An ideal controlled-NOT gate followed by projective measurements can be used to identify specific Bell states of its two input qubits. When the input qubits are each members of independent Bell states, these projective measurements can be used to swap the post-selected entanglement onto the remaining two qubits. Here we apply this strategy to produce heralded two-photon polarization entanglement using Bell states that originate from independent parametric down-conversion sources, and a particular probabilistic controlled-NOT gate that is constructed from linear optical elements. The resulting implementation is closely related to an earlier proposal by Sliwa and Banaszek [quant-ph/0207117], and can be intuitively understood in terms of familiar quantum information protocols. The possibility of producing a "pseudo-demand" source of two-photon entanglement by storing and releasing these heralded pairs from independent cyclical quantum memory devices is also discussed.The entanglement of two (or more) particles remains one of the most fascinating aspects of quantum mechanics [1]. In addition to its relevance in a number of fundamental issues [2], quantum entanglement has recently been identified as a valuable resource for a variety of quantum information processing tasks [3]. One promising approach to the practical realization of many of these tasks relies on qubits that are encoded in the polarization states of single photons. Consequently, a reliable source of heralded or even "push-button"[4] two-photon polarization entanglement is of great interest at the present time.One recent suggestion for such a source involves photon-pair production from controlled biexciton emission of a single quantum dot [5,6]. Alternatively, one can consider a source based on the photon-pairs produced in parametric down-conversion [7]. However, the random nature of this spontaneous emission process prohibits the direct use of a single two-photon down-conversion source for the production of on-demand pairs, and schemes based on conventional entanglement swapping [8,9] between two down-conversion sources can lead to false heralding signals due to double pair emission from one of the sources [10]. In fact, Kok and Braunstein have shown that the production of one heralded polarizationentangled photon pair using only conventional downconversion sources, linear optical elements, and projective measurements requires at least three initial pairs [11].In this brief paper, we describe a method for producing heralded two-photon entanglement along theses lines. We consider the use of our previously proposed probabilistic controlled-NOT gate [12], which consumes one entangled photon pair as a resource, to essentially perform an entanglement swapping procedure on two additional entangled photon pairs. The end result is a unique detection signature of four photons that heralds the presence of one remaining polarization-entangled pair, with a potentially negligible probability of false heralding due to undesired multiple pair emission from the three i...
Quantum logic operations can be performed using linear optical elements, additional photons (ancilla photons), and postselection based on measurements made on the ancilla. Here we describe a method for generating the required entangled state of n ancilla photons using elementary logic gates and postselection. This approach is capable of generating the ancilla states required for either the original proposal by Knill, Laflamme, and Milburn [E. Knill, R. Laflamme, and G. J. Milburn, Nature 409, 46 (2001)] or those required for the more general high-fidelity approach [J. D. Franson, M. M. Donegan, M. J. Fitch, B. C. Jacobs, and T. B. Pittman, Phys. Rev. Lett. 89, 137901 (2002)]. We also show that the entangled ancilla photons could be generated using a series of quantum wells coupled with tunnel junctions.
Abstract:The quantum-mechanical state vector is not directly observable even though it is the fundamental variable that appears in Schrodinger's equation. In conventional time-dependent perturbation theory, the state vector must be calculated before the experimentally-observable expectation values of relevant operators can be computed. We discuss an alternative form of time-dependent perturbation theory in which the observable expectation values are calculated directly and expressed in the form of nested commutators. This result is consistent with the fact that the commutation relations determine the properties of a quantum system, while the commutators often have a form that simplifies the calculation and avoids canceling terms. The usefulness of this method is illustrated using several problems of interest in quantum optics and quantum information processing.
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