Two-mode Squeezed Vacuum State Research Articles

Two-axis two-spin squeezed states

The states generated by the two-spin generalization of the two-axis countertwisting Hamiltonian are examined. We analyze the behavior at both short and long timescales, by calculating various quantities such as squeezing, spin expectation values, probability distributions, entanglement, Wigner functions, and Bell correlations. In the limit of large spin ensembles and short interaction times, the state can be described by a two-mode squeezed vacuum state; for qubits, Bell state entanglement is produced. We find that the Hamiltonian approximately produces two types of spin-EPR states, and the time evolution produces aperiodic oscillations between them. In a similar way to the basis invariance of Bell states and two-mode squeezed vacuum states, the Fock state correlations of spin-EPR states are basis invariant. We find that it is possible to violate a Bell inequality with such states, although the violation diminishes with increasing ensemble size. Effective methods to detect entanglement are also proposed, and formulas for the optimal times to enhance various properties are calculated.

Nonlinear phase estimation enhanced by an actively correlated Mach-Zehnder interferometer

A nonlinear phase shift is introduced to a Mach-Zehnder interferometer (MZI), and we present a scheme for enhancing the phase sensitivity. In our scheme, one input port of a standard MZI is injected with a coherent state and the other input port is injected with one mode of a two-mode squeezed-vacuum state. The final interference output of the MZI is detected with the method of active correlation output readout. Based on the optimal splitting ratio of beam splitters, the phase sensitivity can beat the standard quantum limit and approach the quantum Cram\'{e}r-Rao bound. The effects of photon loss on phase sensitivity are discussed. Our scheme can also provide some estimates for units of $\chi^{(3)}$, due to the relation between the nonlinear phase shift and the susceptibility $\chi^{(3)}$ of the Kerr medium.

Quantum entanglement and teleportation in superposition of multiple-photon-added two-mode squeezed vacuum state

In this paper, a new state called superposition of multiple-photon-added two-mode squeezed vacuum state (SMPA-TMSVS) is introduced by adding the multiple photons to both modes of a two-mode squeezed vacuum state (TMSVS). We explicitly investigate the degree of quantum entanglement, the Einstein–Podolsky–Rosen (EPR) correlation and the quantum steering in the SMPA-TMSVS. The results show in the SMPA-TMSVS that the degree of entanglement and the EPR correlation can be enhanced by nonlocal adding photons to a TMSVS. The quantum steering appears in the SMPA-TMSVS in case the superposition of single-photon addition [Formula: see text], in which mode [Formula: see text] can steer mode [Formula: see text]. By using the SMPA-TMSVS as an entangled resource, the quantum teleportation process is studied in detail based on the Vaidman–Braunstein–Kimble (VBK) protocol.

Optimal quantum phase estimation with generalized multi-component Schrödinger cat states

In this paper, we are interested in detecting the presence of a nearby phase-sensitive object, where traveling light works out under a low-photon loss rate. Here we investigate the optimal quantum phase estimation with generalized multi-component Schrödinger cat states. In addition, we show the optimal conditions of the generalized multi-component cat states for the phase estimation in a lossless scenario. We then demonstrate that the generalized multi-component cat states can beat the performances of the NOON and two-mode squeezed vacuum states in the presence of small loss, while maintaining the quantum advantage over the standard quantum limit, attainable by coherent states. Finally, we propose a generation scheme of the entangled multi-component cat states with current or near-term optical technologies.

Probing Spin Correlations in a Bose-Einstein Condensate Near the Single-Atom Level.

Using parametric conversion induced by a Shapiro-type resonance, we produce and characterize a two-mode squeezed vacuum state in a sodium spin 1 Bose-Einstein condensate. Spin-changing collisions generate correlated pairs of atoms in the m=±1 Zeeman states out of a condensate with initially all atoms in m=0. A novel fluorescence imaging technique with sensitivity ΔN∼1.6 atom enables us to demonstrate the role of quantum fluctuations in the initial dynamics and to characterize the full distribution of the final state. Assuming that all atoms share the same spatial wave function, we infer a squeezing parameter of 15.3dB.

Nonclassicality and entanglement properties of non-Gaussian entangled states via a superposition of number-conserving operations

We theoretically investigate the nonclassicality and entanglement properties of non-Gaussian entangled states generated by using a number-conserving generalized superposition of products (GSP), i.e., $$\left( saa^{\dag }+ta^{\dag }a\right) ^{m}$$ with $$s^{2}+t^{2}=1$$ on each mode of an input two-mode squeezed coherent (TMSC) state. The simulation results show that, compared to the typical two-mode squeezed vacuum state, the usage of small coherent amplitude is conductive to offering an opportunity for not only effectively enhancing the nonclassicality in terms of antibunching effect and Wigner function, but also significantly improving the entanglement quantified by Einstein–Podolsky–Rosen correlation and Hillery–Zubairy correlation. For the increase of the number of operations, the region of both the existing antibunching effect and the improved entanglement decreases, but this region of the improved teleportation fidelity and the negative distribution of the Wigner function is on the increase. Under an ideal Braunstein and Kimble teleportation protocol, when the generated states are treated as an entangled resource, the optimal teleportation fidelity can be achieved by taking a suitable squeezing parameter and the number of operations for the optimal choices of s. In order to highlight the advantages of the use of the GSP-embedded TMSC, under the same parameters, we also make a comparison about the performances of both the entanglement and the fidelity for different non-Gaussian entangled states, involving the photon-subtracted-then-added TMSC states and the photon-added-then-subtracted TMSC states. It is found that in the regime of small squeezing values, both of the entanglement and the fidelity for the generated states can perform better than the other cases.

Fundamental limits of quantum illumination

In quantum illumination (QI), a signal beam initially entangled with an idler beam held at the receiver interrogates a target region bathed in thermal background light. The returned beam is measured jointly with the idler in order to determine whether a weakly reflecting target is present. Using tools from quantum information theory, we derive lower bounds on the average error probability of detecting both specular and fading targets and on the mean squared error of estimating the reflectance of a detected target, which are obeyed by any QI transmitter satisfying a signal energy constraint. For bright thermal backgrounds, we show that the QI system using multiple copies of low-brightness two-mode squeezed vacuum states is nearly optimal. More generally, our results place limits on the best possible performance achievable using QI systems at all wavelengths, and at all signal and background noise levels.

In situ characterization of linear-optical networks in randomized boson sampling

We introduce a method for efficient, in situ characterization of linear-optical networks (LONs) in randomized boson-sampling (RBS) experiments. We formulate RBS as a distributed task between two parties, Alice and Bob, who share two-mode squeezed-vacuum states. In this protocol, Alice performs local measurements on her modes, either photon counting or heterodyne. Bob implements and applies to his modes the LON requested by Alice; at the output of the LON, Bob performs photon counting, the results of which he sends to Alice via classical channels. In the ideal situation, when Alice does photon counting, she obtains from Bob samples from the probability distribution of the RBS problem, a task that is believed to be classically hard to simulate. When Alice performs heterodyne measurements, she converts the experiment to a problem that is classically efficiently simulable, but more importantly, enables her to characterize a lossy LON on the fly, without Bob's knowing and without changing anything at Bob's end (this is what we mean by in situ). We introduce and calculate the fidelity between the joint states shared by Alice and Bob after the ideal and lossy LONs as a measure of distance between the two LONs. Using this measure, we obtain an upper bound on the total variation distance between the ideal probability distribution for the RBS problem and the probability distribution achieved by a lossy LON. Our method displays the power of the entanglement of the two-mode squeezed-vacuum states: the entanglement allows Alice to choose for each run of the experiment between RBS and a simple characterization protocol based on first-order coherence between complex amplitudes.

Continuous-variable quantum repeater based on quantum scissors and mode multiplexing

Quantum repeaters are indispensable for high-rate, long-distance quantum communications. The vision of a future quantum internet strongly hinges on realizing quantum repeaters in practice. Numerous repeaters have been proposed for discrete-variable (DV) single-photon-based quantum communications. Continuous variable (CV) encodings over the quadrature degrees of freedom of the electromagnetic field mode offer an attractive alternative. For example, CV transmission systems are easier to integrate with existing optical telecom systems compared to their DV counterparts. Yet, repeaters for CV have remained elusive. We present a novel quantum repeater scheme for CV entanglement distribution over a lossy bosonic channel that beats the direct transmission exponential rate-loss tradeoff. The scheme involves repeater nodes consisting of a) two-mode squeezed vacuum (TMSV) CV entanglement sources, b) the quantum scissors operation to perform nondeterministic noiseless linear amplification of lossy TMSV states, c) a layer of switched, mode multiplexing inspired by second-generation DV repeaters, which is the key ingredient apart from probabilistic entanglement purification that makes DV repeaters work, and d) a non-Gaussian entanglement swap operation. We report our exact results on the rate-loss envelope achieved by the scheme.

Finite-dimensional quantum states generated by conditional measurements on beam splitters

In this work, the basic idea of the quantum scissors (QS) device is slightly modified to generate finite-dimensional quantum states by means of conditional measurements on beam splitters (BSs). It turns out that a QS device with two single-photon inputs and two single-photon detections is just a projection operator composed of the vacuum state, one-photon state, and two-photon state, depending upon the transmission coefficients of BSs. As the most general example, we consider the squeezed coherent state as the input state and derive the analytical expression of the output state. Its nonclassical characteristics are analyzed in detail by means of the average photon number, intensity gain, and Wigner function. In addition, we extend this technique to the two-mode squeezed vacuum state (TMSVS). The resulting state is just the generalized Bell state, containing only the twin vacuum, twin one-photon, and twin two-photon components, whose entanglement properties are quantified by the von Neumann entropy and Einstein–Podolsky–Rosen correlation. The results show that the entanglement of the truncated TMSVS is stronger than that of TMSVS within a certain range of squeezing parameter and transmissivity.

Practical Route to Entanglement-Assisted Communication Over Noisy Bosonic Channels

Entanglement offers substantial advantages in quantum information processing, but loss and noise hinder its applications in practical scenarios. Although it has been well known for decades that the classical communication capacity over lossy and noisy bosonic channels can be significantly enhanced by entanglement, no practical encoding and decoding schemes are available to realize any entanglement-enabled advantage. Here, we report structured encoding and decoding schemes for such an entanglement-assisted communication scenario. Specifically, we show that phase encoding on the entangled two-mode squeezed vacuum state saturates the entanglement-assisted classical communication capacity over a very noisy channel and overcomes the fundamental limit of covert communication without entanglement assistance. We then construct receivers for optimum hypothesis testing protocols under discrete phase modulation and for optimum noisy phase estimation protocols under continuous phase modulation. Our results pave the way for entanglement-assisted communication and sensing in the radio-frequency and microwave spectral ranges.

Suppression of quantum noise by two-mode squeezed states for photon propagation under conditions of electromagnetically induced transparency and four-wave mixing

Quantum vacuum noise is very detrimental for photon propagation and optical quantum memory, which particularly occurs in optically thick atomic media working under the condition of electromagnetically induced transparency (EIT) accompanied by a process of four-wave mixing (FWM). The suppression of quantum vacuum noise becomes now an imperative task for advancing the research and application of quantum memory. Here we present a scheme to suppress quantum vacuum noise and hence to improve the fidelity of photon propagation, by assuming that signal and idler laser fields are initially prepared in a two-mode squeezed vacuum state. With such a scheme, we show that the normal gain mode inherent in the EIT-based FWM system, which contributes optical gain to both the signal and idler fields, can be largely inhibited, giving rise to a significant suppression of the quantum vacuum noise along with their amplification and hence a large enhancement of the fidelity for photon propagation. The results reported here may have promising applications for high-fidelity quantum information processing and transformation, especially for improving the quality of multimode optical quantum memory based on EIT techniques.

Changing Fock matrix elements of two-mode squeezed vacuum state by employing three conditional operations in one-sided lossy channel

This paper focuses on changing Fock matrix elements of two-mode squeezed vacuum state (TMSVS) by employing three conditional operations in one-sided lossy channel. These three conditional operations include one-photon replacement (OPR), one-photon substraction (OPS) and one-photon addition (OPA). Indeed, three conditional quantum states have been generated from the original TMSVS. Using the characteristic function (CF) representation of quantum density operator, we derive the analytical expressions of their Fock matrix elements, which depend on the interaction parameters, including the squeezing parameter of the input TMSVS, the loss factor and the transmissivity of the variable beam splitter. For convenience of discussion, we only give the Fock matrices in the subspace span for these two-mode states. Obviously, the TMSVS only has the populations in and in such subspace. By comparing the generated states with the TMSVS, we find that: (1) the generated state after OPR will remain the populations in and , and add the populations in and (2) the generated state after OPS will lost the populations in and , but add the populations in and (3) the generated state after OPA will remain the population only in and add the population in .

Generation and control of frequency-dependent squeezing via Einstein–Podolsky–Rosen entanglement

Quantum noise-limited displacement sensors such as gravitational wave detectors can be improved by using non-classical light1. This has been achieved in limited bands and in a single quadrature (that is, only one of a pair of conjugate variables) by injecting single-mode squeezed vacuum states2,3. Quantum noise in gravitational wave detectors, however, results from input noise in both quadratures, with the dominant quadrature being a function of Fourier frequency. Broadband reduction of this noise via squeezed light injection then requires a method of rotating this quadrature. This can be accomplished with a low-loss, all-pass optical filter with bandwidth in the low audio frequencies4,5, a substantial technical challenge. We present a proof-of-principle demonstration of a recent proposal6 to use two-mode squeezed vacuum states with Einstein–Podolsky–Rosen (EPR) entanglement, which allows the gravitational detector to simultaneously serve as the optical filter, eliminating the need for a separate apparatus. Einstein–Podolsky–Rosen entangled beams are sent to a 0.5-m-long optical resonator. To reduce quantum noise in a frequency-dependent manner in the gravitational detector, two-mode frequency-dependent squeezed vacuum states are generated.

Optical enhanced interferometry with two-mode squeezed twin-Fock states and parity detection**Project supported by the National Natural Science Foundation of China (Grant No. 11404040) and Qing Lan Project of the Higher Educations of Jiangsu Province of China.

We theoretically investigate the quantum enhanced metrology using two-mode squeezed twin-Fock states and parity detection. Our results indicate that, for a given initial squeezing parameter, compared with the two-mode squeezed vacuum state, both phase sensitivity and resolution can be enhanced when the two-mode squeezed twin-Fock state is considered as an input state of a Mach–Zehnder interferometer. Within a constraint on the total photon number, although the two-mode squeezed vacuum state gives the better phase sensitivity when the phase shift φ to be estimated approaches to zero, the phase sensitivity offered by these non-Gaussian entangled Gaussian states is relatively stable with respect to the phase shift itself. When the phase shift slightly deviates from φ = 0, the phase sensitivity can be still enhanced by the two-mode squeezed twin-Fock state over a broad range of the total mean photon number where the phase uncertainty is still below the quantum standard noise limit. Finally, we numerically prove that the quantum Cramér–Rao bound can be approached with the parity detection.

Application of photon-added two-mode squeezed vacuum states to phase estimation based on Mach-Zehnder interferometer

Quantum metrology is to estimate accurately the value of an unknown parameter with the assistance of the quantum effects, in order to break through the standard quantum limit, even reach the Heisenberg limit. In this work, we study the performance of a general photon-added two-mode squeezed vacuum state that is taken as a detection state of a Mach-Zehnder interferometer. Based on quantum Fisher information, within the constraint on the total mean photon number, symmetric and asymmetric photon addition cannot improve the ultimate phase sensitivity. However, for a given initial squeezing parameter, on this occasion, the symmetric and asymmetric photon addition can improve the ultimate phase sensitivity. Compared with the asymmetric photon-added two-mode squeezed vacuum state, the symmetric one can well improve the ultimate phase sensitivity. This may be because it is always better to implement the symmetric photon addition rather than the asymmetric one in order to increase the mean photon number of the resulting state. On the other hand, via parity detection, the symmetric and asymmetric photon-added two-mode squeezed vacuum state can indeed improve the phase sensitivity of a Mach-Zehnder interferometer for a given initial squeezing parameter. Based on the parity detection, within a constraint on the mean photon number, although the two-mode squeezed vacuum state can give the better phase sensitivity at the optimal phase shift (<i>φ</i> = 0), the phase sensitivity offered by the symmetric and asymmetric photon-added two-mode squeezed vacuum states are both more stable around <i>φ</i> = 0 than by the two-mode squeezed vacuum state. In addition, we show that for the symmetric photon-added two-mode squeezed vacuum state, parity detection is an optimal detection only when the optimal phase shift approaches to zero. When the phase shift slightly deviates from zero, the parity detection is not an optimal detection scheme. Finally, for all values of the phase shift, our results also clearly show that the parity detection is not an optimal detection scheme for the asymmetric photon-added two-mode squeezed vacuum state serving as an interferometer state.

Entanglement properties of a tunable non-Gaussian quantum state by virtue of multi-photon conditional measurement

In this work, we present a theoretical scheme for generating a new kind of tunable non-Gaussian entangled state, by means of beam splitters and multi-photon conditional measurement with two-mode squeezed vacuum state (TMSVS) inputs. The output state is proven to be two-variable Hermite polynomial excited squeezed vacuum states, whose success probability of detection relates to the Jacobi polynomials. We then mainly study the entanglement properties of the output state for the symmetric case quantified by the von Neumann entropy and Einstein–Podolsky–Rosen correlation. It is shown that the entropy of entanglement is valid for verifying the improvement of entanglement within a certain range of squeezing parameter and transmissivity, and the resulting state case may possess a stronger correlation than the initial TMSVS by increasing the transmissivity or photon number of detection. In addition, the violation of the Clauser–Horne–Shimony–Holt (CHSH) inequality for the output state is also evaluated in terms of Wigner representation in phase space. It is found that the negative region of Wigner function distribution becomes more visible with the increase of the photon number of detection, and the degree of the violation of the CHSH inequality significantly increases as the photon number of detection for the symmetrical case increases. The resulting state with highly nonclassical characteristics will provide a useful application in the fields of quantum information processing.

Multiphoton quantum-state engineering using conditional measurements

The quantum theory of electromagnetic radiation predicts characteristic statistical fluctuations for light sources as diverse as sunlight, laser radiation, and molecule fluorescence. Indeed, these underlying statistical fluctuations of light are associated with the fundamental physical processes behind their generation. In this contribution, we experimentally demonstrate that the manipulation of the quantum electromagnetic fluctuations of two-mode squeezed vacuum states leads to a family of quantum-correlated multiphoton states with tunable mean photon numbers and degree of correlation. Our technique relies on the use of conditional measurements to engineer the excitation mode of the field through the simultaneous subtraction of photons from two-mode squeezed vacuum states. The experimental generation of nonclassical multiphoton states by means of photon subtraction unveils novel mechanisms to control fundamental properties of light. As a remarkable example, we demonstrate the engineering of a quantum state of light with up to ten photons, exhibiting nearly Poissonian photon statistics, that constitutes an important step towards the generation of entangled lasers. Our technique enables a robust protocol to prepare quantum states with multiple photons in high-dimensional spaces and, as such, it constitutes a novel platform for exploring quantum phenomena in mesoscopic systems.

A quantum secure direct communication protocol using entangled beam pairs

We propose a feasible high-dimensional two-step quantum secure direct communication scheme by using the Einstein-Podolsky-Rosen entangled beam pair. Accoding to the quality of the two superposition forms of the EPR entangled state (two-mode squeezed vacuum state), we select the mutually unbiased bases for quantum measurement. With the unitary operation, we can subtly encode the confidential information in the quantum state. We also conducted a more detailed analysis of the security of this protocol.

Measurement-induced nonclassical state from two-mode squeezed vacuum states via beam splitter and its entanglement properties

A theoretical scheme of generating a new kind of two-mode non-Gaussian entangled state is presented by means of beam splitters (BSs) and conditional measurement. Here, after detecting photon numbers at the output port of each BS with two kinds of two-mode squeezed vacuum-state inputs, the output state is proved to be two-variable Hermite polynomial excited squeezed vacuum states. Its success probability of detection, namely, normalization factor, is derived in compact expression related to the Jacobi polynomials. Based on the general expression of expectation value, the statistical properties are discussed by exploring the cross-correlation function and anti-bunching effect. The entanglement properties are also investigated by using the Shchukin–Vogel criteria and Einstein–Podolsky–Rosen correlation. The results show that the entanglement of the output state can be enhanced with the increasing photon detection number under the condition of simultaneously detecting the same photon number at the two output ports, which may have good potential for applications in the field of quantum information processing.