Le-Man Kuang, Ai-Hua Zeng, Zhen-Hua Kuang
A method for producing entangled squeezed states (ESSs) for atomic Bose-Einstein condensates (BECs) is proposed by using a BEC with three internal states and two classical laser beams. We show that it is possible to generate two-state and multi-state ESSs under certain circumstances.
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We prove that a pure entangled state of two subsystems with equal spin is equivalent to a two-mode spin-squeezed state under local operations except for a set of bipartite states with measure zero, and we provide a counterexample to the generalization of this result to two subsystems of unequal spin.
This theoretical proposal investigates how resonant interactions occurring when a harmonic oscillator is fed with a stream of entangled qubits allow us to stabilize squeezed states of the harmonic oscillator. We show that the properties of the squeezed state stabilized by this engineered reservoir, including the squeezing strength, can be tuned at will through the parameters of the "input" qubits, albeit in tradeoff with the convergence rate. We also discuss the influence of the type of entanglement in the input, from a pairwise case to a more widely distributed case. This paper can be read in…
We study a continuous-variable entangled state composed of two states which are squeezed in two opposite quadratures in phase space. Various entanglement conditions are tested for the entangled squeezed state and we study decoherence models for noise, producing a mixed entangled squeezed state. We briefly describe a probabilistic protocol for entanglement swapping based on the use of this class of entangled states and the main features of a general generation scheme.
We study the dissipative preparation of many-body entangled Gaussian states in bosonic lattice models which could be relevant for quantum technology applications. We assume minimal resources, represented by systems described by particle-conserving quadratic Hamiltonians, with a single localized squeezed reservoir. We show that in this way it is possible to prepare, in the steady state, the wide class of pure states which can be generated by applying a generic passive Gaussian transformation on a set of equally squeezed modes. This includes non-trivial multipartite entangled states such as clus…
In this study, we explore the theoretical application of entangled multi-mode squeezed light for label-free optical super-resolution imaging. By generating massively entangled multi-mode squeezed light through an array of balanced beam splitters, using a single-mode squeezed light input, we create a multi-mode quantum light state with exceptional entanglement and noise suppression below the shot noise level. This significantly reduces imaging measurement errors compared to classical coherent state light imaging when the same number of photons are used on the imaging sample. We demonstrate how …
Photon-number correlation measurements are performed on bright squeezed vacuum states using a standard Bell-test setup, and quantum correlations are observed for conjugate polarization-frequency modes. We further test the entanglement witnesses for these states and demonstrate the violation of the separability criteria, which infers that all the macroscopic Bell states, containing typically $10^6$ photons per pulse, are polarization entangled. The study also reveals the symmetry of macroscopic Bell states with respect to local polarization transformations.
Squeezed state of light is one of the important subjects in quantum optics which is generated by optical nonlinear interactions. In this paper, we especially focus on qubit like entangled squeezed states (ESS's) generated by beam splitters, phase-shifter and cross Kerr nonlinearity. Moreover the Wigner function of two-mode qubit and qutrit like ESS are investigated. We will show that the distances of peaks of Wigner functions for two-mode ESS are entanglement sensitive and can be a witness for entanglement. Like the qubit cases, monogamy inequality is fulfilled for qutrit like ESS. These trend…
We study the exact decoherence dynamics of the entangled squeezed state of two single-mode optical fields interacting with two independent and uncorrelated environments. We analyze in detail the non-Markovian effects on the entanglement evolution of the initially entangled squeezed state for different environmental correlation time scales. We find that the environments have dual actions on the system: backaction and dissipation. In mparticular, when the environmental correlation time scale is comparable to the time scale for significant change in the system, the backaction would counteract the…
It has been shown that entanglement distillation of Gaussian entangled states by means of local photon subtraction can be improved by local Gaussian transformations. Here we show that a similar effect can be expected for the distillation of an asymmetric Gaussian entangled state that is produced by a single squeezed beam. We show that for low initial entanglement, our largely simplified protocol generates more entanglement than previous proposed protocols. Furthermore, we show that the distillation scheme also works efficiently on decohered entangled states as well as with a practical photon s…
We investigate the systematic use of the Schwinger representation, by virtue of which two boson fields are equivalent to an effective spin, for casting multimode squeezed states into multipartite spin entangled states. The motivation for this endeavor is the following established fact: finitely squeezed, two-mode entangled states can be recast into maximally entangled bipartite spin states, irrespective of their level of squeezing (in the lossless case). This work explores the generalization of this interesting property to multipartite entanglement. While we found that the generalization of mu…
Dynamics of entangled states of two independent single-mode cavities in squeezed reservoirs is investigated in the context of matching of the correlations contained in the entangled states to those contained in the squeezed reservoir. We illustrate our considerations by examining the time evolution of entanglement of single and double excitation NOON and EPR states. A comparison is made when each cavity is coupled to own reservoir or both cavities are coupled to a common reservoir. It is shown that the evolution of the initial entanglement and transfer of entanglement from the squeezed reservo…
Many non-classicality indicators are used to measure quantum effects of different systems. Kenfack's and Sadeghi's non-classicality indicators are introduced in terms of the amount of Wigner function's negativities and interferences in phase space quantum mechanics, respectively. They are, effectively, applied for some real distribution functions. In this paper, we compared these non-classicality indicators for the entangled state of photonic number states in the Wigner, Husimi and Rivier representations. It is shown that for a two-level entangled state, Sadeghi's indicator has more benefits w…
The ability of parameter recently proposed by Sorensen et al. (Nature, 409, 63 (2001)) to characterize entanglement or inseparability is investigated for a system of two two-level atoms interacting with a single mode of radiation field. For comparison we employ the necessary and sufficient criterion of Peres and Horodecki for inseparability of bipartite states. We show that for diagonal atomic density matrix the parameter of Sorensen et al. fails to show entangled nature of collective atomic state whereas same state is inseparable in accordance with Peres-Horodecki criterion.
We investigate and model the behaviour of split spin-squeezed Bose-Einstein condensates (BECs) system. In such a system, a spin-polarized BEC is first squeezed using a $ (S^z)^2 $ interaction, then are split into two separate clouds. After the split, we consider that the particle number in each cloud collapses to a fixed number. We show that this procedure is equivalent to applying an interaction corresponding to squeezing each cloud individually plus an entangling operation. We analyse the system's entanglement properties and show that it can be detected using correlation-based entanglement c…
How to detect quantum correlations in bi-partite scenarios using a split many-body system and collective measurements on each party? We address this question by deriving entanglement witnesses using either only first or first and second order moments of local collective spin components. In both cases, we derive optimal witnesses for spatially split spin squeezed states in the presence of local white noise. We then compare the two optimal witnesses with respect to their resistance to various noise sources operating either at the preparation or at the detection level. We finally evaluate the sta…
Matters Arising: Distributed quantum sensing with mode-entangled spin-squeezed atomic states
本文是对Malia等人2022年发表于《Nature》的分布式量子传感研究的商榷，指出其声称的四节点时钟网络纠缠精度比量子投影噪声极限高11.6 dB的结论错误，实际结果比该极限差两个数量级以上，未实现纠缠带来的精度提升。
Entanglement plays a crucial role in quantum information protocols, thus the dynamical behavior of entangled states is of a great importance. In this paper we suggest a useful scheme that permits a direct measure of entanglement in a two-qubit cavity system. It is realized in the cavity-QED technology utilizing atoms as fying qubits. To quantify entanglement we use the concurrence. We derive the conditions, which assure that the state remains entangled in spite of the interaction with the reservoir. The phenomenon of sudden death entanglement (ESD) in a bipartite system subjected to squeezed v…
This paper proposes a scheme for teleporting an arbitrary coherent superposition state of two equal-amplitude and opposite-phase squeezed vacuum states (SVS) via a symmetric 50/50 beam splitter and photodetectors. It is shown that the quantum teleportation scheme has the successful probability 1/4. Maximally entangled SVS's are used as quantum channel for realizing the teleportation scheme. It is shown that if an initial quantum channel is in a pure but not maximally entangled SVS, the quantum channel may be distilled to a maximally entangled SVS through entanglement concentration.
In this paper, we investigate theoretically a system consisting of a one dimensional Bose-Einstein condensate trapped inside the optical lattice of an optical cavity. In the weak-interaction regime and under the Bogoliubov approximation, the wave function of the Bose-Einstein condensate can be described by a classical field (condensate mode) having some quantum fluctuations (the Bogoliubov mode) about the mean value. Such a system behaves as a so-called atomic parametric amplifier, similar to an optical parametric amplifier, where the condensate and the Bogoliubov modes play respectively, the …
We investigate theoretically a hybrid system consisting of a Bose-Einstein condensate (BEC) trapped inside a laser driven membrane-in-the-middle optomechanical cavity assisted with squeezed vacuum injection whose moving membrane interacts both linearly and quadratically with the radiation pressure of the cavity. It is shown that such a hybrid system is very suitable for generating strong quadrature squeezing in the mechanical mode of the membrane and the Bogoliubov mode of the BEC in the unresolved sideband regime. More interestingly, by choosing a suitable sign for the quadratic optomechanica…
Nonlinear optical generation of entangled squeezed states in lossy nonorthogonal quasimodes: an analytic solution
本研究推导得出纳米腔损耗非正交准模下非线性光量子态密度算符的多模压缩热态解析形式，通过耦合微分方程描述参数时变特性，在双准模系统中验证了与模拟的一致性，为混合高斯簇态的高效建模优化提供了新方法。
The quantum Rabi model accepts analytical solutions in the so-called degenerate qubit and relativistic regimes with discrete and continuous spectrum, in that order.We show that solutions in the laboratory frame are the superposition of even and odd displaced number states, in the former, and infinitely squeezed coherent states, in the latter, of the boson field correlated to the internal states of the qubit. We propose a single parameter model that interpolates between these discrete and continuous spectrum regimes to study the spectral statistics for first and second neighbor differences befo…
Geometric phase for two-mode entangled squeezed-coherent states
本文研究双模纠缠压缩相干态的几何相位，揭示平衡与非平衡情形下压缩参数对几何相位的椭圆型和双曲型压缩规律，并提出利用干涉测量生成平衡态的理论方案。
We propose a method to refine entanglement via swapping from a pair of squeezed vacuum states by performing the Bell measurement of number sum and phase difference. The resultant states are maximally entangled by adjusting the two squeezing parameters to the same value. We then describe the teleportation of number states by using the entangled states prepared in this way.
Entangled coherent states are shown to emerge, with high fidelity, when mixing coherent and squeezed vacuum states of light on a beam-splitter. These maximally entangled states, where photons bunch at the exit of a beamsplitter, are measured experimentally by Fock-state projections. Entanglement is examined theoretically using a Bell-type nonlocality test and compared with ideal entangled coherent states. We experimentally show nearly perfect similarity with entangled coherent states for an optimal ratio of coherent and squeezed vacuum light. In our scheme, entangled coherent states are genera…
Entangled multi-spatial-mode fields have interesting applications in quantum information, such as parallel quantum information protocols, quantum computing, and quantum imaging. We study the use of a nondegenerate four-wave mixing process in rubidium vapor at 795 nm to demonstrate generation of quantum-entangled images. Owing to the lack of an optical resonator cavity, the four-wave mixing scheme generates inherently multi-spatial-mode output fields. We have verified the presence of entanglement between the multi-mode beams by analyzing the amplitude difference and the phase sum noise using a …
We consider two-mode squeezed states which are parametrized by the squeezing parameter and the phase. We present a scheme for teleporting such entangled states of continuous variables from Alice to Bob. Our protocol is operationalized through the creation of a four-mode entangled state shared by Alice and Bob using linear amplifiers and beam splitters. Teleportation of the entangled state proceeds with local operations and the classical communication of four bits. We compute the fidelity of teleportation and find that it exhibits a trade-off with the magnitude of entanglement of the resultant …
Multimode Entangled Squeezed Light Generation and Propagation in a Coupled-Cavity Photonic Crystal
本文提出了一种高效方法，用于在多模式光子晶体耦合谐振腔系统中生成并维持纠缠压缩光态。
We study a protocol for constructing a squeezed atom laser for a model originating from the generalized uncertainty principle. We show that the squeezing effects arising from such systems do not require any squeezed light as an input, but the squeezing appears automatically because of the structure of the model it owns. The output atom laser beam becomes squeezed due to the nonlinear interaction between the Bose-Einstein condensate and the deformed radiation field created due to the noncommutative structure. We analyze several standard squeezing techniques based on the analytical expressions f…
Entangled states play a crucial role in quantum information protocols, thus the dynamical behavior of entanglement is of a great importance. In this paper we consider a two-mode squeezed vacuum state coupled to one thermal reservoir as a model of an entangled state embedded in an environment. As a criterion for entanglement we use a continuous-variable equivalent of the Peres-Horodecki criterion, namely the Simon criterion. To quantify entanglement we use the logarithmic negativity. We derive a condition, which assures that the state remains entangled in spite of the interaction with the reser…
We examine the properties of an atom laser produced by outcoupling from a Bose-Einstein condensate with squeezed light. We introduce a method which allows us to model the full multimode dynamics of the squeezed optical field and the outcoupled atoms. We show that for experimentally reasonable parameters that the quantum statistics of the optical field are almost completely transferred to the outcoupled atoms, and investigate the robustness to the coupling strength and the two-photon detuning.
Two-mode squeezed number states (TMSNS) are natural generalization of two-mode squeezed vacuum states. It has been known that every TMSNS is entangled whenever the squeezing parameter is non-zero. For a pair of entangled pure states Nielsen's majorization theorem tells us whether one state can be transformed into the other state through local operation and classical communication based on the majorization property on their probability distributions of Schmidt bases. In this report we find two examples of majorization relations for a set of TMSNS.
We examine the properties of an atom laser produced by outcoupling from a Bose-Einstein condensate with squeezed light. We model the multimode dynamics of the output field and show that a significant amount of squeezing can be transfered from an optical mode to a propagating atom laser beam. We use this to demonstrate that two-mode squeezing can be used to produce twin atom laser beams with continuous variable entanglement in amplitude and phase.
We introduce a new class of quantum many-particle entangled states, called the Dicke squeezed (or DS) states, which can be used to improve the precision in quantum metrology beyond the standard quantum limit. We show that the enhancement in measurement precision is characterized by a single experimentally detectable parameter, called the Dicke squeezing $ξ_{D}$, which also bounds the entanglement depth for this class of states. The measurement precision approaches the ultimate Heisenberg limit as $ξ_{D}$ attains the minimum in an ideal Dicke state. Compared with other entangled states, we show…
Conditions to generate high-purity entangled vacuum-evacuated coherent states ($|0>|α>^0 - |-α>^0 |0>$ were studied for two cascade-placed beam splitters, with one squeezed state input and two coherent state inputs whenever a single photon is detected. Controlling the amplitudes and the phases of the beams allows for various amplitudes of the vacuum-evacuated coherent states ($|α>^ 0 = |α> -e^{-|α|^2} |0> $) up to $α= 2.160$ to be manipulated with high-purity.
Parametric amplification of continuous variable entangled state for loss-tolerant multi-phase estimation
本文提出利用光学参数放大技术实现抗损耗的多相位估计，通过双模纠缠态和四模簇态分析，提升量子计量的鲁棒性。
To gain an advantage, quantum technologies utilize phenomena particular to quantum mechanics. Two such phenomena are squeezing and entanglement. Having generated states that exhibit these features, verification of their generation with local measurements can be a difficult process. Here we consider the states that are generated using the two-qudit single-axis squeezing Hamiltonian, that not only produces entangled two-qudit squeezed states but also results in various forms of interesting entangled states. We show how one can use local measurements to both efficiently verify and directly estima…
Quantum multiparameter estimation with multi-mode photon catalysis entangled squeezed state
本研究提出基于Fredkin门生成多模纠缠催化压缩真空态的方法，将其用于多相位同时估计，证实可提升QCRB性能且对光子损耗鲁棒性更强，可应用于量子计量多参数估计场景。
We study a device consisting of a dc-SQUID with two sections of its loop acting as two mechanical resonators. An analog of the parametric down-conversion process in quantum optics can be realized with this device. We show that a two-mode squeezed state can be generated for two overdamped mechanical resonators, where the damping constants of the two mechanical resonators are larger than the coupling strengths between the dc-SQUID and the two mechanical resonators. Thus we show that entangled states of these two mechanical resonators can be generated.
Optimizing realistic continuous-variable quantum teleportation with non-Gaussian resources
该研究在含光子损耗、非理想测量的现实条件下，对比三种纠缠资源的连续变量量子隐形传态性能，发现减光子压缩态在低压缩区间保真度更高、EPR关联更强，为高保真量子隐形传态提供了非高斯资源方案。
This paper has been withdrawn. It is based on numerical results limited by computing resources to N=3000 atoms. Using a newly understood geometric method we find that the observed scaling with N saturates at around N=7000 or even higher. In light of this new finding we withdraw the paper and will submit a revised manuscript reflecting our new understanding.
A quantum memory for light is a key element for the realization of future quantum information networks. Requirements for a good quantum memory are (i) versatility (allowing a wide range of inputs) and (ii) true quantum coherence (preserving quantum information). Here we demonstrate such a quantum memory for states possessing Einstein-Podolsky-Rosen (EPR) entanglement. These multi-photon states are two-mode squeezed by 6.0 dB with a variable orientation of squeezing and displaced by a few vacuum units. This range encompasses typical input alphabets for a continuous variable quantum information …
We provide a scheme for the generation of controlled entangled number states of Bose-Einstein condensates in multiple wells, and also provide a novel method for the creation of squeezed states without severe adiabatic constraints on barrier heights. The condensate in a multiple well trap can be evolved, starting with a specific initial phase difference between the neighboring wells, to a tunable entangled state or a squeezed state. We propose a general formula for the initial phase difference between the neighboring wells that is valid for any number of wells, even and odd.
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…
We propose and analyze a protocol for observing a violation of the Clauser-Horne-Shimony-Holt (CHSH) Bell inequality using two spatially separated Bose-Einstein condensates (BECs). To prepare the Bell-correlated state, spin-changing collisions are used to first prepare a two-mode squeezed BEC. This is then split into two BECs by controlling the spatial wavefunction, e.g., by modifying the trapping potential. Finally, spin-changing collisions are also exploited locally, to compensate local squeezing terms. The correlators appearing in the inequality are evaluated using three different approache…
We analyse a novel squeezing and entangling mechanism which is due to correlated Stokes and anti-Stokes photon forward scattering in a multi-level atom vapour. Following the proposal we present an experimental demonstration of 3.5 dB pulsed frequency nondegenerate squeezed (quadrature entangled) state of light using room temperature caesium vapour. The source is very robust and requires only a few milliwatts of laser power. The squeezed state is generated in the same spatial mode as the local oscillator and in a single temporal mode. The two entangled modes are separated by twice the Zeeman fr…
We examine how to signify and quantify the mesoscopic quantum coherence of approximate two-mode NOON states and spin-squeezed two-mode Bose-Einstein condensates (BEC). We identify two criteria that verify a nonzero quantum coherence between states with quantum number different by $n$. These criteria negate certain mixtures of quantum states, thereby signifying a generalised $n$-scopic Schrodinger cat-type paradox. The first criterion is the correlation $\langle\hat{a}^{\dagger n}\hat{b}^{n}\rangle\neq0$ (here $\hat{a}$ and $\hat{b}$ are the boson operators for each mode). The correlation manif…
We propose a generalization of the Feynman path integral using squeezed coherent states. We apply this approach to the dynamics of Bose-Einstein condensates, which gives an effective low energy description that contains both a coherent field and a squeezing field. We derive the classical trajectory of this action, which constitutes a generalization of the Gross Pitaevskii equation, at linear order. We derive the low energy excitations, which provides a description of second sound in weakly interacting condensates as a squeezing oscillation of the order parameter. This interpretation is also su…
We show that two qubits can be entangled by local interactions with an entangled two-mode continuous variable state. This is illustrated by the evolution of two two-level atoms interacting with a two-mode squeezed state. Two modes of the squeezed field are injected respectively into two spatially separate cavities and the atoms are then sent into the cavities to resonantly interact with the cavity field. We find that the atoms may be entangled even by a two-mode squeezed state which has been decohered while penetrating into the cavity.
A challenge in precision measurement with squeezed spin state arises from the spin dephasing due to stray magnetic fields. To suppress such environmental noises, we employ a continuous driving protocol, rotary echo, to enhance the spin coherence of a spin-1 Bose-Einstein condensate in stray magnetic fields. Our analytical and numerical results show that the coherent and the squeezed spin states are preserved for a significantly long time, compared to the free induction decay time, if the condition $hτ= mπ$ is met with $h$ the pulse amplitude and $τ$ pulse width. In particular, both the spin av…
Practical schemes for creation of multi-mode squeezed (entangled) states of atomic ensembles located inside a high-Q ring cavity are discussed. It is assumed that the cavity is composed of two degenerate mutually counter-propagating modes that can simultaneously couple to the atomic ensembles with the same coupling strengths. The ensembles are composed of ultra-cold atoms which are modeled as four-level systems driven by two laser fields, both co-propagating with one of the cavity directions. We illustrate a procedure that constructs multi-mode squeezed states from the vacuum by a unitary tran…
Spectrally shaped and pulse-by-pulse multiplexed multimode squeezed states of light
本文利用飞秒光源的完整重复频率与超快光谱整形，首次结合频率复用和时间复用，在156 MHz下同时生成21个压缩光谱模式，为可扩展、可重构的多体纠缠态奠定基础。
In this work we find explicitly the decoherence free subspace (DFS) for a two two-level system in a common squeezed vacuum bath. We also find an orthogonal basis for the DFS composed of a symmetrical and an antisymmetrical (under particle permutation) entangled state. For any initial symmetrical state, the master equation has one stationary state which is the symmetrical entangled decoherence free state. In this way, one can generate entanglement via common squeezed bath of the two systems. If the initial state does not have a definite parity, the stationary state depends strongly on the initi…
We construct an explicit Wigner function for N-mode squeezed state. Based on a previous observation that the Wigner function describes correlations in the joint measurement of the phase-space displaced parity operator, we investigate the non-locality of multipartite entangled state by the violation of Zukowski-Brukner N-qubit Bell inequality. We find that quantum predictions for such squeezed state violate these inequalities by an amount that grows with the number N.
Transfer of nonlocal two-mode squeezed vacuum state through symmetrical and asymmetrical lossy channel is analysed and we demonstrate that the nonlocality is more robust against losses, than it has been previously suggested. It can be important for security of continuous-variable quantum cryptography employing entangled states.
We propose a scheme to implement a supersensitive estimation of the coupling strength in a hybrid optomechanical system which consists of a cavity-Bose-Einstein condensate system coupled to an impurity. This method can dramatically improve the estimation precision even when the involved photon number is small. The quantum Fisher information indicates that the Heisenberg scale sensitivity of the coupling rate could be obtained when the photon loss rate is smaller than the corresponding critical value in the input of either coherent state or squeezed state. The critical photon decay rate for the…
We introduce the concept of initial-phase spectroscopy as a control of the dynamics of entangled states encoded into a two-atom system interacting with a broadband squeezed vacuum field. We illustrate our considerations by examining the transient spectrum of the field emitted by two systems, the small sample (Dicke) and the spatially extended (non-Dicke) models. It is found that the shape of the spectral components depends crucially on the relative phase between the initial entangled state and the squeezed field. We follow the temporal evolution of the spectrum and show that depending on the r…
Quantum sensors are used for precision timekeeping, field sensing, and quantum communication. Comparisons among a distributed network of these sensors are capable of, for example, synchronizing clocks at different locations. The performance of a sensor network is limited by technical challenges as well as the inherent noise associated with the quantum states used to realize the network. For networks with only local entanglement at each node, the noise performance of the network improves at best with square root of the number of nodes. Here, we demonstrate that nonlocal entanglement between net…
In this paper at first we successfully teleport the unknown quantum state which is a superposition of squeezed vacuum state and squeezed one-photon state using the beam splitter in the absence of dissipation. In the continuation, we try to implement the same teleportation protocol, however, in the presence of dissipation effects. To do this task, we use proper entangled channel to reach to perfect teleportation under the in uence of decoherence. Finally, we consider another superposition of two squeezed vacuum states with separation in phase and teleport it with a different appropriate entangl…
In this paper we present a study of the quantum phase estimation problem employing continuous-variable, entangled squeezed coherent (quasi-Bell) states as probe states. We show that their inherent squeezing and entanglement properties might bring advantages, increasing the precision of phase estimation compared to protocols which employ other continuous variable states e.g., two-mode, entangled coherent states or single-mode, squeezed states. We also analyze the phase estimation process considering: i) a linear (unitary) perturbation, and ii) dissipation, and conclude that the use of entangled…
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