Universal quantum cloning in cavity QED

Abstract

We propose an implementation of an universal quantum cloning machine [UQCM, Hillery and Buzek, Phys. Rev. A 56, 3446 (1997)] in a Cavity Quantum Electrodynamics (CQED) experiment. This UQCM acts on the electronic states of atoms that interact with the electromagnetic field of a high Q cavity. We discuss here the specific case of the 1 → 2 cloning process using either a one-or a two-cavity configuration. What is the best quantum copying operation? The answer to this question is context-dependent. On the one hand, there is a single transformation that produces the best identical copies of a qubit prepared in any input states. This "universal quantum cloning machine" (UQCM) has been discussed for the first time in [2]. On the other hand, many other rules of the game can be considered, such as state dependent cloning [3], cloning of 3-dimensional states [4] and cloning of orthogonal qubits [5].The quality of a copy is usually measured by the quantum fidelity [6]. This quantity is discussed, in the context of universal quantum cloning machine (UQCM), in [2] and [7]. When M copies are produced from N identical pure 2-dimensional states, the fidelity of the copies is given by (N + 2)). For the simplest case of two copies produced from one input state, this expression reduces to F (1, 2) = 5/6. The complete understanding of the fidelity behavior versus N and M is still a subject of debate, with connections to the measurement and state estimation problems [8]. Beyond these fundamental problems, the interest of quantum cloning machines also encompasses a wide area of quantum information processing, including quantum cryptography, teleportation [9], eavesdropping, state preservation and measurement-related problems, as well as quantum algorithm improvements [10].The derivation of the optimal UQCM transformation led to several proposals [11] for its experimental implementation. Most of them, based on the Buzek and Hillery quantum logics network [12], use the quantum optics framework. Experimental quantum cloning has been realized up to now only with photons as the carriers of quantum information. This information was either encoded in different degrees of freedom of the same photon (polarization and position) [13] or in the photon polarization only [14]. An alternative network adapted to NMRbased quantum information processors has also been proposed and experimentally implemented [15].In this paper, we propose an implementation of the 1 → 2 UQCM operating for atomic states in the Cavity QED (CQED) context [16]. The quantum information is coded on electronic levels of long-lived highly excited Rubidium (Rb) atoms. Our protocol realizes, with four atoms, the transformation described in [2], with an original quantum logics network based on the resonant interaction between the atoms and two high-Q niobium superconducting microwave cavities C a and C b . We discuss, at the end of this paper, an adaptation of the scheme using two different modes of a single cavity [17], making the proposal implementation more realistic with the ...

Scheme for the implementation of a universal quantum cloning machine via cavity-assisted atomic collisions in cavity QED

“…At this scale the time, which is needed to rotate the single qubit, is negligible. Thus, the interaction time, which is needed to perform the total procedure is shorter than the time, which is needed by the scheme [19]. This time interval is much shorter than T r and the photon lifetime 1ms in the present cavity.…”

“…In contrast to the scheme [19], our scheme requires a cavity-assisted collisions between atoms [20]. This technique has been experimentally demonstrated [21].…”

“…In contrast to the scheme [19], only simple two-level atoms are required, which interact with the cavity fields. This might simplify the experimental implementation of the scheme of Buzek et al In contrast to the scheme of Milman et al [19], our scheme requires a cavity-assisted collisions between atoms [20]. This technique has been experimentally demonstrated [21].…”

“…An alternative experimental implementation of the cloning network, which is based on the NMR system, has been reported [18]. More recently, a cavity QED scheme is proposed to implement a 1 → 2 universal quantum cloning machine by using a resonant atom-cavity interaction [19]. In this scheme, cavities act as memories, which store the information of an electric system and transfer it back to this electric system after the conditional dynamics.…”

Quantum Cloning and Cavity QED

“…Several protocols have been advanced recently [9]. The reference [9] makes use of three atomic levels |e , |g and |i ; the |g ↔ |e transition determines the frequencies of the two cavities and |i corresponds to an auxiliary state that is out of resonance with the fields in the cavities.…”