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arXiv:quant-ph/0304031 · Physical Review A

Interaction-free generation of entanglement

Hiroo Azuma

Published Aug 28, 2003• 23 citations
arXivHTMLPDF

Abstract

In this paper, we study the generation of entanglement by interaction-free measurements. Using Kwiat et al.'s interferometer, we construct a two-qubit quantum gate that changes one particle's trajectory according to the other particle's trajectory. We propose methods for generating the Bell state from an electron and a positron and from a pair of photons using this gate. We also show that, by using this gate, we can carry out the Bell measurement with a probability of 3/4 at the maximum and execute a controlled-NOT operation by the method proposed by Gottesman and Chuang with a probability of 9/16 at the maximum. We estimate the success probability for generating the Bell state by our procedure under imperfect interaction.

DOI
10.1103/physreva.68.022320

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In this paper, we study the generation of entanglement by interaction-free measurements. Using Kwiat et al.'s interferometer, we construct a two-qubit quantum gate that changes one particle's trajectory according to the other particle's trajectory. We propose methods for generating the Bell state from an electron and a positron and from a pair of photons using this gate. We also show that, by using this gate, we can carry out the Bell measurement with a probability of 3/4 at the maximum and execute a controlled-NOT operation by the method proposed by Gottesman and Chuang with a probability of 9/16 at the maximum. We estimate the success probability for generating the Bell state by our procedure under imperfect interaction.
In this paper, we study the quantum computation realized by an interaction-free measurement (IFM). Using the interferometer of Kwiat et al., we construct a two-qubit quantum gate that changes one particle's trajectory according to whether or not the other particle exists in the interferometer. We propose a method for distinguishing Bell-basis vectors, each of which consists of a pair of an electron and a positron, by this gate. (This is called the Bell-basis measurement.) This method succeeds with probability 111 in the limit of $N\ensuremath{\rightarrow}\ensuremath{\infty}$, where NNN is the number of beam splitters in the interferometer. Moreover, we can carry out a controlled-NOT gate operation by the above Bell-basis measurement and the method proposed by Gottesman and Chuang. Therefore, we can prepare a universal set of quantum gates by the IFM. This means that we can execute any quantum algorithm by the IFM.
Quantum entanglement is a cornerstone of quantum mechanics. While the entanglement of confined electron pairs has been established early on, the entanglement of free-traveling electron pairs, particularly at high energies, remains largely unexplored due to the substantial challenges involved in measuring the spins of free-traveling electrons. In this study, we investigate the entanglement and the Bell inequality violation of free-traveling electron-positron pairs generated in a fixed-target experiment. This experimental setup facilitates the creation of a controllable source of entangled electron-positron pairs, where entangled events are produced in specific phase spaces. Based on this source and the prior knowledge of the entangled state, we demonstrate the feasibility of measuring the polarization correlations of the entangled e + e − pairs through their individual secondary scatterings off two separate additional targets.
QUANTUM CONTROL AND GENERATION OF QUANTUM ENTANGLEMENT In this thesis, the generation of entanglement is studied in a controlled environment. The model system of interest includes a cavity field interacting with a pair of atoms. The cavity field is heavily damped and it is pumped in order to maintain a steady state field population. Thus, we can eliminate the cavity field adiabatically and obtain the master equation describing only the qubits evolution in time. At first, this system is analyzed in the steady state, without making any measurement on the photons leaking through the cavity walls. In this way, the ideal physical parameter set for maximum entanglement in this model is investigated. In the second step, we assume a direct measurement on the leaking cavity photons, and observe the evolution of entanglement in a quantum trajectories approach. We simulate quantum trajectories approach by applying Monte Carlo method. The amount of entanglement is obtained as a function of time and number of photon detections.
We propose probabilistic controlled-NOT and controlled-phase gates for qubits stored in the polarization of photons. The gates are composed of linear optics and photon detectors, and consume polarization entangled photon pairs. The fraction of the successful operation is only limited by the efficiency of the Bell-state measurement. The gates work correctly under the use of imperfect detectors and lossy transmission of photons. Combined with single-qubit gates, they can be used for producing arbitrary polarization states and for designing various quantum measurements.
Entangled photons are a crucial resource for linear optical quantum communication and quantum computation. Besides the remarkable progress of photon state engineering using atomic memories (Kimble (2008); Yuan et al. (2008)) the majority of current experiments is based on the production of photon pairs in the process of spontaneous parametric down-conversion (SPDC), where the entangled photon pair is concluded from post-selection of randomly occurring coincidences. Here we present new insights into the heralded generation of photon states (Barz et al. (2010); Wagenknecht et al. (2010)) that are maximally entangled in polarization (Schrodinger (1935)) with linear optics and standard photon detection from SPDC (Kwiat et al. (1995)). We utilize the down-conversion state corresponding to the generation of three pairs of photons, where the coincident detection of four auxiliary photons unambiguously heralds the successful preparation of the entangled state (Śliwa & Banaszek (2003)). This controlled generation of entangled photon states is a significant step towards the applicability of a linear optics quantum network (Nielsen & Chuang (2000)), in particular for entanglement distribution (Bennett et al. (1996)), entanglement swapping (Kaltenbaek et al. (2009); Pan et al. (1998)), quantum teleportation (Bouwmeester et al. (1997)), quantum cryptography (Bennett & Brassard (1984); Ekert (1991); Jennewein et al. (2000)) and scalable approaches towards photonics-based quantum computing schemes (Browne & Rudolph (2004); Gottesman & Chuang (1999); Knill et al. (2001)).