, considered for both bipartite and pairwise entanglement, yields a signature of quantum chaos. Whereas bipartite entanglement is enhanced in the chaotic region, pairwise entanglement is su…
We investigate entanglement properties of a recently introduced class of macroscopic quantum superpositions in two-mode mixed states. One of the tools we use in order to infer the entanglement in this non-Gaussian class of states is the power to entangle a qubit system. Our study reveals features which are hidden in a standard approach to entanglement investigation based on the uncertainty principle of the quadrature variables. We briefly describe the experimental setup corresponding to our theoretical scenario and a suitable modification of the protocol which makes our proposal realizable wit…
We discuss the generation of two-atom entanglement inside a resonant microcavity under stimulated emission (STE) interaction. The amount of entanglement is shown based on different atomic initial state. For each kind of intial state, we obtain the entanglement period and the entanglement critical point, which are found to deeply depend on driving field density. In case of atomic state $| ee >$, the entanglement can be induced due to STE. In case of atomic state $| eg >$, there is a competition between driving field indued entanglement and STE induced entanglement. When two atoms are initially …
We present a random-matrix analysis of the entangling power of a unitary operator as a function of the number of times it is iterated. We consider unitaries belonging to the circular ensembles of random matrices (CUE or COE) applied to random (real or complex) non-entangled states. We verify numerically that the average entangling power is a monotonic decreasing function of time. The same behavior is observed for the "operator entanglement" --an alternative measure of the entangling strength of a unitary. On the analytical side we calculate the CUE operator entanglement and asymptotic values f…
We investigate a possible scheme for entangling two mode thermal fields through the quantum erasing process, in which an atom is coupled with two mode fields via the interaction governed by the two-mode two-photon Jaynes-Cummings model. The influence of phase decoherence on the entanglement of two mode fields is discussed. It is found that quantum erasing process can transfer part of entanglement between the atom and fields to two mode fields initially in the thermal states. The entanglement achieved by fields heavily depends on their initial temperature and the detuning. The entanglement of s…
In this thesis there are two topics: On the entangling capacity, in terms of negativity, of quantum operations, and on the supremum of negativity for symmetric Gaussian states. Positive partial transposition (PPT) states are an important class of states in quantum information. We show a method to calculate bounds for entangling capacity, the amount of entanglement that can be produced by a quantum operation, in terms of negativity, a measure of entanglement. The bounds of entangling capacity are found to be associated with how non-PPT (PPT preserving) an operation is. A length that quantifies …
We investigate the entangling capability of passive optical elements, both qualitatively and quantitatively. We present a general necessary and sufficient condition for the possibility of creating distillable entanglement in an arbitrary multi-mode Gaussian state with the help of passive optical elements, thereby establishing a general connection between squeezing and the entanglement that is attainable by non-squeezing operations. Special attention is devoted to general two-mode Gaussian states, for which we provide the optimal entangling procedure, present an explicit formula for the attaina…
We study the evolution of quantum entanglement during exciton energy transfer (EET) in a network model of the Fenna-Matthews-Olson (FMO) complex, a biological pigment-protein complex involved in the early steps of photosynthesis in sulphur bacteria. The influence of Markovian, as well as spatially and temporally correlated (non-Markovian) noise on the generation of entanglement across distinct chromophores (site entanglement) and different excitonic eigenstates (mode entanglement) is studied for different injection mechanisms, including thermal and coherent laser excitation. Additionally, we s…
When a quantum system is distributed to spatially separated parties, it is natural to consider how the system evolves when the parties perform local quantum operations with classical communication (LOCC). However, the structure of LOCC channels is exceedingly complex leaving many important physical problems unsolved. In this paper we consider generalized resource theories of entanglement based on different relaxations to the class of LOCC. The behavior of various entanglement measures is studied under non-entangling channels, as well as the newly introduced classes of dually non-entangling and…
We propose a feasible scheme to realize the optical entanglement of single-photon-added coherent state (SPACS) and show that, besides the Sanders entangled coherent state, the entangled SPACS also leads to new forms of hybrid entanglement of quantum Fock state and classical coherent state. We probe the essential difference of two types of hybrid entangled state (HES). This HES provides a novel link between the discrete- and the continuous-variable entanglement in a natural way.
We compare three different characterizations of the globalness of bipartite unitary operations, namely, delocalization power, entanglement cost, and entangling power, to investigate global properties of unitary operations. We show that the globalness of the same unitary operation depends on whether input states are given by unknown states representing pieces of quantum information, or a set of known states for the characterization. We extend our analysis on the delocalization power in two ways. First, we show that the delocalization power differs whether the global operation is applied on one …
We introduce a modification of the standard entanglement swapping protocol where the generation of entanglement between two distant modes is realized and verified using only local optical measurements. We show, indeed, that a simple condition on the purity of the initial state involving also an ancillary mode is sufficient to guarantee the success of the protocol by local measurements {M. Abdi \textit{et al.}, Phys. Rev. Lett. \textbf{109}, 143601 (2012)}]. We apply the proposed protocol to a tripartite optomechanical system where the never interacting mechanical modes become entangled and cer…
We investigate the creation of entanglement by the application of phases whose value depends on the state of a collection of qubits. First we give the necessary and sufficient conditions for a given set of phases to result in the creation of entanglement in a state comprising of an arbitrary number of qubits. Then we analyze the creation of entanglement between any two qubits in three qubit pure and mixed states. We use our result to prove that entanglement is necessary for Deutsch-Jozsa algorithm to have an exponential advantage over its classical counterpart.
Superconducting microwave circuits with Josephson junctions are a major platform for quantum computing. To unleash their full capabilities, the cooperative operation of multiple microwave superconducting circuits is required. Therefore, designing an efficient protocol to distribute microwave entanglement remotely becomes a crucial open problem. Here, we propose a continuous-variable entanglement-swap approach based on optical-microwave entanglement generation, which can boost the ultimate rate by two orders of magnitude at state-of-the-art parameter region, compared with traditional approaches…
We discuss the use of Rydberg blockade techniques for entanglement of 1 atom qubits with collective $N$ atom qubits. We show how the entanglement can be used to achieve fast readout and transmission of the state of single atom qubits without the use of optical cavities.
We show that intrinsic fluctuations in system control parameters impose limits on the ability of two-qubit (exchange) Hamiltonians to generate entanglement starting from mixed initial states. We find three classes for Gaussian and Laplacian fluctuations. For the Ising and XYZ models there are qualitatively distinct sharp entanglement-generation transitions, while the class of Heisenberg, XY, and XXZ Hamiltonians is capable of generating entanglement for any finite noise level. Our findings imply that exchange Hamiltonians are surprisingly robust in their ability to generate entanglement in the…
Notions of circuit complexity and cost play a key role in quantum computing and simulation where they capture the (weighted) minimal number of gates that is required to implement a unitary. Similar notions also become increasingly prominent in high energy physics in the study of holography. While notions of entanglement have in general little implications for the quantum circuit complexity and the cost of a unitary, in this note, we discuss a simple such relationship when both the entanglement of a state and the cost of a unitary take small values, building on ideas on how values of entangling…
We clarify the microscopic structure of the entangling quantum measurement superoperators and examine their possible physical realization in a simple three-qubit model, which implements the entangling quantum measurement with an arbitrary degree of entanglement.
This letter details a simple scheme to entangle two neutrons by successive scattering from a macroscopic sample. In zero magnetic field the entanglement falls as the sample size increases. However, by applying a field and tuning the momentum of the neutrons, one can achieve a substantial degree of entanglement irrespective of the size of the sample.
A scheme is presented for entangling two separated nanomechanical oscillators by injecting broad band squeezed vacuum light and laser light into the ring cavity. We work in the resolved sideband regime. We find that in order to obtain the maximum entanglement of the two oscillators, the squeezing parameter of the input light should be about 1. We report significant entanglement over a very wide range of power levels of the pump and temperatures of the environment.
We propose an experiment for entangling two spatially separated Bose-Einstein condensates by Bragg scattering of light. When Bragg scattering in two condensates is stimulated by a common probe, the resulting quasiparticles in the two condensates get entangled due to quantum communication between the condensates via probe beam. The entanglement is shown to be significant and occurs in both number and quadrature phase variables. We present two methods of detecting the generated entanglement.
We propose a simple method to generate quantum entanglement between two macroscopic mechanical resonators in a two-cavity optomechanical system. This entanglement is induced by the radiation pressure of a single photon hopping between the two cavities. Our results are analytical, so that the entangled states are explicitly shown. Up to local operations, these states are two-mode three-component states, and hence the degree of entanglement can be well quantified by the concurrence. By analyzing the system parameters, we find that, to achieve a maximum average entanglement, the system should wor…
It is shown that radiation pressure can be profitably used to entangle {\it macroscopic} oscillators like movable mirrors, using present technology. We prove a new sufficient criterion for entanglement and show that the achievable entanglement is robust against thermal noise. Its signature can be revealed using common optomechanical readout apparatus.
Quantum correlations between identical particles are at the heart of quantum technologies. Several studies with two identical particles have shown that the spatial overlap and indistinguishability between the particles are necessary for generating bipartite entanglement. On the other hand, researches on the extension to more than two-particle systems are limited by the practical difficulty to control multiple identical particles in laboratories. In this work, we propose schemes to generate two fundamental classes of genuine tripartite entanglement, i.e., GHZ and W classes, which are experiment…
Particle identity and entanglement are two fundamental quantum properties that work as major resources for various quantum information tasks. However, it is still a challenging problem to understand the correlation of the two properties in the same system. While recent theoretical studies have shown that the spatial overlap between identical particles is necessary for nontrivial entanglement, the exact role of particle indistinguishability in the entanglement of identical particles has never been analyzed quantitatively before. Here, we theoretically and experimentally investigate the behavior…
We study the entangling properties of multipartite unitary gates with respect to the measure of entanglement called one-tangle. Putting special emphasis on the case of three parties, we derive an analytical expression for the entangling power of an $n$-partite gate as an explicit function of the gate, linking the entangling power of gates acting on $n$-partite Hilbert space of dimension $d_1 \ldots d_n$ to the entanglement of pure states in the Hilbert space of dimension $(d_1 \ldots d_n)^2$. Furthermore, we evaluate its mean value averaged over the unitary and orthogonal groups, analyze the m…
We in theory proposed a hybrid system consisting of a mechanical resonator, an optical Fabry-Pérot cavity, and two superconducting microwave circuits to generate stationary continuous-variable quantum entanglement between two microwave modes. We show that the hybrid system can also achieve quantum entanglement of other bipartite subsystems in experimentally accessible parameter regimes, which has the potential to be useful in quantum information processing and quantum illumination radar.
Inspired by the experimental measurement of the Renyi entanglement entropy in a lattice of ultracold atoms by Islam et al., [Nature 528, 77 (2015)] we propose a method to entangle two spatially-separated qubits using the quantum many-body state as a resource. Through local operations accessible in an experiment, entanglement is transferred to a qubit register from atoms at the ends of a one-dimensional chain. We compute the operational entanglement, which bounds the entanglement physically transferable from the many-body resource to the register, and discuss a protocol for its experimental mea…
We discuss the creation of entanglement between two two-level atoms in the dissipative process of spontaneous emission. It is shown that spontaneous emission can lead to a transient entanglement between the atoms even if the atoms were prepared initially in an unentangled state. The amount of entanglement created in the system is quantified by using two different measures: concurrence and negativity. We find analytical formulas for the evolution of concurrence and negativity in the system. We also find the analytical relation between the two measures of entanglement. The system consists of two…
Quantum information processing rests on our ability to manipulate quantum superpositions through coherent unitary transformations, and to establish entanglement between constituent quantum components of the processor. The quantum information processor (a linear ion trap, or a cavity confining the radiation field for example) exists in a dissipative environment. We discuss ways in which entanglement can be established within such dissipative environments. We can even make use of a strong interaction of the system with its environment to produce entanglement in a controlled way.
The information obtained from the operation of a quantum gate on only two complementary sets of input states is sufficient to estimate the quantum process fidelity of the gate. In the case of entangling gates, these conditions can be used to predict the multi qubit entanglement capability from the fidelities of two non-entangling local operations. It is then possible to predict highly non-classical features of the gate such as violations of local realism from the fidelities of two completely classical input-output relations, without generating any actual entanglement.
We calculate the amount of polarization-entanglement induced by two-photon interference at a lossless beam splitter. Entanglement and its witness are quantified respectively by concurrence and the Bell-CHSH parameter. In the presence of a Mandel dip, the interplay of two kinds of which-path information -- temporal and polarization -- gives rise to the existence of entangled polarization-states that cannot violate the Bell-CHSH inequality.
We show that the Unruh effect can create net quantum entanglement between inertial and accelerated observers depending on the choice of the inertial state. This striking result banishes the extended belief that the Unruh effect can only destroy entanglement and furthermore provides a new and unexpected source for finding experimental evidence of the Unruh and Hawking effects.
Nitrogen-vacancy (NV) defect centers in diamond are strong candidates to generate entangled states in solid-state environments even at room temperature. Quantum correlations in spatially separated NV systems, for distances between NVs ranging from a few nanometers to a few kilometers, have been recently reported. In the present work we consider the entanglement transfer from two- mode microwave squeezed (entangled) photons, which are in resonance with the two lowest NV electron spin states, to initially unentangled NV centers. We first demonstrate that the entanglement transfer process from qu…
We study target space entanglement in gauged multi-matrix models as models of entanglement between groups of D-branes separated by a planar entangling surface, paying close attention to the implementation of gauge invariance. We open with a review of target space entanglement between identical particles, which shares some important features (specifically a gauged permutation symmetry) with our main problem. For our matrix models, we implement a gauge fixing well-adapted to the entangling surface. In this gauge, we map the matrix model problem to that of entanglement of a $U(1)$ gauge theory on…
We consider the dynamics of a vibrating and rotating end-mirror of an optical Fabry-P{érot} cavity that can sustain Laguerre-Gaussian modes. We demonstrate theoretically that since the intra-cavity field carries linear as well as angular momentum, radiation pressure can create bipartite entanglement between a vibrational and a rotational mode of the mirror. Further we show that the ratio of vibrational and rotational couplings with the radiation field can easily be adjusted experimentally, which makes the generation and detection of entanglement robust to uncertainties in the cavity manufactur…
We study entanglement of the cavity modes in a double-cavity optomechanical system in strong-coupling regime. The system consists of two optomechanical systems coupled by a single photon hopping between them. With the radiation pressure of the photon, entanglement of the cavity modes can be generated. The concurrence between the cavity modes is at least twice larger than that between the mechanical modes. Moreover, when we change the ratio between coupling strength and resonant frequency of mechanical modes, the entanglement in cavity and mechanical modes are influenced differently.
The entangling power and operator entanglement entropy are state independent measures of entanglement. Their growth and saturation is examined in the time-evolution operator of quantum many-body systems that can range from the integrable to the fully chaotic. An analytically solvable integrable model of the kicked transverse field Ising chain is shown to have ballistic growth of operator von Neumann entanglement entropy and exponentially fast saturation of the linear entropy with time. Surprisingly a fully chaotic model with longitudinal fields turned on shares the same growth phase, and is co…
