Photonic two-qubit parity gate with tiny cross–Kerr nonlinearity

Abstract

The cross-Kerr nonlinearity (XKNL) effect can induce efficient photon interactions in principle with which photonic multiqubit gates can be performed using far fewer physical resources than linear optical schemes. Unfortunately, it is extremely challenging to generate giant cross-Kerr nonlinearities. In recent years, much effort has been made to perform multiqubit gates via weak XKNLs. However, the required nonlinearity strengths are still difficult to achieve in the experiment. We here propose an XKNL-based scheme for realizing a twophoton polarization-parity gate, a universal two-qubit gate, in which the required strength of the nonlinearity could be orders of magnitude weaker than those required for previous schemes. The scheme utilizes a ring cavity fed by a coherent state as a quantum information bus which interacts with a path mode of the two polarized photons (qubits). The XKNL effect makes the bus pick up a phase shift dependent on the photon number of the path mode. Even when the potential phase shifts are very small they can be effectively measured using photon-number resolving detectors, which accounts for the fact that our scheme can work in the regime of tiny XKNL. The measurement outcome reveals the parity (even parity or odd parity) of the two polarization qubits.

Quantum Fourier transform of polarization photons mediated by weak cross-Kerr nonlinearity

“…In particular, electromagnetically induced transparencies (EIT) [73][74][75], whispering-gallery mode microresonators (toroid microcavities) [50,76,77], optical fibers [78], and cavity QED systems [79,80] can be applied to amplify the nonlinear strength. The atomic systems working under EIT [81] can amplify the cross-Kerr nonlinear interaction, and lower the absorbtion or losses of the signal photons and the coherent beam under the condition of weak nonlinearity (θ ≪ 1).…”

“…Provided with the nonlinear interaction, the light beams in the Kerr media can generate cross-phase modulation, which enables a coherent state to pick up a phase shift due to the presence of signal photons. Based on it, considerable related works were achieved [31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50].…”

Nonlinearity enhancement in optomechanical systems

“…It also can be used to perform quantum gate [31,32], quantum information procession [33,34], and entanglement generation [35][36][37][38]. As a usage of the present scheme, we now study the QND measurement of phonon and photon.…”

“…If the system contains the cross-Kerr nonlinearity with the term η 1ĉ † 1ĉ 1ĉ † 2ĉ 2 , then we will have e −iη 1ĉ † 1ĉ 1ĉ † 2ĉ 2 t |α,1 c 1 ,c 2 = |αe iη 1 t ,1 , the c 1 mode acquires a phase. When the phase equals to π , a two-photon controlled-phase gate is naturally implemented, from which a CNOT gate can also be easily constructed [31,32]. Performing quadrature operator x = c 1 + c † 1 measurement by the homodyne apparatus, we know x = 2α cos η 1 t. Employing the HamiltonianĤ I =Ĥ af 2 +Ĥ f o1 (temporarily ignoring the driving fields), we plot ĉ † 1ĉ 1 , ĉ † 2ĉ 2 , X c 1 and X c 2 in Fig.…”

Remote Quantum-Information Concentration: Reversal of Ancilla-Free Phase-Covariant Telecloning

“…Very recently, we have also proposed a near deterministic scheme [39] for realizing nondestructively the photonic Bell-state (or GHZ-state) measurement with the two-photon parity gate based on cross-Kerr nonlinearity (see Ref. [40] and the references therein). All these achievements may contribute to our RQIC scheme in physical realization.…”