Multimode Entangled States Research Articles

Remote implementation of hidden or partially unknown quantum operators using optimal resources: a generalized view

Two protocols are proposed for two closely linked but different variants of remote implementation of quantum operators of specific forms The first protocol is designed for the remote implementation of the single qubit hidden quantum operator, whereas the second one is designed for the remote implementation of the partially unknown single qubit quantum operator. In both cases two-qubit maximally entangled state, which is entangled in the spatial degree of freedom is used. The quantum resources used here are optimal and easy to realize and maintain in comparison to the multi-partite or multi-mode entangled states used in earlier works. The impact of photon loss due to interaction with the environment is analyzed for both the schemes. The proposed protocols are also generalized to their controlled, bidirectional, cyclic, controlled cyclic, and controlled bidirectional versions and it is shown that either Bell state alone or products of Bell states will be sufficient to perform these tasks with some additional classical communications in the controlled cases only. This is in sharp contrast to the earlier proposals that require large entangled states. In addition, it’s noted that remote implementation of hidden or partially unknown operators involving multiple controllers and/or multiple players who jointly apply the desired operator(s) would require quantum channels more complex than the Bell states and their products. Explicit forms of such quantum channels are also provided.

Exact dynamics of multimode periodic input states in coupled waveguide arrays

In this work, we investigate the quantum state reconstruction of the periodic input state in a 1-D waveguide array. In particular, we consider a single-photon multimode entangled W-state with different periodicities as an input to the array and study the effect of periodicity in the output. For comparison, we also study separable single photon periodic input states. We study the evolution of average photon number and the fidelity of the periodic input state and give the exact solution to investigate the revival of single photon multimode periodic input. Our solution is valid for any number of waveguides in the array. Our findings show the revival of the average photon number and almost complete quantum state reconstruction of the initial multimode entangled state for certain periodicities. The results reported here are significant because multimode-entangled states are essential resources for various applications in the physical implementation of photonic quantum technologies.

Time-domain measurement of twin beams produced by fiber amplifiers with an ultra-fast pulse train as a pump.

A pulsed pumped four-wave mixing process via χ(3) nonlinearity in an optical fiber can generate optical pulses with continuous variable quantum correlation. However, pairwise correlation of the generated pulses in this system has not been demonstrated. Here we report a time-domain measurement of an intensity difference squeezed state generated in a fiber. With a fast response differential detection system, we show the generated twin-beam pulses are pairwisely correlated, and -3.8-dB (-8.1 dB after detection losses correction) intensity difference squeezing degree is measured in the time domain. Our result is beneficial for generating multi-mode entangled state by time-division multiplexing in fiber system.

Fault-Tolerant Multiqubit Geometric Entangling Gates Using Photonic Cat-State Qubits

We propose a theoretical protocol to implement multiqubit geometric gates (i.e., the M{\o}lmer-S{\o}rensen gate) using photonic cat-state qubits. These cat-state qubits stored in high-$Q$ resonators are promising for hardware-efficient universal quantum computing. Specifically, in the limit of strong two-photon drivings, phase-flip errors of the cat-state qubits are effectively suppressed, leaving only a bit-flip error to be corrected. Because this dominant error commutes with the evolution operator, our protocol preserves the error bias, and, thus, can lower the code-capacity threshold for error correction. A geometric evolution guarantees the robustness of the protocol against stochastic noise along the evolution path. Moreover, by changing detunings of the cavity-cavity couplings at a proper time, the protocol can be robust against parameter imperfections (e.g., the total evolution time) without introducing extra noises into the system. As a result, the gate can produce multi-mode entangled cat states in a short time with high fidelities.

Simple way to incorporate loss when modeling multimode-entangled-state generation

We show that the light generated via spontaneous four-wave mixing or parametric down conversion in multiple, coupled, lossy cavities is a multimode squeezed thermal state. Requiring this state to be the solution of the Lindblad master equation results in a set of coupled first-order differential equations for the time-dependent squeezing parameters and thermal photon numbers of the state. The benefit of this semianalytic approach is that the number of coupled equations scales linearly with the number of modes and is independent of the number of photons generated. With this analytic form of the state, correlation variances are easily expressed as analytic functions of the time-dependent mode parameters. Thus, our solution makes it computationally tractable and relatively straightforward to calculate the generation and evolution of multimode entangled states in multiple coupled, lossy cavities, even when there are a large number of modes and/or photons.

Efficient Verification of Continuous-Variable Quantum States and Devices without Assuming Identical and Independent Operations.

Continuous-variable quantum information, encoded into infinite-dimensional quantum systems, is a promising platform for the realization of many quantum information protocols, including quantum computation, quantum metrology, quantum cryptography, and quantum communication. To successfully demonstrate these protocols, an essential step is the certification of multimode continuous-variable quantum states and quantum devices. This problem is well studied under the assumption that multiple uses of the same device result in identical and independently distributed (i.i.d.) operations. However, in realistic scenarios, identical and independent state preparation and calls to the quantum devices cannot be generally guaranteed. Important instances include adversarial scenarios and instances of time-dependent and correlated noise. In this Letter, we propose the first set of reliable protocols for verifying multimode continuous-variable entangled states and devices in these non-i.i.d scenarios. Although not fully universal, these protocols are applicable to Gaussian quantum states, non-Gaussian hypergraph states, as well as amplification, attenuation, and purification of noisy coherent states.

Hot-spots and gain enhancement in a doubly pumped parametric down-conversion process.

We experimentally investigate the parametric down-conversion process in a nonlinear bulk crystal, driven by two non-collinear pump modes. The experiment shows the emergence of bright hot-spots in modes shared by the two pumps, similar to the phenomenology recently observed in 2D nonlinear photonic crystals. By exploiting the spatial walk-off between the two extraordinary pump modes, we have been able to recreate a peculiar resonance condition, reported by a local enhancement of the parametric gain, which corresponds to a transition from a three-mode to a four-mode coupling. From a quantum point of view, this opens the way to the generation of multimode entangled states of light, such as tripartite or quadripartite states, in simple bulk nonlinear sources.

Realizing a deterministic source of multipartite-entangled photonic qubits

Sources of entangled electromagnetic radiation are a cornerstone in quantum information processing and offer unique opportunities for the study of quantum many-body physics in a controlled experimental setting. Generation of multi-mode entangled states of radiation with a large entanglement length, that is neither probabilistic nor restricted to generate specific types of states, remains challenging. Here, we demonstrate the fully deterministic generation of purely photonic entangled states such as the cluster, GHZ, and W state by sequentially emitting microwave photons from a controlled auxiliary system into a waveguide. We tomographically reconstruct the entire quantum many-body state for up to N = 4 photonic modes and infer the quantum state for even larger N from process tomography. We estimate that localizable entanglement persists over a distance of approximately ten photonic qubits.

Computable genuine multimode entanglement measure: Gaussian versus non-Gaussian

Genuine multimode entanglement in continuous variable systems can be quantified by exploring the geometry of the state-space, namely via the generalized geometric measure (GGM) which is defined as the shortest distance of a given multimode state from a nongenunely multimode entangled state. For multimode Gaussian states, we derive a closed form expression of GGM in terms of the symplectic invariants of the reduced states. Following that prescription, the characteristics of GGM for typical three- and four-mode Gaussian states are investigated. In the non-Gaussian paradigm, we compute GGM for photon-added as well as -subtracted states having three- and four-modes and find that both addition and subtraction of photons lead to enhancement of the genuine multimode entanglement content of the state compared to its Gaussian counterpart. Our analysis reveals that when an initial three-mode vacuum state is evolved according to an interacting Hamiltonian, photon addition is more beneficial in increasing GGM compared to photon subtraction while the picture is opposite for four-mode case. Specifically, subtracting photons from four-mode squeezed vacuum states almost always results in higher multimode entanglement content than that of photon addition with both single as well as multimode and constrained as well as unconstrained operations. Furthermore, we observe a novel freezing feature of GGM during some specific cases of photon subtraction with respect to the number of photons subtracted.

Nearly maximal violation of the Mermin-Klyshko inequality with multimode entangled coherent states

Entangled coherent states for multiple bosonic modes, also referred to as multimode cat states, not only are of fundamental interest but also have practical applications. The nonclassical correlation among these modes is well characterized by the violation of the Mermin-Klyshko inequality. We here study Mermin-Klyshko inequality violations for such multi-mode entangled states with rotated quantum-number parity operators. It is shown that the Mermin-Klyshko signal obtained with these operators can approach the maximal value even when the average quantum number in each mode is only 1, and the inequality violation exponentially increases with the number of entangled modes. This is in distinct contrast with the framework based on displaced parity operators, with which a nearly maximal Mermin-Klyshko inequality violation requires the size of the cat state to be increased by about 15 times.

Methods for Derivation of Density Matrix of Arbitrary Multi-Mode Gaussian States from Its Phase Space Representation**Supported by the National Natural Science Foundation of China under Grant Nos 11574400 and 11204379, the Beijing Institute of Technology Research Fund Program for Young Scholars, and the NSFC-ICTP Proposal under Grant No 11981240356.

We present a method for derivation of the density matrix of an arbitrary multi-mode continuous variable Gaussian entangled state from its phase space representation. An explicit computer algorithm is given to reconstruct the density matrix from Gaussian covariance matrix and quadrature average values. As an example, we apply our method to the derivation of three-mode symmetric continuous variable entangled state. Our method can be used to analyze the entanglement and correlation in continuous variable quantum network with multi-mode quantum entanglement states.

Generating Multimode Entangled Microwaves with a Superconducting Parametric Cavity

In this Letter, we demonstrate the generation of multimode entangled states of propagating microwaves. The entangled states are generated by parametrically pumping a multimode superconducting cavity. By combining different pump frequencies, applied simultaneously to the device, we can produce different entanglement structures in a programable fashion. The Gaussian output states are fully characterized by measuring the full covariance matrices of the modes. The covariance matrices are absolutely calibrated using an in situ microwave calibration source, a shot noise tunnel junction. Applying a variety of entanglement measures, we demonstrate both full inseparability and genuine tripartite entanglement of the states. Our method is easily extensible to more modes.

Detecting topology change via correlations and entanglement from gauge/gravity correspondence

We compute a momentum space version of the entanglement spectrum and entanglement entropy of general Young tableau states and one-point functions on Young tableau states. These physical quantities are used to measure the topology of the dual spacetime geometries in the context of gauge/gravity correspondence. The idea that Young tableau states can be obtained by superposing coherent states is explicitly verified. In this quantum superposition, a topologically distinct geometry is produced by superposing states dual to geometries with a trivial topology. Furthermore, we have a refined bound for the overlap between coherent states and the rectangular Young tableau state, by using the techniques of symmetric groups and representations. This bound is exponentially suppressed by the total edge length of the Young tableau. It is also found that the norm squared of the overlaps is bounded above by inverse powers of the exponential of the entanglement entropies. We also compute the overlaps between Young tableau states and other states including squeezed states and multi-mode entangled states which have similarities with those appeared in quantum information theory.

Entanglement properties of multi-cascaded beamsplitter and its applications

Beam splitter,as a kind of linear optics instruments,has many applications such as in quantum optics and quantum information,including the preparation of nonclassical quantum states and entangled state representation.In Heisenberg picture,on the one hand,the relation of input-output of beam splitter can be easily obtained.Especially for the multicascaded beam-splitters,the input-output relation can also be directly obtained by the input-output relation of single beam splitter.On the other hand,we often need to calculate the probabilities of detecting photon number in many cases,thus we need to turn into Schrdinger picture for simplifying our calculation.Based on the equivalence between both pictures,the relation between transformation matrixes connecting these two pictures is derived.That is to say, the transform matrix corresponding to the Schrdinger picture can be obtained by transposing the transform matrix in Heisenberg picture.This concise relation constructs a bridge connecting two pictures and simplifies our calculation in the Schrdinger picture rather than step by step.Using the relation between transform matrixes of both pictures and combining the technique of integration within ordered product of operator,we further consider the coordination representation,normally ordering form and exponential expression of single beam-splitter.Then we further examine the coordination representation,normally ordering form and exponential expression of two-cascaded beam-splitters.As a generalization,the method is extended to the case of multi-cascaded beam-splitters.These investigations provide an effective way to prepare multi-mode entangled states and qubit states.In addition,a general method is shown of obtaining the total operator and its normally ordering form as well as Schmidt decomposition of the linear systems consisting of beam-splitters.As applications,2-cascaded beam-splitters is used to generate a new quantum mechanics representation and prepare the qubit states with the help of conditional measurement.The Schmidt decomposition of three-mode entangled state representation can be directly obtained by the coordination representation of 2-cascaded beam-splitters,which shows the property of entanglement.In addition,based on this representation we can clearly see that when the input states of first beam splitter are two coordinate states,the output states cannot be entangled.This implies that although the coordinate states are nonclassical,the entangled state can not be prepared either.The new proposed quantum mechanics representation will be further used to investigate the optical transformations,including wavelet transformation,Fourier transform,fractional Fourier transform,et al.Therelevant discussion will be our aim in the future research.

Multimode entanglement in reconfigurable graph states using optical frequency combs

Multimode entanglement is an essential resource for quantum information processing and quantum metrology. However, multimode entangled states are generally constructed by targeting a specific graph configuration. This yields to a fixed experimental setup that therefore exhibits reduced versatility and scalability. Here we demonstrate an optical on-demand, reconfigurable multimode entangled state, using an intrinsically multimode quantum resource and a homodyne detection apparatus. Without altering either the initial squeezing source or experimental architecture, we realize the construction of thirteen cluster states of various sizes and connectivities as well as the implementation of a secret sharing protocol. In particular, this system enables the interrogation of quantum correlations and fluctuations for any multimode Gaussian state. This initiates an avenue for implementing on-demand quantum information processing by only adapting the measurement process and not the experimental layout.

Quantum multiparameter estimation with generalized balanced multimode NOON-like states

The simultaneous multi-parameter estimation problem using a class of multi-mode entangled states is investigated in this paper. Specifically, the problem of optical phase imaging is considered and the quantum probe is taken to be a balanced coherent superposition of components with an arbitrary quantum state in one mode and vacuum states in all the other modes, which is a generalization of the multi-mode NOON state. The analytical form for the quantum Cramer-Rao bound (QCRB) is presented, which shows the performance by providing a lower bound of the estimation uncertainty. It is shown that the NOON state has the worst performance among those in the class of the entangled states considered. We also analyze in detail four different scenarios, which are the NOON state, the entangled coherent state, the entangled squeezed coherent state, and the entangled squeezed vacuum state. From the comparison among these four states, we find that when the mean photon number is fixed, the squeezed vacuum state has the smallest QCRB, followed by the squeezed coherent state, entangled coherent state, and NOON state. We also illustrate that the balanced entangled state can perform better than a more generalized unbalanced form studied in previous works for certain scenarios. Finally, we give an experimental setup for producing a two-mode entangled state that can beat the NOON state in quantum metrology.

Quantum state measurement of any arbitrary entangled field-state via Ramsey interferometry

Multipartite entangled states are the key resource and play a crucial role in latest applications of quantum mechanics. We propose a scheme for the measurement of quantum state of multimode entangled field state trapped in multiple cavities. The scheme is based on the measurement of photon statistics of the displaced entangled field state in Ramsey type set-up. In this set-up, the atoms undergo a dispersive phase shift when they pass through the off-resonant entangled field in cavities. By measuring the internal states of the atoms, the photon statistics and the Wigner function can be reconstructed.

Multiplication of a ghost image by means of multimode entangled quantum states

It has been shown that multimode (multifrequency) entangled quantum states of light fields make it possible to simultaneously reconstruct several ghost images of an object from the measurement of the spatial correlation function between photons of the object channel and reconstruction channels, where radiation of a single frequency propagates. The detection of radiation in the object channel does not give information on the object. Calculations have been performed for four-frequency entangled quantum light fields.

Ghost Images with Four-Mode Entangled States

We demonstrate that the use of multimode entangled states of light fields can restore multiple ghost images of the object illuminated by radiation of one of the modes. The analysis, performed on the example of four-mode entangled light fields, is able to obtain three copies of ghost images.

Full characterization of a highly multimode entangled state embedded in an optical frequency comb using pulse shaping

An in-depth analysis of the correlation and entanglement properties of an optical frequency comb produced by a synchronously pumped optical parametric oscillator is presented, providing a unique capability for the continued development of specialized quantum networks within highly multimode structures.