We present a protocol for generating multipartite quantum correlations across a quantum network with a continuous-variable architecture. An arbitrary number of users possess two-mode entangled states, keeping one mode while sending the other to a central relay. Here a suitable multipartite Bell detection is performed which conditionally generates a cluster state on the retained modes. This cluster state can be suitably manipulated by the parties and used for tasks of quantum communication in a fully optical scenario. More interestingly, the protocol can be used to create a purely-mechanical cluster state starting from a supply of optomechanical systems. We show that detecting the optical parts of optomechanical cavities may efficiently swap entanglement into their mechanical modes, creating cluster states up to 5 modes under suitable cryogenic conditions.
Nonlocality swapping of bipartite binary correlated boxes can be realized by a \emph{coupler} ($χ$) in nonsignaling models. By studying the swapping process we find that the previous bipartite coupler can be applied to the swapping of two multipartite boxes, and then generate a multipartite box with more users than that of any of the boxes before swapping. Here quantum bound still appears in the scheme. The bipartite coupler also can be applied to a hybrid scheme of generating a multipartite extremal box from many PR boxes. As the analogue of multipartite entanglement swapping, we generalize t…
Quantum entanglement swapping is one of the most promising ways to realize the quantum connection among local quantum nodes. In this Letter, we present an experimental demonstration of the entanglement swapping between two independent multipartite entangled states, each of which involves a tripartite Greenberger-Horne-Zeilinger (GHZ) entangled state of an optical field. The entanglement swapping is implemented deterministically by means of a joint measurement on two optical modes coming from the two multipartite entangled states respectively and the classical feedforward of the measurement res…
In this paper, an optimal scheme of four-level quantum teleportation and swapping of quantum entanglement is given. We construct a complete orthogonal basis of the bipartite ququadrit systems. Using this basis, the four-level quantum teleportation and swapping can be achieved according to the standard steps. In addition, associate the above bases with the unextendible product bases and the exact entanglement bases, we prove that in the $2\times 2\times 2$ systems or $3\times 3$ systems the collective translations of multipartite quantum entanglement can be realized. PACC numbers: 03.67.Mn, 03.…
Characterizing pairwise swapping capabilities of dense coding channels
Harish-Chandra Research Institute（哈里什-钱德拉研究所）；Homi Bhabha National Institute（霍米·巴巴国立研究所）；International Institute of Information Technology Hyderabad（海得拉巴国际信息技术学院）；Birla Institute of Technology and Science, Pilani, Hyderabad Campus（比拉理工学院皮拉尼校区海得拉巴分校）
We propose a scheme for generating multipartite entangled coherent states via entanglement swapping, with an example of a physical realization in ion traps. Bipartite entanglement of these multipartite states is quantified by the concurrence. We also use the $N$--tangle to compute multipartite entanglement for certain systems. Finally we establish that these results for entanglement can be applied to more general multipartite entangled nonorthogonal states.
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 present a scheme for entangling two micromechanical oscillators. The scheme exploits the quantum effects of radiation pressure and it is based on a novel application of entanglement swapping, where standard optical measurements are used to generate purely mechanical entanglement. The scheme is presented by first solving the general problem of entanglement swapping between arbitrary bipartite Gaussian states, for which simple input-output formulas are provided.
Sideband cooling is a technique that potentially allows mechanical resonators to be prepared in their ground states, important for future applications in quantum technologies. Tian has recently shown that side-band cooling can be implemented by modulating the coupling between a nano-resonator and a superconducting oscillator, a process of frequency conversion [L. Tian, PRB 79, 193407 (2009)]. While side-band cooling is usually treated in the steady-state regime, the effective resonant coupling will also generate near perfect state-swapping from the superconductor to the mechanical resonator. W…
We classify multipartite entangled states in the 2 x 2 x n (n >= 4) quantum system, for example the 4-qubit system distributed over 3 parties, under local filtering operations. We show that there exist nine essentially different classes of states, and they give rise to a five-graded partially ordered structure, including the celebrated Greenberger-Horne-Zeilinger (GHZ) and W classes of 3 qubits. In particular, all 2 x 2 x n-states can be deterministically prepared from one maximally entangled state, and some applications like entanglement swapping are discussed.
Using the information content of correlations between multipartite systems, together with the notion of partitioning, we show that some general results about the evolution of correlations in quantum systems can be derived with only elementary methods. In particular, we show that for 2 quantum systems A and B, each comprised of a number of sub-systems, in which a partition of A interacts unitarily with a partition of B, then the total correlation can only increase (or remain unchanged) and is given simply by the sum of the initial correlation and the correlation that develops as a result of the…
In this work we study the production and swapping of non-gaussian multipartite entanglement in a setup containing a parametric amplifier which generates three photons in different modes coupled to three qubits. We prove that the entanglement generated in this setup is of nongaussian nature. We introduce witnesses of genuine tripartite nongaussian entanglement, valid both for mode and qubit entanglement. Moreover, those witnesses show that the entanglement generated among the photons can be swapped to the qubits, and indeed the qubits display nongaussian genuine tripartite entanglement over a w…
We propose a protocol for entanglement swapping which involves tripartite systems. The generation of remote entanglement induced by the Bell measurement can be easily certified by additional local measurements. We illustrate the protocol in the case of continuous variable systems where the certification is effective for an appropriate class of three-mode Gaussian states. We then apply the protocol to optomechanical systems, showing how mechanical entanglement between two remote micromechanical resonators can be generated and certified via local optical measurements.
Experimental demonstration of entanglement needs to have a precise control of experimentalist over the system on which the measurements are performed as prescribed by an appropriate entanglement witness. To avoid such trust problem, recently device-independent entanglement witnesses (\emph{DIEW}s) for genuine tripartite entanglement have been proposed where witnesses are capable of testing genuine entanglement without precise description of Hilbert space dimension and measured operators i.e apparatus are treated as black boxes. Here we design a protocol for enhancing the possibility of identif…
The usual entanglement swapping protocol can entangle two particles that never interact. Here we demonstrate an all-versus-nothing violation of local realism for a partial entanglement swapping process. A Clauser-Horne-Shimony-Holt-type inequality for two particles entangled by entanglement swapping is proposed for a practical experiment and can be violated quantum mechanically up to 4 beyond Cirel'son's bound 2sqr(2). Our result uncovers the intriguing nonlocal character of entanglement swapping and may lead to a conclusive (loophole-free) test of local realism versus quantum mechanics. The e…
Hybrid quantum systems have been developed with various mechanical, optical and microwave harmonic oscillators. The coupling produces a rich library of interactions including two mode squeezing, swapping interactions, back-action evasion and thermal control. In a multimode mechanical system, coupling resonators of different scales (both in frequency and mass) leverages the advantages of each resonance. For example: a high frequency, easily manipulated resonator could be entangled with a low frequency massive object for tests of gravitational decoherence. Here we demonstrate coherent optomechan…
Distinct from Bell's approach, Wigner had derived a form of local realist (LR) inequality which is quantum mechanically violated for a bipartite maximally entangled state. Subsequently, this approach was generalized to obtain a multipartite LR inequality. However, the violation of such generalised Wigner's inequality does not guarantee nonlocality between all possible different bipartitions of the multipartite system. In the present work, this limitation has been overcome by formulating a further generalisation of Wigner's approach through the derivation of a set of LR inequalities with respec…
In this paper, I will discuss the geometrical structures of multipartite quantum systems based on complex projective schemes. In particular, I will explicitly construct multi-qubit states in terms of these schemes and also discuss separability and entanglement of bipartite and multipartite quantum states. These results give some geometrical insight to the fascinating quantum mechanical phenomena of entanglement which is fundamentally important and has many applications in the field of quantum computing.
Einstein-Podolsky-Rosen (EPR) steering is a quantum mechanical phenomenon that allows one party to steer the state of a distant party by exploiting their shared entanglement. It has potential applications in secure quantum communication. In this paper, we present two swapping schemes of Gaussian EPR steering, single-channel and dual-channel schemes, by the technique of entanglement swapping. Two space-separated independent EPR steering states without a direct interaction present EPR steering after deterministic swapping. By comparing the EPR steering of the single-channel and dual-channel sche…
Entanglement swapping, the process to entangle two particles without coupling them in any way, is one of the most striking manifestations of the quantum-mechanical nonlocal characteristic. Besides fundamental interest, this process has applications in complex entanglement manipulation and quantum communication. Here we report a high-fidelity, unconditional entanglement swapping experiment in a superconducting circuit. The measured concurrence characterizing the qubit-qubit entanglement produced by swapping is above 0.75, confirming most of the entanglement of one qubit with its partner is dete…
This letter presents quantum mechanical inequalities which distinguish, for systems of $N$ spin-$\half$ particles ($N>2$), between fully entangled states and states in which at most $N-1$ particles are entangled. These inequalities are stronger than those obtained by Gisin and Bechmann-Pasquinucci [Phys.\ Lett. A {\bf 246}, 1 (1998)] and by Seevinck and Svetlichny [quant-ph/0201046].
The structure of Bell-type inequalities detecting genuine multipartite non-locality, and hence detecting genuine multipartite entanglement, is investigated. We first present a simple and intuitive approach to Svetlichny's original inequality, which provides a clear understanding of its structure and of its violation in quantum mechanics. Based on this approach, we then derive a family of Bell-type inequalities for detecting genuine multipartite non-locality in scenarios involving an arbitrary number of parties and systems of arbitrary dimension. Finally we discuss the thightness and quantum me…
We present a convenient and efficient scheme to generate arbitrarily multipartite continuous-variable entanglement via mechanical oscillator displacement induced by two strong input pump fields in the conventional single-cavity optomechanical system. It is shown that multipartite entanglement among the outputs of the two pump fields and any number of relatively weak probe fields can be realized and optimized when the two pump fields with suitable amplitude ratio and relative initial phase are, respectively, tuned to the red and blue mechanical sidebands of a single cavity mode and each probe f…
A general procedure to construct criteria for identifying genuine multipartite continuous variable entanglement is presented. It relies on the proper definition of adequate global operators describing the multipartite system, the positive partial transpose criterion of separability, and quantum mechanical uncertainty relations. As a consequence, each criterion encountered consists of a single inequality that is nicely computable and experimentally feasible, and that when violated is sufficient condition for genuine multipartite entanglement. Additionally we show that the previous work of van L…
We report the experimental realization of a recently discovered quantum information protocol by Asher Peres implying an apparent non-local quantum mechanical retrodiction effect. The demonstration is carried out by applying a novel quantum optical method by which each singlet entangled state is physically implemented by a two-dimensional subspace of Fock states of a mode of the electromagnetic field, specifically the space spanned by the vacuum and the one photon state, along lines suggested recently by E. Knill et al., Nature 409, 46 (2001) and by M. Duan et al., Nature 414, 413 (2001). The s…
The multipartite correlations derived from local measurements on some composite quantum systems are inconsistent with those reproduced classically. This inconsistency is known as quantum nonlocality and shows a milestone in the foundations of quantum theory. Still, it is NP hard to decide a nonlocal quantum state. We investigate an extended question: how to characterize the nonlocal properties of quantum states that are distributed and measured in networks. We first prove the generic tripartite nonlocality of chain-shaped quantum networks using semiquantum nonlocal games. We then introduce a n…
A compact scheme for the preparation of macroscopic multipartite entanglement is proposed and analyzed. In this scheme the vibrational modes of a mechanical resonator constitute continuous variable (CV) subsystems that entangle to each other as a result of their interaction with a two-level system (TLS). By properly driving the TLS, we show that a selected set of modes can be activated and prepared in a multipartite entangled state. We first study entanglement properties of a three-mode system by evaluating the genuine multipartite entanglement. And investigate its usefulness as a quantum reso…
We discuss the problem of determining whether the state of several quantum mechanical subsystems is entangled. As in previous work on two subsystems we introduce a procedure for checking separability that is based on finding state extensions with appropriate properties and may be implemented as a semidefinite program. The main result of this work is to show that there is a series of tests of this kind such that if a multiparty state is entangled this will eventually be detected by one of the tests. The procedure also provides a means of constructing entanglement witnesses that could in princip…
We construct a set of 2^(2^n) independent Bell correlation inequalities for n-partite systems with two dichotomic observables each, which is complete in the sense that the inequalities are satisfied if and only if the correlations considered allow a local classical model. All these inequalities can be summarized in a single, albeit non-linear inequality. We show that quantum correlations satisfy this condition provided the state has positive partial transpose with respect to any grouping of the n systems into two subsystems. We also provide an efficient algorithm for finding the maximal quantu…
Classical systems can be entangled. Entanglement is defined by coincidence correlations. Quantum entanglement experiments can be mimicked by a mechanical system with a single conserved variable and 77.8% conditional efficiency. Experiments are replicated for four particle entanglement swapping and GHZ entanglement.
Recently, Brassard et. al. conjectured that the fact that the maximal possible correlations between two non-local parties are the quantum-mechanical ones is linked to a reasonable restriction on communication complexity. We provide further support for the conjecture in the multipartite case. We show that any multipartite communication complexity problem could be reduced to triviality, had Nature been more non-local than quantum-mechanics by a quite small gap for any number of parties. Intriguingly, the multipartite nonlocal-box that we use to show the result corresponds to the generalized Bell…
Quantum entanglement is a quantum mechanical phenomenon where the quantum state of a many-body system with many degrees of freedom cannot be described independently of the state of each body with a given degree of freedom, no matter how far apart in space each body is. Entanglement is not only considered a resource in quantum information but also believed to affect complex condensed matter systems. Detecting and quantifying multi-particle entanglement in a many-body system is thus of fundamental significance for both quantum information science and condensed matter physics. Here, we detect and…
The multipartite setting offers much more complexity of nonlocality than the bipartite one. We analyze the structure of tripartite nonlocal correlations by proposing inequalities satisfied by each type: bilocal, broadcasting and quantum, but violated by the other two. One of the inequalities satisfied by broadcasting correlations is generalized for multipartite systems. The study of its quantum mechanical violation reveals that Greenberger-Horne-Zeilinger-like states exhibit new, powerful correlations.
The cavity-optomechanical radiation pressure interaction provides the means to create entanglement between a mechanical oscillator and an electromagnetic field interacting with it. Here we show how we can utilize this entanglement within the framework of time-continuous quantum control, in order to engineer the quantum state of the mechanical system. Specifically, we analyze how to prepare a low-entropy mechanical state by (measurement-based) feedback cooling operated in the blue detuned regime, the creation of bipartite mechanical entanglement via time-continuous entanglement swapping, and pr…
Controllable multipartite entanglement is a crucial element in quantum information processing. Here we present a scheme that generates switchable bipartite and genuine tripartite entanglement between microwave and optical photons via an optoelectromechanical interface, where microwave and optical cavities are coupled to a mechanical mode with controllable coupling constants. We show that by tuning an effective gauge phase between the coupling constants to the "sweet spots", bipartite entanglement can be generated and switched between designated output photons. The bipartite entanglement is rob…
We expose the information flow capabilities of pure bipartite entanglement as a theorem -- which embodies the exact statement on the `seemingly acausal flow of information' in protocols such as teleportation. We use this theorem to re-design and analyze known protocols (e.g. logic gate teleportation and entanglement swapping) and show how to produce some new ones (e.g. parallel composition of logic gates). We also show how our results extend to the multipartite case and how they indicate that entanglement can be measured in terms of `information flow capabilities'. Ultimately, we propose a sch…
The three-tangle-dependence of $S_{max} = \max <S>$, where $S$ is Svetlichny operator, are explicitly derived when one party moves with an uniform acceleration with respect to other parties in the generalized Greenberger-Horne-Zeilinger and maximally slice states. The $π$-tangle-dependence of $S_{max}$ are also derived implicitly. From the dependence we conjecture that the multipartite entanglement is not the only physical resource for quantum mechanical multipartite non-locality.
Cellular automata can show well known features of quantum mechanics, such as a linear updating rule that resembles a discretized form of the Schrödinger equation together with its conservation laws. Surprisingly, a whole class of "natural" Hamiltonian cellular automata, which are based entirely on integer-valued variables and couplings and derived from an Action Principle, can be mapped reversibly to continuum models with the help of Sampling Theory. This results in "deformed" quantum mechanical models with a finite discreteness scale $l$, which for $l\rightarrow 0$ reproduce the familiar cont…
We propose a novel type of optomechanical coupling which enables a tripartite interaction between a quantum emitter, an optical mode and a macroscopic mechanical oscillator. The interaction uses a mechanism we term mode field coupling: mechanical displacement modifies the spatial distribution of the optical mode field, which in turn modulates the atom-photon coupling rate. In properly designed multimode optomechanical systems, we can achieve situations in which mode field coupling is the only possible interaction pathway for the system. This enables, for example, swapping of a single excitatio…
We investigate absolutely maximally entangled (AME) states, which are multipartite quantum states that are maximally entangled with respect to any possible bipartition. These strong entanglement properties make them a powerful resource for a variety of quantum information protocols. In this paper, we show the existence of AME states for any number of parties, given that the dimension of the involved systems is chosen appropriately. We prove the equivalence of AME states shared between an even number of parties and pure state threshold quantum secret sharing (QSS) schemes, and prove necessary a…
An optomechanical interface that converts quantum states between optical fields with distinct wavelengths is proposed. A mechanical mode couples to two optical modes via radiation pressure and mediates the quantum state mapping between the two optical modes. A sequence of optomechanical $π/2$ pulses enables state-swapping between optical and mechanical states as well as the cooling of the mechanical mode. Theoretical analysis shows that high fidelity conversion can be realized for states with small photon numbers in systems with experimentally achievable parameters. The pulsed conversion proce…
Progress in the development of techniques for the construction of multiuser quantum communications networks is reviewed in light of the plans for an EU quantum communications infrastructure (EU QCI). Quantum key distribution networks may be classified as trusted node; quantum repeater-entanglement-swapping based; point-to-multipoint based on passive beam splitters, active optical switchers or WDM; high dimensional-multipartite entanglement and flexible reconfigurable multipartite networks. Both satellite and terrestrial implementations are possible and ore both planned for EU QCI; their relati…
We propose partial measurements as a conceptual tool to understand how to operate with counterfactual claims in quantum physics. Indeed, unlike standard von Neumann measurements, partial measurements can be reversed probabilistically. We first analyze the consequences of this rather unusual feature for the principle of superposition, for the complementarity principle, and for the issue of hidden variables. Then we move on to exploring non-local contexts, by reformulating the EPR paradox, the quantum teleportation experiment, and the entanglement-swapping protocol for the situation in which one…
In [M. Piani et al., arXiv:1103.4032 (2011)] an activation protocol was introduced which maps the general non-classical (multipartite) correlations between given systems into bipartite entanglement between the systems and local ancillae by means of a potentially highly entangling interaction. Here, we study how this activation protocol can be used to entangle the starting systems themselves via entanglement swapping through a measurement on the ancillae. Furthermore, we bound the relative entropy of quantumness (a naturally arising measure of non-classicality in the scheme of Piani et al. abov…
We propose a solid-state hybrid platform based on an array of implanted nitrogen-vacancy (NV) centers in diamond magnetically coupled to a mechanical oscillator. The mechanical oscillator and the NV electronic spins both act as a quantum bus and allow us to induce an effective long-range interaction between distant nuclear spins, relaxing the requirements on their spatial distance. The coherent nuclear spin-spin interaction, having the form of an Ising model, can be maintained in the presence of mechanical damping and spin dephasing via a pulsed dynamical decoupling of the nuclear spins in add…
Decoherence is one of the main obstacles in long-distance quantum communication. Recently, the theoretical work of Fröwis and W. Dür (Phys. Rev. Lett. \textbf{106}, 110402 (2011)) and the experiment of Lu \emph{et al.} (Nat. Photon. \textbf{8}, 364 (2014)) both showed that the logic qubits entanglement say the concatenated Greenberger-Horne-Zeilinger (C-GHZ) state is more robust under decoherence. In this paper, we describe a protocol for Bell-state analysis for this logic qubits entanglement. This protocol can also be extended to the multipartite C-GHZ state analysis. Also, we discuss its app…
Where do entangled multiple-qubit systems store information? For information injected into a qubit, this question is nontrivial and interesting since the entanglement delocalizes the information. So far, a common picture is that of a qubit and its purification partner sharing the information quantum mechanically. Here, we introduce a new picture of a single qubit in the correlation space, referred to as quantum information capsule (QIC), confining the information perfectly. This picture is applicable for the entangled multiple-qubit system in an arbitrary state. Unlike the partner picture, in …
In this paper, we propose a scheme for generating steady-state entanglement of remote micromechanical oscillators in unidirectionally-coupled cavities. For the system of two mechanical oscillators, we show that when two cavity modes in each cavity are driven at red- and blue-detuned sidebands, respectively, a stationary two-mode squeezed vacuum state of the two mechanical oscillators can be generated with the help of the cavity dissipation. The degree of squeezing is controllable by adjusting the relative strength of the pump lasers. Our calculations also show that the achieved mechanical enta…
We propose a protocol able to prepare two remote and initially uncorrelated microwave modes in an entangled stationary state, which is certifiable using only local optical homodyne measurements. The protocol is an extension of continuous variable entanglement swapping, and exploits two hybrid quadripartite opto-electro-mechanical systems in which a nanomechanical resonator acts as a quantum interface able to entangle optical and microwave fields. The proposed protocol allows to circumvent the problems associated with the fragility of microwave photons with respect to thermal noise and may repr…
