Measurement-induced chaos and quantum state discrimination in an iterated Tavis-Cummings scheme

Abstract

A cavity quantum electrodynamical scenario is proposed for implementing a Schrödinger microscope capable of amplifying differences between nonorthogonal atomic quantum states. The scheme involves an ensemble of identically prepared two-level atoms interacting pairwise with a single mode of the radiation field as described by the Tavis-Cummings model. By repeated measurements of the cavity field and of one atom within each pair a measurement-induced nonlinear quantum transformation of the relevant atomic states can be realized. The intricate dynamical properties of this nonlinear quantum transformation, which exhibits measurement-induced chaos, allow approximate orthogonalization of atomic states by purification after a few iterations of the protocol and thus the application of the scheme for quantum state discrimination.

Quantum state identification of qutrits via a nonlinear protocol

“…Various protocols have been proposed for efficient quantum state discrimination (QSD) (see reviews [17,18]). A crucial ingredient of these methods is to have an ensemble of identical quantum systems for implementing QSD [19][20][21][22]. Measurement-induced nonlinear dynamics is experimentally feasible in quantum optics [23], and it has been shown [20,22] that nonlinear quantum transformations could be a possible way for implementing QSD of two-level quantum systems.…”

“…A crucial ingredient of these methods is to have an ensemble of identical quantum systems for implementing QSD [19][20][21][22]. Measurement-induced nonlinear dynamics is experimentally feasible in quantum optics [23], and it has been shown [20,22] that nonlinear quantum transformations could be a possible way for implementing QSD of two-level quantum systems. In this report we propose a scheme which can be used for QSD of three-level quantum systems.…”

Iterált harmadfokú kvantuminformatikai protokollok

“…Az így létrejövő folyamat megfeleltethető egy komplex polinomok hányadosaként előálló komplex függvény iterált dinamikájának, ha a qubitet egy komplex számmal reprezentáljuk, ezért bizonyos kezdőfeltételek esetén kaotikus viselkedésre vezet [2]. Az ilyen nemlineáris folyamatoknak számos kvantuminformatikai alkalmazása lehet, mint például a kvantumállapotok tisztítása [3] vagy a kvantumállapot-megkülönböztetés [4,5,6]. Egy másik, érzékenységükön alapuló gyakorlati felhasználásuk lehet a kvantum-áramkörök, kvantum-chipek tesztelése, a fellépő zaj és hibaforrások feltérképezése.…”

Experimental orthogonalization of highly overlapping quantum states with single photons

“…The resulting protocols, when applied iteratively, lead to highly nontrivial dynamics, with several intriguing features, such as a variety of fractals on the Bloch sphere representing the initial state of the qubit, leading to nonconvergent, chaotic behavior [7][8][9]. One obviously cannot beat usual quantum efficiency limits in this way, since the emergent nonlinearity is an effective feature and one has to pay its cost in the form of discarded qubits [7], nevertheless, these protocols may find applications for specific tasks, e.g.…”

“…Linear optics is a natural candidate among a variety of physical systems [18,19] for realizing the protocols of quantum information processing [20]. In order to effectively implement quantum gates, linear optics has to be complemented by either optical elements exhibiting strong optical non-linearity [21] or, alternatively, apply post-selection with ancilla modes and projective measurements [7,8,10] resulting in probabilistic realizations.…”