We propose an experimentally feasible scheme to generate Greenberger-Horne-Zeilinger (GHZ) type of maximal entanglement between many atomic ensembles based on laser manipulation and single-photon detection. The scheme, with inherent fault tolerance to the dominant noise and efficient scaling of the efficiency with the number of ensembles, allows to maximally entangle many atomic ensemble within the reach of current technology. Such a maximum entanglement of many ensembles has wide applications in demonstration of quantum nonlocality, high-precision spectroscopy, and quantum information processing.
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…
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 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 demonstrate theoretically a scheme for cluster state generation, based on atomic ensembles and the dipole blockade mechanism. In the protocol, atomic ensembles serve as single qubit systems. Therefore, we review single-qubit operations on qubit defined as collective states of atomic ensemble. Our entangling protocol requires nearly identical single-photon sources, one ultra-cold ensemble per physical qubit, and regular photodetectors. The general entangling procedure is presented, as well as a procedure that generates in a single step Q-qubit GHZ states with success probability p_success ~ …
We present a new scheme for cluster states generation based on atomic ensembles and the dipole blockade mechanism. The protocol requires identical single photon sources, one ensemble per physical qubit, and regular photodetectors. The general entangling procedure is presented, as well as a procedure that generates Q-qubit GHZ states with probability p ~ eta^{Q/2}, where eta is the combined detection and source efficiency. This is significantly more efficient than any known robust probabilistic entangling operation. The GHZ states form the basic building block for universal cluster states - a r…
We analyze various scenarios for entangling two initially unentangled qubits. In particular, we propose an optimal universal entangler which entangles a qubit in unknown state $|Ψ>$ with a qubit in a reference (known) state $|0>$. That is, our entangler generates the output state which is as close as possible to the pure (symmetrized) state $(|Ψ>|0> +|0>|Ψ>)$. The most attractive feature of this entangling machine, is that the fidelity of its performance (i.e. the distance between the output and the ideally entangled -- symmetrized state) does not depend on the input and takes the constant val…
We demonstrate the connection between an operator's matrix element distribution and entangling power via numerical simulations of random, pseudo-random, and quantum chaotic operators. Creating operators with a random distribution of matrix elements is more difficult than creating operators that reproduce other statistical properties of random matrices. Thus, operators that fulfill many random matrix statistical properties may not generate states of high multi-partite entanglement. To quantify the randomness of various statistical distributions and, by extension, entangling power, we use proper…
We consider entanglement purification protocols for multiple copies of qubit states. We use high-dimensional auxiliary entangled systems to learn about number and positions of errors in the noisy ensemble in an explicit and controlled way, thereby reducing the amount of noise in the ensemble and purifying the remaining states. This allows us to design entanglement purification protocols for any number of copies that work particularly well for a small number of expected errors, i.e. high fidelity of initial states. The main tool is a counter gate with which the required non-local information ca…
Entanglement is a fundamental property of quantum mechanics, and is a primary resource in quantum information systems. Its manipulation remains a central challenge in the development of quantum technology. In this work, we demonstrate a device which can generate, manipulate, and analyse two-qubit entangled states, using miniature and mass-manufacturable silicon photonics. By combining four photon-pair sources with a reconfigurable six-mode interferometer, embedding a switchable entangling gate, we generate two-qubit entangled states, manipulate their entanglement, and analyse them, all in the …
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…
Maximally entangled bipartite unitary operators or gates find various applications from quantum information to being building blocks of minimal models of many-body quantum chaos, and have been referred to as "dual unitaries". Dual unitary operators that can create the maximum average entanglement when acting on product states have to satisfy additional constraints. These have been called "2-unitaries" and are examples of perfect tensors that can be used to construct absolutely maximally entangled states of four parties. Hitherto, no systematic method exists, in any local dimension, which resul…
We propose a scheme that employs dissipation to deterministically generate entanglement in an ensemble of strongly interacting Rydberg atoms. With a combination of microwave driving between different Rydberg levels and a resonant laser coupling to a short lived atomic state, the ensemble can be driven towards a dark steady state that entangles all atoms. The long-range resonant dipole-dipole interaction between different Rydberg states extends the entanglement beyond the van der Walls interaction range with perspectives for entangling large and distant ensembles.
We study how to efficiently manipulate and store quantum information between optical fields and atomic ensembles. We show how various non-dissipative transfer schemes can be used to transfer and store quantum states such as squeezed vacuum states or entangled states into the long-lived ground state spins of atomic ensembles.
Nonlocal properties of an ensemble of diagonal random unitary matrices of order $N^2$ are investigated. The average Schmidt strength of such a bipartite diagonal quantum gate is shown to scale as $\log N$, in contrast to the $\log N^2$ behavior characteristic to random unitary gates. Entangling power of a diagonal gate $U$ is related to the von Neumann entropy of an auxiliary quantum state $ρ=AA^{\dagger}/N^2$, where the square matrix $A$ is obtained by reshaping the vector of diagonal elements of $U$ of length $N^2$ into a square matrix of order $N$. This fact provides a motivation to study t…
We propose a feasible scheme to achieve quantum computation based on geometric manipulation of ensembles of atoms, and analyze it for neutral rubidium atoms magnetically trapped in planoconcave microcavities on an atom chip. The geometric operations are accomplished by optical excitation of a single atom into a Rydberg state in a constant electric field. Strong dipole-dipole interactions and incident lasers drive the dark state of the atom ensembles to undergo cyclic evolutions that realize a universal set of quantum gates. Such geometric manipulation turns out naturally to protect the qubits …
Excitonic transitions offer a possible route to ultrafast optical spin manipulation in coupled nanostructures. We perform here a detailed study of the three principal exciton-mediated decoherence channels for optically-controlled electron spin qubits in coupled quantum dots: radiative decay of the excitonic state, exciton-phonon interactions, and Landau-Zener transitions between laser-dressed states. We consider a scheme to produce an entangling controlled-phase gate on a pair of coupled spins which, in its simplest dynamic form, renders the system subject to fast decoherence rates associated …
Scalable and efficient quantum computation with photonic qubits requires (i) deterministic sources of single-photons, (ii) giant nonlinearities capable of entangling pairs of photons, and (iii) reliable single-photon detectors. In addition, an optical quantum computer would need a robust reversible photon storage devise. Here we discuss several related techniques, based on the coherent manipulation of atomic ensembles in the regime of electromagnetically induced transparency, that are capable of implementing all of the above prerequisites for deterministic optical quantum computation with sing…
We study the properties of a two-body random matrix ensemble for distinguishable spins. We require the ensemble to be invariant under the group of local transformations and analyze a parametrization in terms of the group parameters and the remaining parameters associated with the "entangling" part of the interaction. We then specialize to a spin chain with nearest neighbour interactions and numerically find a new type of quantum phase transition related to the strength of a random external field i.e. the time reversal breaking one body interaction term.
We analyze a similar scheme for producing light-mediated entanglement between atomic ensembles, as first realized by Julsgaard, Kozhekin and Polzik [Nature {\bf 413}, 400 (2001)]. In the standard approach to modeling the scheme, a Holstein-Primakoff approximation is made, where the atomic ensembles are treated as bosonic modes, and is only valid for short interaction times. In this paper, we solve the time evolution without this approximation, which extends the region of validity of the interaction time. For short entangling times, we find this produces a state with similar characteristics as …
We present an analysis of transfer of quantum information between the collective spin degrees of freedom of a large ensemble of two-level systems and a single central qubit. The coupling between the central qubit and the individual ensemble members may be varied and thus provides access to more than a single storage mode. Means to store and manipulate several independent qubits are derived for the case where the variation in coupling strengths does not allow addressing of orthogonal modes of the ensemble. While our procedures and analysis may apply to a number of different physical systems, fo…
We propose a protocol for the deterministic generation of entanglement between two ensembles of nuclear spins surrounding two distant quantum dots. The protocol relies on the injection of electrons with definite polarization in each quantum dot and the coherent transfer of electrons from one quantum dot to the other. Computing the exact dynamics for small systems, and using an effective master equation and approximate non-linear equations of motion for larger systems, we are able to confirm that our protocol indeed produces entanglement for both homogeneous and inhomogeneous systems. Last, we …
A quantum gravity-gradiometer consists of two spatially separated ensembles of atoms interrogated by pulses of a common laser beam. Laser pulses cause the probability amplitudes of atomic ground-state hyperfine levels to interfere, producing two motion-sensitive phase shifts which allow the measurement of the average acceleration of each ensemble, and, via simple differencing, of the acceleration gradient. Here I propose entangling the quantum states of the two ensembles prior to the pulse sequence, and show that entanglement encodes their relative acceleration in a single interference phase w…
We present a classical model for bulk-ensemble NMR quantum computation: the quantum state of the NMR sample is described by a probability distribution over the orientations of classical tops, and quantum gates are described by classical transition probabilities. All NMR quantum computing experiments performed so far with three quantum bits can be accounted for in this classical model. After a few entangling gates, the classical model suffers an exponential decrease of the measured signal, whereas there is no corresponding decrease in the quantum description. We suggest that for small numbers o…
Coupling photons to Rydberg excitations in a cold atomic gas yields unprecedentedly large optical nonlinearities at the level of individual light quanta, where the formation of nearby dark-state polaritons is blocked by the strong interactions between Rydberg atoms. This blockade mechanism, however, realizes an inherently dissipative nonlinearity, which limits the performance of practical applications. In this work, we propose a new approach to strong photon interactions via a largely coherent mechanism at drastically suppressed photon losses. Rather than a polariton blockade, it is based on a…
We consider an experiment in which quantum tomography data is collected before and after an entangling measurement performed on two independently prepared, maximally-mixed ensembles. We show that each sub-ensemble that is, as expected, entangled after the measurement is also entangled before it. We call the latter pre-entanglement. If individual systems possessed quantum states, their independent preparations would mean the sub-ensembles were in separable states prior to the entanglement event. The contradiction can be resolved by assigning states only to ensembles and not individual quantum s…
Hybrid matter-photon entanglement is the building block for quantum networks. It is very favorable if the entanglement can be prepared with a high probability. In this paper, we report the deterministic creation of entanglement between an atomic ensemble and a single photon by harnessing Rydberg blockade. We design a scheme that creates entanglement between a single photon's temporal modes and the Rydberg levels that host a collective excitation, using a process of cyclical retrieving and patching. The hybrid entanglement is tested via retrieving the atomic excitation as a second photon and pe…
We demonstrate the use of high-Q superconducting coplanar waveguide (CPW) microresonators to perform rapid manipulations on a randomly distributed spin ensemble using very low microwave power (400 nW). This power is compatible with dilution refrigerators, making microwave manipulation of spin ensembles feasible for quantum computing applications. We also describe the use of adiabatic microwave pulses to overcome microwave magnetic field ($B_{1}$) inhomogeneities inherent to CPW resonators. This allows for uniform control over a randomly distributed spin ensemble. Sensitivity data are reported …
We report the first experimental realization of single-qubit manipulation for single spinwaves stored in an atomic ensemble quantum memory. In order to have high-fidelity gate operations, we make use of stimulated Raman transition and controlled Lamor precession jointly. We characterize the gate performances with quantum state tomography and quantum process tomography, both of which imply that high-fidelity operations have been achieved. Our work complements the experimental toolbox of atomic-ensemble quantum memories by adding the capability of single-qubit manipulation, thus may have importa…
We consider an ensemble of atoms with $Λ$-type level structure trapped in a single-mode cavity, and propose a geometric scheme of coherent manipulation of quantum states on the subspace of zero-energy states within the quantum Zeno subspace of the system. We find that the particular subspace inherits the decoherence-free nature of the quantum Zeno subspace and features a symmetry-protected degeneracy, fulfilling all the conditions for a universal scheme of arbitrary unitary operations on it.
Quantum correlations present in a broadband two-line squeezed microwave state can induce entanglement in a spatially separated bipartite system consisting of either two single qubits or two qubit ensembles. By using an appropriate master equation for a bipartite quantum system in contact with two separate but entangled baths, the generating entanglement process in spatially separated quantum systems is thoroughly characterized. Our results provide evidence that this entanglement transfer by dissipation is feasible yielding to a steady-state amount of entanglement in the bipartite quantum syste…
We numerically study the hyperfine induced nuclear spin dynamics in a system of two coupled quantum dots in zero magnetic field. Each of the electron spins is considered to interact with an individual bath of nuclear spins via homogeneous coupling constants (all coupling coefficients being equal). In order to lower the dimension of the problem, the two baths are approximated by two single long spins. We demonstrate that the hyperfine interaction enables to utilize the nuclear baths for quantum information purposes. In particular, we show that it is possible to swap the nuclear ensembles on tim…
Reliable quantum information processing requires high-fidelity universal manipulation of quantum systems within the characteristic coherence times. Non-adiabatic holonomic quantum computation offers a promising approach to implement fast, universal, and robust quantum logic gates particularly useful in nano-fabricated solid-state architectures, which typically have short coherence times. Here, we propose an experimentally feasible scheme to realize high-speed universal geometric quantum gates in nano-engineered pseudo-spin charge qubits. We use a system of three coupled quantum dots containing…
We propose an experimentally feasible scheme to demonstrate quantum nonlocality, using Greenberger-Horne-Zeilinger (GHZ) and $W$ entanglement between atomic ensembles generated by a new developed method based on laser manipulation and{} single-photon detection.
A fundamental requirement in the circuit model of quantum information processing is the realization of fault-tolerant multi-qubit quantum gates with entangling capabilities. A key step towards this end is to achieve control of qubit states through geometric phases at very small spatial scales in an effective and feasible way. A spin-electric coupling present in antiferromagnetic triangular single-molecule magnets (SMMs) allows for manipulation of the spin (qubit) states with a great flexibility. Here, we establish an all-electrical two-qubit geometric phase shift gate acting on the four-fold g…
This work studies the variational quantum eigensolver algorithm, designed to determine the ground state of a quantum mechanical system by combining classical and quantum hardware. Methods of reducing the number of required qubit manipulations, prone to induce errors, for the variational quantum eigensolver are studied. We formally justify the qubit removal process as sketched by Bravyi, Gambetta, Mezzacapo and Temme [arXiv:1701.08213 (2017)]. Furthermore, different classical optimization and entangling methods, both gate based and native, are surveyed by computing ground state energies of H$_2…
This dissertation studies spin squeezing, entanglement and decoherence in large ensembles of cold, trapped alkali atoms with hyperfine spin f interacting with optical fields. Restricting the state of each atom to a qutrit embedded in the 2f+1 dimensional hyperfine spin enables us to efficiently model the coherent and dissipative dynamics of the ensemble. This formalism also allows us to explore the effects of local control on the internal hyperfine spins of the atoms. State preparation using such control increases the entangling power of the atom-light interface for f>1/2. Subsequent control o…
We develop a measurement operator formalism to handle quantum nondemolition (QND) measurement induced entanglement generation between two atomic gases. We first derive how the QND entangling scheme reduces to a positive operator-valued measure, and consider its limiting case when it can be used to construct a projection operator that collapses the state to a total spin projection state. We then analyze how a stroboscopic sequence of such projections made in the x and z basis evolves the initial wave function. Such a sequence of QND projections can enhance the entanglement between the atomic en…
Motivated by the recent interest in thermodynamics of micro- and mesoscopic quantum systems we study the maximal amount of work that can be reversibly extracted from a quantum system used to store temporarily energy. Guided by the notion of passivity of a quantum state we show that entangling unitary controls extract in general more work than independent ones. In the limit of large number of copies one can reach the thermodynamical bound given by the variational principle for free energy.
We propose an experimentally feasible scheme to generate nonmaximal entanglement between two atomic ensembles. The degree of entanglement is readily tunable. The scheme involves laser manipulation of atomic ensembles, adjustable quarter- and half-wave plates, beam splitter, polarizing beam splitters, and single-photon detectors, and well fits the status of the current experimental technology. Finally we use the nonmaximally entangled state of ensembles to demonstrate quantum nonlocality by detecting the Clauser-Horne-Shimony-Holt inequality.
Quantum theoretical treatment of coherent forward scattering of light in a polarized atomic ensemble with an arbitrary angular momentum is developed. We consider coherent forward scattering of a weak radiation field interacting with a realistic multi-level atomic transition. Based on the concept of an effective Hamiltonian and on the Heisenberg formalism, we discuss the coupled dynamics of the quantum fluctuations of the polarization Stokes components of propagating light and of the collective spin fluctuations of the scattering atoms. We show that in the process of coherent forward scattering…
We show that entangling capacities based on the Jamiolkowski isomorphism may be used to place lower bounds on the communication capacities of arbitrary bipartite unitaries. Therefore, for these definitions, the relations which have been previously shown for two-qubit unitaries also hold for arbitrary dimensions. These results are closely related to the theory of the entanglement-assisted capacity of channels. We also present more general methods for producing ensembles for communication from initial states for entanglement creation.
Entanglement between two macroscopic atomic ensembles induced by measurement on an ancillary light system has proven to be a powerful method for engineering quantum memories and quantum state transfer. Here we investigate the feasibility of such methods for generation, manipulation and detection of genuine multipartite entanglement between mesoscopic atomic ensembles. Our results extend in a non trivial way the EPR entanglement between two macroscopic gas samples reported experimentally in [B. Julsgaard, A. Kozhekin, and E. Polzik, Nature {\bf 413}, 400 (2001)]. We find that under realistic co…
We describe an experimental scheme of preparing multipartite W class of maximally entangled states between many atomic ensembles. The scheme is based on laser manipulation of atomic ensembles and single-photon detection, and well fits the status of the current experimental technology. In addition, we show one of the applications of the kind of W class states, teleporting an entangled state of atomic ensembles with unknown coefficients to more than one distant parties, either one of which equally likely receives the transmitted state.
We suggest to interface nanomechanical systems via an optical quantum bus to atomic ensembles, for which means of high precision state preparation, manipulation and measurement are available. This allows in particular for a Quantum Non-Demolition Bell measurement, projecting the coupled system, atomic ensemble - nanomechanical resonator, into an entangled EPR-state. The entanglement is observable even for nanoresonators initially well above their ground states and can be utilized for teleportation of states from an atomic ensemble to the mechanical system.
We describe a theoretical scheme that allows for transfer of quantum states of atomic collective excitation between two macroscopic atomic ensembles localized in two spatially-separated domains. The conception is based on the occurrence of double-exciton dark states due to the collective destructive quantum interference of the emissions from the two atomic ensembles. With an adiabatically coherence manipulation for the atom-field couplings by stimulated Ramann scattering, the dark states will extrapolate from an exciton state of an ensemble to that of another. This realizes the transport of qu…
A strongly confined light field necessarily exhibits a local polarization that varies on a subwavelength scale. We demonstrate that a single optical mode of such kind can be used to selectively and simultaneously manipulate atomic ensembles that are less than a micron away from each other and equally coupled to the light field. The technique is implemented with an optical nanofiber that provides an evanescent field interface between a strongly guided optical mode and two diametric linear arrays of cesium atoms. Using this single optical mode, the two atomic ensembles can simultaneously be opti…
We propose and analyze a quantum repeater architecture in which Rydberg blocked atomic ensembles inside optical cavities are linked by optical fibers. Entanglement generation, swapping and purification are achieved through collective laser manipulations of the ensembles and photon transmission. Successful transmission and storage of entanglement are heralded by ionization events rather than by photon detection signal used in previous proposals. We demonstrate how the high charge detection efficiency allows for a shortened average entanglement generation time, and we analyze an implementation o…
The efficient generation of high-fidelity entangled states is the key element for long-distance quantum communication, quantum computation and other quantum technologies, and at the same time the most resource-consuming part in many schemes. We present a new class of entanglement-assisted entanglement purification protocols that can generate high-fidelity entanglement from noisy, finite-size ensembles with improved yield and fidelity as compared to previous approaches. The scheme utilizes high-dimensional auxiliary entanglement to perform entangling non-local measurements and determine the num…
