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Journal of Optics B Quantum and Semiclassical Optics

Distinguishing Schrödinger cats in a lossy environment

A. Gábris, Петер Адам, Mátyás Koniorczyk, József Janszky

Published Mar 1, 2004• 7 citations
Publisher

Abstract

Optical Schrödinger cat states—that is, even and odd coherent states—are considered as possible candidates for forming a computational basis for a coherent state qubit. The distinguishability of the two originally orthogonal states after experiencing loss is quantified in terms of quantum relative entropy. This is a physically instructive quantity related to probabilities of faults in identifying the state. This distinguishability is important for classical communication and for the problem of reading out the result of a quantum computation by a lossy device. It is shown that the distinguishability can significantly increase if the environment is prepared in an appropriately chosen squeezed state.

DOI
10.1088/1464-4266/6/3/014

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Optical Schrödinger cat states—that is, even and odd coherent states—are considered as possible candidates for forming a computational basis for a coherent state qubit. The distinguishability of the two originally orthogonal states after experiencing loss is quantified in terms of quantum relative entropy. This is a physically instructive quantity related to probabilities of faults in identifying the state. This distinguishability is important for classical communication and for the problem of reading out the result of a quantum computation by a lossy device. It is shown that the distinguishability can significantly increase if the environment is prepared in an appropriately chosen squeezed state.
The optical cat state plays an essential role in quantum computation and quantum metrology. Here, we experimentally quantify quantum coherence of an optical cat state by means of relative entropy and the l 1 norm of coherence in a Fock basis based on the prepared optical cat state at the rubidium D1 line. By transmitting the optical cat state through a lossy channel, we also demonstrate the robustness of quantum coherence of the optical cat state in the presence of loss, which is different from the decoherence properties of fidelity and Wigner function negativity of the optical cat state. Our results confirm that quantum coherence of optical cat states is robust against loss and pave the way for the application of optical cat states.
Quantum coherence is one of the most fundamental features of quantum mechanics that underlines the unique characteristics of quantum technology. Optical cat state is a superposition of two coherent states and has broad applications in quantum information and quantum metrology. In the application of optical cat state, it is essential to investigate the quantum coherence of it when it interacts with the environment. In this manuscript, we present the quantum coherence of an optical cat state in a noisy channel by calculating the relative entropy in Fock basis. We show that the quantum coherence of an optical cat state is robust against loss and noise in a noisy channel. Different from quantum coherence, the negativity of the Wigner function and the fidelity of the cat state are not robust against loss and noise. Our result provides a reference for applying optical cat states in a noisy environment.
We present novel theory of effective realization of large-size optical Schrödinger cat states, which play an important role for quantum communication and quantum computation in the optical domain using laser sources. The treatment is based on the α-representation in infinite Hilbert space which is the decomposition of an arbitrary quantum state in terms of displaced number states characterized by the displacement amplitude α. We find analytical form of the α-representation for both even and odd Schrödinger cat states which is essential for their generation schemes. Two schemes are proposed for generating even/odd Schrödinger cat states of large size |β| (|β| ≥ 2) with high fidelity F (F ≈ 0.99). One scheme relies on an initially offline prepared two-mode entangled state with a fixed total photon number, while the other scheme uses separable photon Fock states as the input. In both schemes, generation of the desired states is heralded by the corresponding measurement outcomes. Conditions for obtaining states useful for quantum information processing are established and success probabilities for their generation are evaluated.
A Schrödinger-cat state is a coherent superposition of macroscopically distinguishable quantum states, in quantum optics usually realized as superposition of coherent states.Protocols to prepare photonic cats have been presented for atomic systems.Here we investigate in what manner and how well the preparation protocols can be transferred to a solid-state platform, namely, a semiconductor quantum-dot-cavity system.In quantum-dotcavity systems there are many disruptive influences like cavity losses, the radiative decay of the quantum dot, and the coupling to longitudinal acoustic phonons.We show that for one of the protocols these influences kill the quantum coherence between the states forming the cat, while for a second protocol a parameter regime can be identified where the essential characteristics of Schrödinger-cat states survive the environmental influences under conditions that can be realized with current equipment.
Most quantum computation schemes propose encoding qubits in two-level systems. Others exploit the use of an infinite-dimensional system. In "Encoding a qubit in an oscillator" [Phys. Rev. A 64, 012310 (2001)], Gottesman, Kitaev, and Preskill (GKP) combined these approaches when they proposed a fault-tolerant quantum computation scheme in which a qubit is encoded in the continuous position and momentum degrees of freedom of an oscillator. One advantage of this scheme is that it can be performed by use of relatively simple linear optical devices, squeezing, and homodyne detection. However, we lack a practical method to prepare the initial GKP states. Here we propose the generation of an approximate GKP state by using superpositions of optical coherent states (sometimes called "Schrödinger cat states"), squeezing, linear optical devices, and homodyne detection.
Abstract Generation of nonclassical states is a necessary requirement for all quantum science and technology protocols. In this regard, Schrödinger cat states, as quantum superpositions of mocroscopically distinguishable coherent states with equal amplitude and opposite phases, have been of great importance in recent years. In this paper, using some appropriate nonlinear optical media, a theoretical scheme is employed to generate various classes of cat-like states with the help of the connection between quantum and nonlinear optics. In fact, we have exploited a single simple method to produce even, odd and also Yurke-Stoler cat-like states by considering different input states such as coherent squeezed, squeezed coherent, photon-added coherent, pair coherent and trio coherent states. To achieve the purpose, we extensively use cross-Kerr interaction and its further generalizations to higher-orders. Projective measurement is the original conception behind the represented approach by which distinct types of nonclassical states are obtained. At last, we pay our attention to the unavoidable effect of field dissipation and show that in most of the above-studied states we may still achieve the cat-like states, however, with attenuated amplitudes.