Single-mode Squeezed Vacuum States Research Articles

Optimal quantum metrology of two-photon absorption

Two-photon absorption (TPA) is a nonlinear optical process with wide-ranging applications from spectroscopy to super-resolution imaging. Despite this, the precise measurement and characterisation of TPA parameters are challenging due to their inherently weak nature. We study the potential of single-mode quantum light to enhance TPA parameter estimation through the quantum Fisher information (QFI). Discrete variable quantum states (defined to be a finite superposition of Fock states) are optimised to maximise the QFI for given absorption, revealing a quantum advantage compared to both the coherent state (classical) benchmark and the single-mode squeezed vacuum state. For fixed average energy n¯∈2N , the Fock state is shown to be optimal for large TPA parameters, while a superposition of vacuum and a particular Fock state is optimal for small absorption for all n¯ . This differs from single-photon absorption where the Fock state is always optimal. Notably, photon counting is demonstrated to offer optimal or nearly optimal performance compared to the QFI bound for all levels of TPA parameters for the optimised quantum probes, and their quantum advantage is shown to be robust to single-photon loss. Our findings provide insight into known limiting behaviours of Gaussian probes and their different FI scalings under photon counting ( ∝n¯2 for squeezed vacuum states versus n¯3 for coherent states). The squeezed state outperforms coherent states for small TPA parameters but underperforms in the intermediate regime, becoming comparable in the large absorption limit. This can be explained through fundamental differences between behaviours of even and odd number Fock states: the former’s QFI diverges in both large and small absorption limits, while the latter diverges only in the small absorption limit, dominating at intermediate scales.

Enhancement of the phase sensitivity with two-mode squeezed coherent state based on a Mach-Zehnder interferometer.

We theoretically study the phase estimation based on a Mach-Zehnder interferometer (MZI) with a two-mode squeezed coherent state. By maximizing the quantum Fisher information, we find that the quantum Cramér-Rao bounds (QCRB) can reach sub-Heisenberg limit under the phase-matched condition. The optimal phase sensitivity can reach the sub-shot noise limit (SNL) and approach the QCRB by employing the intensity difference detection. Meanwhile, compared with the MZI fed with a coherent plus a single-mode squeezed vacuum state, this scheme can have better performance by adjusting the squeezing parameter and the mean photon number. With the same parameter, our scheme shows more sensitive phase measurement than the SU(1,1) interferometer with a coherent plus a vacuum state. We also show that the phase sensitivity of our proposal can still reach the SNL when the loss of the photon is 36%. This scheme can provide potential applications in optical sensors.

Continuous-variable (3,3)-threshold quantum secret sharing based on one-sided device-independent security

In this paper, we investigate a feasible scheme for continuous-variable (3,3)-threshold quantum secret sharing (QSS) protocol, which owns unconditional security against arbitrary attacks by an eavesdropper and/or dishonest participants. Our scheme is based on a one-sided device-independent approach. It treats a dealer as a trusted party while treating all participants as untrusted. We demonstrate that the (3,3)-threshold QSS protocol with unconditional security against eavesdropping and/or dishonest participants can be fulfilled by an analog of van Loock-Braunstein (vLB) entangled states, which uses only two single-mode squeezed vacuum states and linear optics. Such a vLB-like entangled state may find its potential applications in multipartite QSS with unconditional security.

Realistic conversion of single-mode squeezed vacuum state to large-amplitude high-fidelity Schrödinger cat states by inefficient photon number resolving detection

We theoretically propose an efficient way to generate optical analogs of both even and odd Schrӧdinger cat states (SCSs) of large amplitude with high fidelity and reasonable generation rate. The resources consumed are a single-mode squeezed vacuum state (SMSV) and possibly a single photon or nothing. We report the generation of even (odd) SCS with amplitude fidelity higher than with success probability a little more than by subtraction of photons from SMSV by ideal photon number detection. In order to reduce the requirements for the sensitivity of photon number resolving (PNR) detector, we show the implementation of even/odd SCSs with the same characteristics with two PNR detectors resolving only photons each instead of In the case of inefficient detector, SCS’s size and its fidelity can be kept close to perfect by using highly transmitting beam splitter, but at the cost of very dramatic reduction of the success probability. In order to have certain harmony between the characteristics (large amplitude, high fidelity and acceptable success probability) in the case of imperfect detection, highly transmitting beam splitters should not be used and number of the subtracted photons must be reduced to

Evaluating the quantum Ziv-Zakai bound for phase estimation in noisy environments.

In the highly non-Gaussian regime, the quantum Ziv-Zakai bound (QZZB) provides a lower bound on the available precision, demonstrating the better performance compared with the quantum Cramér-Rao bound. However, evaluating the impact of a noisy environment on the QZZB without applying certain approximations proposed by Tsang [Phys. Rev. Lett.108, 230401 (2012)10.1103/PhysRevLett.108.230401] remains a difficult challenge. In this paper, we not only derive the asymptotically tight QZZB for phase estimation with the photon loss and the phase diffusion by invoking the variational method and the technique of integration within an ordered product of operators, but also show its estimation performance for several different Gaussian resources, such as a coherent state (CS), a single-mode squeezed vacuum state (SMSVS) and a two-mode squeezed vacuum state (TMSVS). In this asymptotically tight situation, our results indicate that compared with the SMSVS and the TMSVS, the QZZB for the CS always shows the better estimation performance under the photon-loss environment. More interestingly, for the phase-diffusion environment, the estimation performance of the QZZB for the TMSVS can be better than that for the CS throughout a wide range of phase-diffusion strength. Our findings will provide an useful guidance for investigating the noisy quantum parameter estimation.

Entangled states shaping with CV states of definite parity

We present a new method to entangle continuous variable (CV) states of certain parity and photonic states for the purpose of generating optical hybrid cluster (HC) states. To do it we introduce two families of the CV states of definite parity which stems from single mode squeezed vacuum (SMSV) state. Potential to apply the CV states of certain parity is high. We report on the generation of the even/odd Schrödinger cat state like (SCS-like) states whose fidelities with even/odd SCS of amplitude of 4.2 are more of 0.99, when 30,31 photons are detected in auxiliary mode of input SMSV state initially mixed with single photon. We show that the quantum efficiency of a photon number resolving (PNR) detector is crucial to maintaining the success rate of even/odd SCSs generator at an acceptable level. The scheme with delocalized photon implements deterministic imperfect entanglement operation between macro and micro states. We show that the beam splitter implements the two-qubits operation control-Z (CZ) for input CV states of definite parity and photonic states, provided that certain result is detected in measurement mode. An extension of the entangling operation for two entangled delocalized photons (TEDP) allows one to realize three-qubit HC state. Seven-qubit HC state is the result of conjunction of two three-qubit HC states through TEDP state.

Preparation of nonclassical states by displacement-based quantum scissors

We theoretically study the statistical properties of non-Gaussian states generated by inputting coherent state, single-mode squeezed vacuum state and thermal state to the displacement-based single-side quantum scissor. Compared to the case without the displacement, it is shown that the displacement-based single-side quantum scissor with large coherent amplitudes can not only effectively enhance the success probability of quantum state preparation in the high-transmittance range, but also improve the statistical properties of the generated states involving the average photon number, the signal to noise ratio and the nonclassicality. These results indicate that the usage of the displacement-based single-side quantum scissor may have potential applications for the optical interferometry.

Optimal distributed quantum sensing using Gaussian states

We find and investigate the optimal scheme of quantum distributed Gaussian sensing for estimation of the average of independent phase shifts. We show that the ultimate sensitivity is achievable by using an entangled symmetric Gaussian state, which can be generated using a single-mode squeezed vacuum state, a beam-splitter network, and homodyne detection on each output mode in the absence of photon loss. Interestingly, the maximal entanglement of a symmetric Gaussian state is not optimal although the presence of entanglement is advantageous as compared to the case using a product symmetric Gaussian state. It is also demonstrated that when loss occurs, homodyne detection and other types of Gaussian measurements compete for better sensitivity, depending on the amount of loss and properties of a probe state. None of them provide the ultimate sensitivity, indicating that non-Gaussian measurements are required for optimality in lossy cases. Our general results obtained through a full-analytical investigation will offer important perspectives to the future theoretical and experimental study for quantum distributed Gaussian sensing.

Vibrational enhancement of quadrature squeezing and phase sensitivity in resonance fluorescence

Vibrational environments are commonly considered to be detrimental to the optical emission properties of solid-state and molecular systems, limiting their performance within quantum information protocols. Given that such environments arise naturally it is important to ask whether they can instead be turned to our advantage. Here we show that vibrational interactions can be harnessed within resonance fluorescence to generate optical states with a higher degree of quadrature squeezing than in isolated atomic systems. Considering the example of a driven quantum dot coupled to phonons, we demonstrate that it is feasible to surpass the maximum level of squeezing theoretically obtainable in an isolated atomic system and indeed come close to saturating the fundamental upper bound on squeezing from a two-level emitter. We analyse the performance of these vibrationally-enhanced squeezed states in a phase estimation protocol, finding that for the same photon flux, they can outperform the single mode squeezed vacuum state.

Distillation of single-mode-squeezed entangled state in presence of strong squeezing

Recently, the strong single-mode squeezed vacuum state of light with $-15$−15 dB of classic noise has been created [Phys. Rev. Lett.117, 110801 (2016)10.1103/PhysRevLett.117.110801]. This is an important resource in continuous variable (CV) quantum communication and fault-tolerant quantum computing. Nevertheless, strong squeezing means a non-negligible population in high-photon-number subspace and may pose a strong challenge to photon-based technology, for example, entanglement distillation. Entanglement distillation is an efficient method for retrieving a higher quality of entanglement from a weakly entangled state. Up till now, almost all the schemes for entanglement distillation are restricted to the low-squeezing regime. The distillation of strong-squeezing induced entanglement is an interesting but open topic in the near future. Here, we take the single-mode squeezed entangled state (SMSE) as an example and show that conventional photon subtraction based distillation fails to generate a higher quality of entanglement with experimentally feasible optical beam splitters. To this point, we show that the superposition of photon annihilation and creation could be an effective method. A practical scheme for implementing such a superposition with on-line squeezing is suggested. Our method is verified numerically by the calculation of a 25 dB SMSE state with an ideal photon detector and for distillation of 20.5 dB SMSE state with practical dichotic on-off detectors. The analysis of the distillation of the strong squeezing effect could be extended straightforwardly to other squeezing-based quantum information processing, such as quantum metrology and quantum illumination.

New approach to the fidelity of quantum teleportation based on the entangled state generated by beam splitter

Entangled states play an important role in quantum computation and quantum information processing. Beam splitter, a linear device, is often used to prepare entangled states and quantum mechanics representations. For any two input states, the formula for the fidelity is derived, including the Q function representation, the P function representation, and the Wigner function representation, by using the output states from beam splitter as a source of quantum teleportation. This provides a new way to calculate the fidelity. As applications, two single-mode squeezed vacuum states and coherent superposition state together with coherent state are used as inputs, and the fidelity for teleporting coherent state is discussed. Our method provide more alternatives for calculating fidelity of teleportaion.

Nonclassical properties of induced states from single-mode squeezed vacuum state related with Hermite excited elementary superposition operation

Based on single-mode squeezed vacuum state (SVS) and Hermite-excited elementary superposition operator $ H_{m} (xa^{\dagger}+ya)$ , we induce two new quantum states, i.e., Hermite-excited squeezed vacuum state (HSVS) and Hermite-excite-orthogonalized squeezed vacuum state (HOSVS). HSVS is obtained by applying the operator on SVS and HOSVS is obtained by applying the orthogonalizer on SVS, where HSVS is just HOSVS for odd m. We study and compare mathematical and nonclassical properties for SVS, HSVS and HOSVS, including photon number distribution, Mandel’s Q parameter, quadrature squeezing, and Wigner function. Numerical results show that i) HSVS and HOSVS have only even (odd) photon components for even (odd) m; ii) HSVS and HOSVS can exhibit sub-Poissonian statistics in low-squeezing parameter regime and squeezing effect in large-squeezing parameter regime; iii) moreover, squeezing is always incompatible with sub-Poissonianity; iv) Wigner functions for HSVS and HOSVS have negative values in phase space.

Single-mode squeezed vacuum state orthogonalization via photon-addition operation

We construct some orthogonal states for single-mode squeezed vacuum state (SVS) and study their nonclassicality by virtue of the quadrature squeezing and the Wigner function. The orthogonalizer is based on the photon-addition operation, i.e., the repeated (m times) application of the photon creation operator. The orthogonal state and the photon-addition single-mode SVS are same for odd m but different for even m. The squeezing effect of the orthogonal states will exhibit when the origin squeezing parameter is greater than a certain value. Moreover, the negativity of the Wigner function shows their nonclassicality.

Preparation and properties of a non-classical state by quantum catalysis and two-mode squeezing

In this work, we propose a scheme for generating non-classical quantum catalyzed states, named Laguerre polynomial-weighted squeezed states, via inputting a single-mode squeezed vacuum state and an m-photon Fock state by quantum catalysis and two-mode squeezing. The non-classical properties of the generated catalyzed state are investigated using the degree of squeezing and Wigner function. It is found that these non-classical properties, including squeezing degree and the negativity of the Wigner function, can be improved and modulated by both squeezing parameters and the catalyzed photon number.

Entanglement of coherent superposition of photon-subtraction squeezed vacuum

A new kind of non-Gaussian quantum state is introduced by applying nonlocal coherent superposition (τa + sb) m of photon subtraction to two single-mode squeezed vacuum states, and the properties of entanglement are investigated according to the degree of entanglement and the average fidelity of quantum teleportation. The state can be seen as a single-variable Hermitian polynomial excited squeezed vacuum state, and its normalization factor is related to the Legendre polynomial. It is shown that, for τ = s, the maximum fidelity can be achieved, even over the classical limit (1/2), only for even-order operation m and equivalent squeezing parameters in a certain region. However, the maximum entanglement can be achieved for squeezing parameters with a π phase difference. These indicate that the optimal realizations of fidelity and entanglement could be different from one another. In addition, the parameter τ/s has an obvious effect on entanglement and fidelity.

Hermite polynomial excited squeezed vacuum state: Generation and nonclassical properties

We proposed a theoretical scheme for generating a new kind of non-Gaussian state—Hermite polynomial excited squeezed vacuum states—by using parametric amplifier process and conditional measurement. Specially, two different single-mode squeezed vacuum states were injected into the signal and idler ports of parametric amplifier and m-photon was detected in idler output port, then the new non-Gaussian state is generated in signal port. It's normalization factor is found to be related with Legendre polynomials that corresponds to the success probability of such event. We investigated the nonclassical properties according to photon-number distribution, sub-Poissonian distribution, anti-bunching effect, quadrature squeezing effect, and Wigner function. It is shown that there is a wide range of nonclassical phenomena created by tuning the interaction parameters. Our study may provide a theoretical reference to generate nonclassical state for experiment.

Synthesis of the Einstein-Podolsky-Rosen entanglement in a sequence of two single-mode squeezers.

We propose and implement a new scheme of generating the optical Einstein-Podolsky-Rosen entangled state. Parametric down-conversion in two nonlinear crystals, positioned back-to-back in the waist of a pump beam, produces single-mode squeezed vacuum states in orthogonal polarization modes; a subsequent beam splitting entangles them and generates the Einstein-Podolsky-Rosen state. The technique takes advantage of the strong nonlinearity associated with type-0 phase-matching configuration while, at the same time, eliminating the need for actively stabilizing the optical phase between the two single-mode squeezers. We demonstrate our method, preparing a 1.4 dB two-mode squeezed state and characterizing it via two-mode homodyne tomography.

Synthesis of Hermite polynomial excited squeezed vacuum states from two separate single-mode squeezed vacuum states

A projection synthesis scheme for generating Hermite polynomial excited squeezed vacuum states (HPESVSs, non-Gaussian quantum states) is proposed. Injecting two separate single-mode squeezed vacuum states into a beam splitter and counting the photons in one of the output channels (conditional measurement or post-detection), the conditional state in the other channel is just the HPESVS. The success probability, related to a Legendre polynomial form, is obtained analytically and analyzed numerically in detail. To exhibit the nonclassical effects of this conditional state, we also present the photon-number distribution, sub-Poissionian distribution, anti-bunching effect, quadrature squeezing effect, and Wigner function, respectively. The results show that by tuning the interaction parameters, a wide range of nonclassical phenomena can be created.

Non-Gaussian entangled states and quantum teleportation of Schrödinger-cat states**A review in honor of V Manko and M Manko.

In continuous-variable quantum information, non-Gaussian entangled states that are obtained from Gaussian entangled states via photon subtraction are known to contain more entanglement. This makes them better resources for quantum information processing protocols, such as, quantum teleportation. We discuss the teleportation of non-Gaussian, non-classical Schrödinger-cat states of light using two-mode squeezed vacuum light that is made non-Gaussian via subtraction of a photon from each of the two modes. We consider the experimentally realizable cat states produced by subtracting a photon from the single-mode squeezed vacuum state. We discuss two figures of merit for the teleportation process, (a) the fidelity, and (b) the maximum negativity of the Wigner function at the output. We elucidate how the non-Gaussian entangled resource lowers the requirements on the amount of squeezing necessary to achieve any given fidelity of teleportation, or to achieve negative values of the Wigner function at the output.

Preparing ground states and squeezed states of nanomechanical cantilevers by fast dissipation

We propose a protocol that enables strong coupling between a flux qubit and the quantized motion of a magnetized nanomechanical cantilever. The flux qubit is driven by microwave fields with suitable parameters to induce sidebands, which will lead to the desired coupling. We show that the nanomechanical modes can be cooled to the ground states and the single-mode squeezed vacuum states can be generated via fast dissipation of the flux qubit. In our scheme, the qubit decay plays a positive role and can help drive the system to the target states.