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a Wigner function of the teleported quantum state for X 0 0.1 and P 1 0.2 and the input state shown in Fig. 3a in the case when the entangled state is a squeezed vacuum with q 0.8178; b same as in a but for the case when the entangled state is the photon-subtracted squeezed vacuum obtained by CM (n 1 n 2 1;r0.15).
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We show that the recently proposed scheme of teleportation of continuous variables [S.L. Braunstein and H.J. Kimble, Phys. Rev. Lett. 80, 869 (1998)] can be improved by a conditional measurement in the preparation of the entangled state shared by the sender and the recipient. The conditional measurement subtracts photons from the original entangled...
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... teleported quantum state that is obtained for a par- ticular measurement of quadrature-component values X 0 and P 1 is shown in Fig. 4. The results in Figs. 4a and 4b, respectively, correspond to the cases when the entangled state is a squeezed vacuum (q0.8178) and a photon- 30 as a function of the reflectance rr 1 r 2 of the beam splitters BS 1 and BS 2 in Fig. 1 for different numbers of detected photons, n 1 n 2 0,1,2,3,4. The dashed line indicates the degree of ...
Context 2
... teleported quantum state that is obtained for a par- ticular measurement of quadrature-component values X 0 and P 1 is shown in Fig. 4. The results in Figs. 4a and 4b, respectively, correspond to the cases when the entangled state is a squeezed vacuum (q0.8178) and a photon- 30 as a function of the reflectance rr 1 r 2 of the beam splitters BS 1 and BS 2 in Fig. 1 for different numbers of detected photons, n 1 n 2 0,1,2,3,4. The dashed line indicates the degree of entanglement of the original ...
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Citations
... Non-Gaussian operations have been shown to enhance the performance of quantum teleportation [9][10][11][12][13][14][15][16], quantum metrology [17][18][19][20][21][22][23][24][25][26] and quantum key distribution [27][28][29][30]. Non-Gaussian operations such as photon subtraction, photon addition, and photon catalysis (PC) operations were considered in the context of CV-MDI-QKD operations [31][32][33][34]. ...
We investigate the benefits of using $m$-photon catalysed two-mode squeezed coherent ($m$-PCTMSC) state in continuous variable measurement device-independent quantum key distribution (CV-MDI-QKD). To that end, we derive the Wigner characteristic function of the $m$-PCTMSC state and show that the 0-PCTMSC state is a Gaussian state and is an inferior choice as compared to the zero photon catalyzed two-mode squeezed vacuum state for CV-MDI-QKD. We carry out the optimization of the secret key rate with respect to all state parameters, namely variance, transmissivity, and displacement. Contrary to many recent proposals, the results show that zero- and single-photon catalysis operation provides only a marginal benefit in improving the maximum transmission distance. Secondly, we find that displacement offers no benefit in improving CV-MDI-QKD.
... † mp18015@iisermohali.ac.in ‡ arvind@iisermohali.ac.in tation [28,29]. Non-Gaussian operations have been shown to improve performance of quantum teleportation [30][31][32], quantum sensing [33,34] and QKD [35][36][37]. For instance, single photon subtraction (SPS) has been shown to enhance the tolerance to channel losses in CV-MDI-QKD, thereby extending the maximum transmission distance [38][39][40]. ...
... While the utility of SPS in other CV-QKD protocols [35][36][37] needs to be properly re-assessed, the potential benefits of other non-Gaussian operations such as photon catalysis [40,52,53] and photon addition [40,54] in CV-QKD also require critical examination. Since SPS has been shown to be useful in quantum teleportation [30][31][32] and quantum metrology [33,34] our work call for a re-examination of these results from an optimality point of view. ...
We critically analyse the role of single photon subtraction (SPS) and displacement in improving the performance of continuous variable measurement device independent quantum key distribution (CV-MDI-QKD). We consider CV-MDI-QKD with resource states generated by SPS on a displaced two-mode squeezed vacuum state. Optimizing the secret key rate with state parameters reveals that implementing SPS yields no benefits in improving the loss tolerance of CV-MDI-QKD. Additionally, we find that displacement too is not useful in improving the performance of CV-MDI-QKD. While our result is in contradistinction with the widely held belief in the field regarding the utility of SPS and displacement in CV-MDI-QKD, it also calls for a re-examination of the role of non-Gaussian operations in increasing the efficiency of various quantum information processing protocols.
... In order to increase nonclassicality and entanglement, non-Gaussian states have been engineered by implementing non-Gaussian operations such as photon subtraction, addition, and catalysis on Gaussian states [24][25][26][27][28][29]. Such non-Gaussian states have been employed to improve the performances of various QIP protocols such as quantum teleportation [30][31][32][33][34][35][36][37], quantum key distribution [38][39][40][41][42][43] and quantum metrology [44][45][46][47][48][49][50][51][52][53]. These non-Gaussian operations, in particular, the photon subtraction (PS) on two-mode squeezed vacuum (TMSV) and two-mode squeezed coherent (TMSC) states, have been shown to enhance the performance of CV-MDI-QKD protocols [39,40]. ...
... Using these expressions, secret key rate (30) can be readily evaluated. Special cases: On setting d = 0, we obtain the SKR for the PSTMSV state. ...
... Photon subtraction has been shown to be useful in quantum teleportation [30][31][32][33][34][35][36][37] and quantum metrology [44][45][46][47][48][49][50][51][52][53]. The potential benefits of photon subtraction and other non-Gaussian operations such as photon catalysis [71,72] and photon addition [73] in CV-QKD and other CV-QIP tasks demand a thorough examination. ...
Non-Gaussian operations, in particular, photon subtraction (PS), have been shown to enhance the performance of various quantum information processing tasks including continuous variable measurement device independent quantum key distribution (CV-MDI-QKD). This work investigates the role of non-Gaussian resource states, namely, the photon subtracted two-mode squeezed coherent (PSTMSC) (which include photon subtracted two-mode squeezed vacuum (PSTMSV) as a special case) states in CV-MDI-QKD. To this end, we derive the Wigner characteristic function for the resource states, from which the covariance matrix and, finally, the secret key rate expressions are extracted. The optimization of the state parameters is undertaken to find the most suitable resource states in this family of states. There have been previous studies on the PSTMSV and PSTMSC states in CV-MDI-QKD that make use of PS operation. We evaluate such proposals and find to our surprise that both PSTMSC and PSTMSV resource states underperform as compared to the TMSV state rendering PS operation and displacement undesirable.
... Conditional photon addition [5][6][7][8] and subtraction [9][10][11][12] are powerful tools in quantum photonics and they are utilized in a wide range of schemes and experiments. Possible applications include continuous-variable entanglement distillation [13][14][15][16][17], implementation of noiseless quantum amplifiers [18][19][20][21][22], enhancement of squeezing [23,24], generation of Schrödinger cat-like states [10][11][12][25][26][27][28][29][30][31][32][33][34], Gottesman-Kitaev-Preskill (GKP) states [35,36] or arbitrary single-mode quantum states [37][38][39], preparation of hybrid entangled states of light [40,41], and emulation of strong Kerr nonlinearity at the fewphoton level [18,42]. On the more fundamental side, coherent combinations of sequences of single-photon addition and subtraction enabled experimental test of the fundamental quantum commutation relation [â,â † ] =1 [43], and the quantum-to-classical transition was studied by adding single photons to coherent states with progressively increasing amplitude [5]. ...
Conditional addition of photons represents a crucial tool for optical quantum state engineering and it forms a fundamental building block of advanced quantum photonic devices. Here we report on experimental implementation of the conditional addition of several photons. We demonstrate the addition of one, two, and three photons to input coherent states with various amplitudes. The resulting highly nonclassical photon-added states are completely characterized with time-domain homodyne tomography, and the nonclassicality of the prepared states is witnessed by the negativity of their Wigner functions. We experimentally demonstrate that the conditional addition of photons realizes approximate noiseless quantum amplification of coherent states with sufficiently large amplitude. We also investigate certification of the stellar rank of the generated multiphoton-added coherent states, which quantifies the non-Gaussian resources required for their preparation. Our results pave the way towards the experimental realization of complex optical quantum operations based on combination of multiple photon additions and subtractions.
... Continuous-variable (CV) non-Gaussian states have been identified as an important resource since they can be exploited to improve the performance of CV quantum information processing, such as quantum teleportation, [1][2][3][4] quantum key distribution, [5] and quantum cloning. [6] Such an improvement is largely attributed to the existence of non-Gaussianity contained in quantum state, which is usually referred to as the departure of a given state from its Gaussian counterpart. ...
The non-Gaussianity of quantum states incarnates an important resource for improving the performance of continuous-variable quantum information protocols. We propose a novel criterion of non-Gaussianity for single-mode rotationally symmetric quantum states via the squared Frobenius norm of higher-order cumulant matrix for the quadrature distribution function. As an application, we study the non-Gaussianities of three classes of single-mode symmetric non-Gaussian states: a mixture of vacuum and Fock states, single-photon added thermal states, and even/odd Schrödinger cat states. It is shown that such a criterion is faithful and effective for revealing non-Gaussianity. We further extend this criterion to two cases of symmetric multi-mode non-Gaussian states and non-symmetric single-mode non-Gaussian states.
... Photon subtraction (PS), which extracts a single photon from a given optical mode, is an important photonic operation in optical quantum information processing [1]. PS is a prerequisite element for verifying the quantum commutation rule [2], optical continuous variable entanglement enhancement [3][4][5][6][7][8][9], and quantum state manipulation [10][11][12]. Thus far, several theories for PS, such as the multi-mode [13], nonlinear PS [14], displaced PS [10,15], and non-mode-selective PS [16] theories, have been developed. ...
... Thus far, several theories for PS, such as the multi-mode [13], nonlinear PS [14], displaced PS [10,15], and non-mode-selective PS [16] theories, have been developed. Moreover, many types of physical systems have been designed to implement PS; examples include the beam splitter and photon detection method [3], sum-frequency generation [17], absorbing environment and adaptive absorption [18], quantum dot-cavity system [19], cascaded Rydberg superatom system [20,21], and nanofiber-coupled microresonator [22]. PS has many applications, including improving the key rate of continuous variable quantum key distribution [23][24][25][26], engineering the nonclassicality in a mechanical system [27], enhancing the gain of quantum linear amplification [28], preparing optical Schrödinger cat states [29][30][31], increasing the mean photon number [32], implementing practical optical Maxwell's demons [33,34], and implementing multiphoton quantum-state engineering [35] and high-dimensional encoding [36]. ...
... Schemes with a photon beam splitter (BS) and photon detector (hereafter, referred to as PSBS) are the simplest and most convenient [3]. Moreover, many flexible options are available for the photon detector. ...
Photon subtraction (PS) is an important operation for optic quantum information processing. Conventional PS is implemented using a single linear beam splitter (BS) and photon detector. However, in this study, we show that the PS effect can be enhanced using two beam splitters and an optional phase modulator. This can be considered PS with an extended version of the well-known Mach–Zehnder (MZ) interferometer. By tuning the transmittance of the two beam splitters and phase modulator, the probability of success can be considerably improved over that of the original PS scheme with a single BS and photon detector. Moreover, if applied to a single-photon input, our proposed scheme can even implement deterministic PS, which is almost impossible for the original scheme with a single BS and photon detector. Owing to the higher probability of success, applying the PSMZ method to the entanglement enhancement of a very weak two-mode squeezed vacuum state is straightforward. Our result is helpful for improving the yield of output entanglement.
... The non-Gaussian states and non-Gaussian operations [2][3][4][5][6] are crucial for a variety of quantum information processing protocols [7] related to quantum key distribution [8][9][10][11], entanglement distillation [12][13][14], quantum error correction [15][16][17][18][19], quantum metrology [20][21][22][23][24][25][26], optimal cloning [27], continuous variable (CV) quantum computing [28][29][30], and quantum computation on cluster states [31,32]. In addition, the non-Gaussian states and operations have been shown to be capable of improving the quality of entanglement [33] and enhancing the accuracy of CV quantum teleportation [34][35][36][37][38][39][40]. ...
In this paper, we consider the preparation of Schrödinger cat states using a measurement-assisted gate based on the Fock resource state, the quantum non-demolition entangling operation, and the homodyne measurement. Previously, we have investigated the gate, which for the same goal uses the ancillary non-Gaussian cubic phase state generated from quadrature squeezed states at realistic (finite) squeezing. It is of evident interest to compare the efficiency of both schemes, that is, their ability to produce cat-like superpositions with high fidelity and probability of success. We introduce, in parallel with the exact theoretical description of the gate operation, a clear visual interpretation of the output state based on the semiclassical mapping of the input field variables. The emergence of the superpositions of “copies” of the input state in both schemes is due to the fact that such mapping is compatible with two (or, in general, more) sets of values of the output field observables. We demonstrate that even fine details of the output of both gates are effectively predicted and interpreted in our approach. We examine the fidelity and success probability and reveal the ranges of physical parameters where the Fock state-based and the cubic phase state-based gates demonstrate comparable fidelity and (or) probability of success.
... This situation was theoretically analyzed in Ref. [18] and experimentally demonstrated as entanglement distillation in Ref. [19]. Such beams with increased entanglement are then useful for improving the performance of quantum teleportation [20,21]. Photon subtraction on such beams has nonlocal character in the sense that subtraction on one beam affects the state of the other beam. ...
... In writing relations (20) we assume w j,a ≡ w a , w 2 j,a ≡ w 2 a , for a = s, i, and w j,s w j,i ≡ w s w i . Thus, according to Eqs. (20), the Fano factors f n,s and f n,i and noise-reduction parameter r n of individual modes coincide with those of the overall field analyzed above. ...
... In writing relations (20) we assume w j,a ≡ w a , w 2 j,a ≡ w 2 a , for a = s, i, and w j,s w j,i ≡ w s w i . Thus, according to Eqs. (20), the Fano factors f n,s and f n,i and noise-reduction parameter r n of individual modes coincide with those of the overall field analyzed above. ...
States obtained from multimode twin beams by symmetric as well as asymmetric photon subtraction are experimentally investigated. Using the joint photocount distributions measured by an intensified CCD camera, their joint photon-number distributions are reconstructed. Mean photon numbers, Fano factors, and noise-reduction parameters are determined for the group of states reached by subtracting up to four photocounts in each beam. Photon subtraction is monitored using the nonclassicality depths and joint quasidistributions of integrated intensities of the emerging states. The non-Gaussianity of the obtained states is also determined. The states reached by coherent photon subtraction are also analyzed. The investigations represent an important step towards the use of photon-subtracted twin beams in sub-shot-noise metrology and imaging.
... The removal of photons from a beam of light in different contexts give rise to the terms "loss" and "photon subtraction" that typically describe scenarios different from the present one. Photon subtraction, for example, is the result of acting on a state with an annihilation operator, which has a significant history [43][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58][59] including experimental demonstrations that conditionally split off a single photon from a state at a weakly reflective beam splitter [47]. That action may indeed leave the overall state intensity unchanged, or even increased, to appear as though no photons have been "subtracted." ...
Given a state of light, how do its properties change when only some of the constituent photons are observed and the rest are neglected (traced out)? By developing formulas for mode-agnostic removal of photons from a beam, we show how the expectation value of any operator changes when only q photons are inspected from a beam, ignoring the rest. We use this to re-express expectation values of operators in terms of the state obtained by randomly selecting q photons. Remarkably, this only equals the true expectation value for a unique value of q: expressing the operator as a monomial in normally ordered form, q must be equal to the number of photons annihilated by the operator. A useful corollary is that the coefficients of any q-photon state chosen at random from an arbitrary state are exactly the qth-order correlations of the original state; one can inspect the intensity moments to learn what any random photon will be doing and, conversely, one need only look at the n-photon subspace to discern what all of the nth-order correlation functions are. The astute reader will be pleased to find no surprises here, only mathematical justification for intuition. Our results hold for any completely symmetric state of any type of particle with any combination of numbers of particles and can be used wherever bosonic correlations are found.
... Non-Gaussian operation is one such technique which has been employed in different quantum protocols such as squeezing and entanglement distillation [19][20][21][22][23], quantum teleportation [24][25][26][27][28][29][30][31], quantum key distri- * manali.verma.31@gmail.com † chandan.quantum@gmail.com ...
We investigate the benefits of probabilistic non-Gaussian operations in phase estimation using difference-intensity and parity detection-based Mach-Zehnder interferometers (MZI). We consider an experimentally implementable model to perform three different non-Gaussian operations, namely photon subtraction (PS), photon addition (PA), and photon catalysis (PC) on a single-mode squeezed vacuum (SSV) state. In difference-intensity detection-based MZI, two PC operation is found to be the most optimal, while for parity detection-based MZI, two PA operation emerges as the most optimal process. We have also provided the corresponding squeezing and transmissivity parameters yielding best performance, making our study relevant for experimentalists. Further, we have derived the general expression of moment-generating function, which shall be useful in exploring other detection schemes such as homodyne detection and quadratic homodyne detection.
