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Color online) Schematic setup for the general two-qubit gate. By a C-path gate in Fig. 3 and an disentangler in Fig. 5, the input two-photon states are transformed to the products single-photon states, with the second photon on paths 1′ and 2′ inheriting the structures of the input biphoton states. Then the second photon becomes a qudit in four spatial modes under two PBSs. Two σx operations on paths 2 and 4 make the same polarization for all spatial modes. An LOMI in the dashed line follows up to implement the gate operation U(4) on the single-photon qudit. The inverse transformation for the second photon back to polarization space relies on entangler-2 in the dash-dotted line, where the qubus beams interact with the photonic modes in the way slightly different from that in entangler of Fig. 7. Finally, a merging gate merges the spatial modes of the second photon, finishing a general two-qubit operation U(4).
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Multiphoton states are widely applied in quantum information technology. By the methods presented in this paper, the structure of a multiphoton state in the form of multiple single-photon qubit products can be mapped to a single-photon qudit, which could also be in a separable product with other photons. This makes possible the manipulation of such...
Contexts in source publication
Context 1
... three CNOT gates (together with the proper one- qubit operations) should be necessary in constructing a general two-qubit gate [31,32]. It looks that three pairs of C-path and Merging involving six number-resolving detections should be used to realize such two-qubit gate. However, fewer resources would be necessary if we work with the design in Fig. ...
Context 2
... Fig. 8, we first use a two-photon transformation to convert an initial state |ψ in in Eq. (3) to the form in Eq. (21). Then, two PBS on the path 1 ′ and 2 ′ followed by two σ x operations on path 2 and 4 achieve the ...
Context 3
... conversion follows with a setup called Entangler-2 in the dash-dotted line of Fig. 8. Entangler-2 is a lit- tle bit different from an Entangler in Fig. 7, with the first (second) qubus beam coupled to |H 1 and |H/V 2 ′ (|V 2 and |H/V 1 ′ ). Through such XPM processes in the Entangler-2, the following state can be ...
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Citations
... For instance, quantum Fredkin and Toffoli gates are two kinds of universal multi-qubit quantum controlled gates that can be utilized as fundamental building blocks in quantum information processing. In recent years, the construction of Fredkin and Toffoli gates has been widely explored both in theory and experiment terms with different quantum effects, such as cross-kerr nonlinearity [9][10][11][12][13][14] and cavity quantum electrodynamics [15][16][17][18][19][20][21]. ...
Quantum logic gates are the foundation of circuit-based quantum computation and quantum simulation. Multi-qubit quantum controlled gates are of vital importance when large-scale quantum circuits are concerned. Here, assisted by diamond nitrogen-vacancy (NV) centers inside single-sided optical cavities, we first introduce the single-photon quantum routing operation, with which a single-photon polarization qubit can be coherently routed to the superposition of two spatial modes according to the state of the other polarization qubit. On this basis, we propose two schemes for the implementation of universal three-qubit quantum Fredkin- and Toffoli-gate operations on single-photon polarization qubits. Moreover, we show that a general multi-qubit controlled-unitary gate can be realized using the same strategy. Compared to other NV-cavity-based schemes, our schemes utilize photonic polarization, spatial, and temporal degrees of freedom (DOFs) simultaneously, so that the quantum circuits are simplified and the required quantum resources are reduced, making our schemes more resource-efficient and highly scalable. Our calculations show that the schemes can posses near-deterministic efficiency and near-unity fidelity with current or near-future techniques, which guarantees the experimental feasibility. Our schemes can therefore provide a new recipe for the construction of multi-qubit quantum gates and for efficient processing of multi-photon states.
... Due to the overlaps between neighboring curves, the error probability of this measurement is given by ε = 1 2 erfc(α(1 − cos θ)/ √ 2). Since the Kerr nonlinearities are extremely weak [35][36][37][38][39][40][41], we here restrict our discussion in the regime of weak nonlinearities. If one takes θ ∼ 10 −2 and α ∼ 10 5 , then ε ∼ 10 −5 , i.e. it is a nearly deterministic detection process with weak nonlinearities. ...
A higher-order parametric down-conversion (PDC) photon state is amazingly different from the states involving independent photon pairs. We focus on the third-order PDC photons. Firstly, we present a symmetry detector which is capable of analyzing twin-beam six-photon symmetric states in the regime of weak nonlinearities. By cascading symmetry detectors, then, it is shown that one can generate third-order PDC photons from a class of twin-beam six-photon symmetric states. Finally, as an example, we describe an application of third-order PDC photons for exploring six-mode-photon entangled states with linear optics.
... Also for the applications, the enhancements and the progress of the theory and experiment about the XKNL have been accomplished by many researchers [23][24][25][26][27][28][29][30][31][32][33]. For XKNL-based quantum information processing schemes, many studies have demonstrated according to the measurement strategies as homodyne [4,5,9,18,[34][35][36] and photon number measurements [15,17,37,38], and also the design as quantum bus beams [13,15,39]. However, in practice, the output state (photon-coherent beam system) of an optical multi-qubit gate will transform to a mixed state by the decoherence effect (photon loss and dephasing) when utilizing homodyne measurement on coherent state (probe beam) [13,17,34,37,38]. ...
We represent the mutual swapping of two unknown states using bidirectional quantum teleportation (BQT) while transferring a single photon. In our BQT scheme, two users (Alice and Bob) can mutually teleport their two unknown states of the electron-spin in quantum dots (QDs) embedded in single-sided cavities. For this BQT scheme, we employ the interactions of a photonic spin (photon) and an electron-spin (excess electron) of QDs confined in a single-sided cavity, which is feasible in practice. The previous BQT scheme which used cross-Kerr nonlinearities (XKNLs) and X-homodyne detection was inevitable the decoherence effect in optical fibers. Consequently, the proposed BQT scheme can enhance an experimental implementation with the use of QD-cavity systems under the decoherence effect and this can also be realized with current technology, compared with the previous BQT scheme based on XKNLs.
... (3) Based on the analysis of the decoherence effect using the process model [11][12][13][42][43][44], based on a master equation, we established an experimental condition using a strong coherent state (probe beam) to obtain high efficiency (low error probability) and reliable performance (high fidelity) of the CP and MP gates via XKNLs to protect against the influences of photon loss and the dephasing coherent parameters. Therefore, compared to previous works [53,[66][67][68][69][70][71] in which the affection of the decoherence effect was ignored, our scheme is experimentally feasible by implementing the demonstrated condition using a high amplitude for the coherent state, as described in section 4. (4) For effective operation using XKNLs, increasing the conditional phase shift to q » -10 2 is difficult using electromagnetically induced transparency [72,73] because the magnitude of the conditional phase shift by XKNL is extremely weak i.e., q » -10 18 [74]. As a result, the CP and MP gates in our scheme require a small magnitude of the conditional phase shift, according to the experimental condition (using a strong coherent state) for robustness against the decoherence effect, as shown in table 1 (i.e. ...
Herein, we present a scheme to prepare a hybrid-entangled W state that possesses the polarization states of two photons and the time-bin using cross-Kerr nonlinearities (XKNLs) and linearly optical devices. To maximize the merit of the entangled W state that can conserve entanglement against the loss of one qubit, we propose a method to prepare a two-photon hybrid-entangled W state correlated with degrees of freedom (polarization and the time-bin) via nonlinearly optical gates using XKNLs. In our scheme, the nonlinear gates consist of weak XKNLs, quantum bus beams, and photon-number-resolving measurements to realize the controlled-path gate and merging-path gate between two photons. To insert the time-bin information into photons, the time-bin encoder employs only linearly optical devices (delay lines and polarizing beam splitters). Subsequently, to evaluate the efficiency and experimental feasibility of our scheme for generating a two-photon hybrid-entangled W state, we analyzed the performance of nonlinear gates using XKNLs under the decoherence effect.
... However, the conditional phase shift −θ is equivalent to the conditional phase shift 2π − θ, which is impossible with the current experimental technology because the giant cross-Kerr nonlinearity is required. In order to replace the conditional phase shift −θ, we can use the approach called double cross phase modulation without conditional phase shift −θ, which had been developed in 2009 [57][58][59]. Moreover, there are some other kinds of interaction that can also provide feasible ways to construct the QND we need, such as cavity-assisted interactions [60] and quantum dot spin in optical microcavity [61]. ...
We present a new method for the complete analysis of hyperentangled Bell state and Greenberger–Horne–Zeilinger state in polarization and spatial-mode degrees of freedom, resorting to weak cross-Kerr nonlinearity and auxiliary frequency entanglement. The weak cross-Kerr nonlinearity with small phase shift is used to construct quantum nondestructive detector, and it is realizable with the current technology. Compared with the previous schemes, our scheme largely reduces the requirement on nonlinearity with the help of auxiliary entanglement in the third degree of freedom. Our method provides an efficient avenue for the hyperentangled state analysis, and will be useful for high-capacity quantum information processing.
... This Kerr nonlinearity can be used to induce a phase modulation in probe mode depended on single-photon state and then it is capable of detecting the state of photons in signal mode nondestructively. Since the Kerr nonlinearities are extremely weak [34][35][36][37][38], we here restrict our discussion in the regime of weak nonlinearities. The setup of symmetry detector is shown in Figure 1. ...
We consider six-photon entangled state emitted from a single third-order parametric down-conversion process. In the regime of weak nonlinearities, we present a symmetry detector which is capable of analyzing the twin-beam six-photon symmetric states. By cascading the symmetry detectors, as an application, it is shown that one can purify the desired six-photon entangled state from an arbitrary twin-beam six-photon symmetric state. With linear optics we propose a fruitful scheme for exploring a class of multimode-photon entangled states from third-order parametric down-conversion process. Furthermore, we provide a method to generate the six-photon polarization entangled Greenberger-Horne-Zeilinger state based on linear optics and weak nonlinearities.
... (2) In Sec. 4, by our analysis using the process model, we demonstrated that nonlinearly optical (CP and MP) gates should employ a strong coherent state (probe beam) to achieve high efficiency (low error probability) and reliable performance (high fidelity). In the previous works [35,58,77], which have proposed the various nonlinearly optical gates (including to CP and MP gates), for quantum information processing schemes, the affection of the decoherence effect, in practice, have been overlooked. Compared with these works [35,58,77], we analyzed the decoherence effect by master equation, and derived the method, using strong coherent state, to reduce photon loss and dephasing (decoherence) in Sec. 4. ...
... In the previous works [35,58,77], which have proposed the various nonlinearly optical gates (including to CP and MP gates), for quantum information processing schemes, the affection of the decoherence effect, in practice, have been overlooked. Compared with these works [35,58,77], we analyzed the decoherence effect by master equation, and derived the method, using strong coherent state, to reduce photon loss and dephasing (decoherence) in Sec. 4. ...
Quantum phase estimation (QPE) is the key procedure in various quantum algorithms. The main aim of the QPE scheme is to estimate the phase of an unknown eigenvalue, corresponding to an eigenstate of an arbitrary unitary operation. The QPE scheme can be applied as a subroutine to design many quantum algorithms. In this paper, we propose the basic structure of a QPE scheme that could be applied in quantum algorithms, with feasibility by utilizing cross-Kerr nonlinearities (controlled-unitary gates) and linearly optical devices. Subsequently, we analyze the efficiency and the performance of the controlled-unitary gate. This gate consists of a controlled-path gate and a merging-path gate via cross-Kerr nonlinearities under the decoherence effect. Also shown in this paper is a method by which to enhance robustness against the decoherence effect to provide a reliable QPE scheme based on controlled-unitary gates.
... To overcome this disadvantage, the weak cross-Kerr nonlinearity is usually used in photonic QIP tasks, such as preparing quantum entangled states, constructing entanglement analysers, and quantum logic gates. [35][36][37][38][39][40][41] In this manuscript, we try to convert multipartite KLM entangled states to GHZ entangled states via weak cross-Kerr nonlinearity (Bell state is viewed as specific two-qubit GHZ state). Fidelities of the two-and three-qubit cases are analyzed, which shows that the conversion schemes have high fidelities and closeto-unity probabilities even in consideration of photon loss. ...
Schemes for converting photonic polarized‐entangled Knill–Laflamme–Milburn (KLM) states to Greenberger–Horne–Zeilinger (GHZ) states are proposed using weak cross‐Kerr nonlinearity and X‐quadrature homodyne measurement. Analyses show that the two‐qubit (Bell state) and three‐qubit conversion cases have very high fidelities and close‐to‐unity probabilities. The conversion processes are robust against photon loss. The schemes linking these two entangled states may be helpful to the study of quantum information processing based on them. Based on weak cross‐Kerr nonlinearity, theoretical schemes are presented to bridge two multiple entanglements: Knill–Laflamme–Milburn (KLM) and Greenberger–Horne–Zeilinger (GHZ) entangled states. Adopting grouping and parity measurement, the KLM entanglement is decomposed into GHZ entanglement completely. Analyses considering photon loss show that high fidelities are reached for the two‐ and three‐qubit cases.
... Here, we demonstrated that nonlinearly optical (controlled-Hadamard and -NOT) gates using XKNLs should employ a strong coherent state to acquire high efficiency (low error probability) and reliable performance (high fidelity) under the decoherence effect, due to our process model in Sec. 4. In the previous works (controlled-path and merging gates) 44,[85][86][87][88] , the affection (photon loss and dephasing) of the decoherence effect have been overlooked in practice. In this point of view, we analyzed the decoherence effect through master equation, in Sec. 4, and proposed the method to enhance affection of photon loss and dephasing by utilizing strong coherent state (probe beam). ...
... In this point of view, we analyzed the decoherence effect through master equation, in Sec. 4, and proposed the method to enhance affection of photon loss and dephasing by utilizing strong coherent state (probe beam). Thus, compared with the previous works 44, [85][86][87][88] (including to other schemes 18,21,89,90 for generation W state using XKNLs), our scheme for the generation of W state will be more robust against the decoherence effect. ...
We represent an optical scheme using cross-Kerr nonlinearities (XKNLs) and quantum dot (QD) within a single-sided optical cavity (QD-cavity system) to generate three-photon entangled W state containing entanglement against loss of one photon of them. To generate W state (three-photon) with robust entanglement against loss of one photon, we utilize effects of optical nonlinearities in XKNLs (as quantum controlled operations) and QD-cavity system (as a parity operation) with linearly optical devices. In our scheme, the nonlinear (XKNL) gate consists of weak XKNLs, quantum bus beams, and photon-number-resolving measurement to realize controlled-unitary gate between two photons while another nonlinear (QD) gate employs interactions of photons and an electron of QD confined within a single-sided optical cavity for implementation of parity gate. Subsequently, for the efficiency and experimental feasibility of our scheme generating W state, we analyze the immunity of the controlled-unitary gate using XKNLs against decoherence effect and reliable performance of parity gate using QD-cavity system.
... Besides two-photon quantum gates, some three-photon quantum gates are also the reversible and universal logic gates for quantum computation, [43] such as a Fredkin gate and a Toffoli gate. [44] Assisted by strong and weak cross-Kerr nonlinearities, the Fredkin gate and the Toffoli gate with high success probability can be constructed, [30,32,35,[45][46][47][48][49] where the spatial degree of freedom is applied to assist their construction. Relying on the ...
... A general multicontrol gate can be expressed as [45] C n (U 1 ) = (I ⊗ · · · ⊗ I − |1 · · · 1 1 · · · 1|) ⊗ I +|1 · · · 1 1 · · · 1| ⊗ U 1 (1) where I = |0 0| + |1 1| and U 1 is the unitary transformation operated on the target qubit 1; |0 and |1 denote two orthogonal qubits. Adopting the polarization of photon |H and |V as qubits |0 and |1 , the above multicontrol gate becomes a polarization multiphoton controlled one-photon unitary gate. ...
In order to fulfill quantum information processing tasks such as quantum computation and scalable quantum networks, quantum logic gates are indispensable parts. A multiqubit logic gate can efficiently reduce the cost of physical resources and complicated operations that are necessary in the combination of fewer‐qubit (e.g., two‐qubit) logic gates to fulfill the same tasks. However, the construction of multiphoton quantum logic gates is a large challenge. Assisted by spatial and temporal degrees of freedom, a polarization multiphoton controlled one‐photon unitary gate is proposed, which can be realized with three processes including the control‐path process based on weak cross‐Kerr nonlinearities, the unitary transformation process, and the output process. In the control‐path process, the control‐path modules are applied, where the entanglement between polarization, spatial and temporal degrees of freedom is generated by beam splitters, time delayers, and nonlinear interaction in cross‐Kerr media. The scheme presented here, assisted by spatial and temporal degrees of freedom reduces the experimental complexity of the schemes assisted by only spatial degree of freedom. Moreover, it will also be a useful reference in optimally constructing multiqubit quantum logic gates with other multiple degrees of freedom in many physical systems. Based on the spatial and temporal degrees of freedom, a construction scheme of a nearly deterministic polarization multiphoton controlled one‐photon unitary gate with a simple construction circuit and available measurement techniques and operations is proposed, which can be realized with three processes including the control‐path process based on weak cross‐Kerr nonlinearities, the unitary transformation process, and the output process.
