Simple pulse sequence for quantum logic operations using photon-exchange interactions
This paper has been withdrawn by the authors due to an error first noted by M. Lukin.
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arXiv subjects
J. D. Franson
Publications and source records attributed to J. D. Franson.
Violation of Bell's Inequality with Photons from Independent Sources
We report a violation of Bell's inequality using one photon from a parametric down-conversion source and a second photon from an attenuated laser beam. The two photons were entangled at a beam splitter using the post-selection technique of Shih and Alley [Phys. Rev. Lett. 61, 2921 (1988)]. A quantum interference pattern with a visibility of 91% was obtained using the photons from these independent sources, as compared with a visibility of 99.4% using two photons from a central parametric down-conversion source.
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Heralded Two-Photon Entanglement from Probabilistic Quantum Logic Operations on Multiple Parametric Down-Conversion Sources
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.
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Cyclical Quantum Memory for Photonic Qubits
We have performed a proof-of-principle experiment in which qubits encoded in the polarization states of single-photons from a parametric down-conversion source were coherently stored and read-out from a quantum memory device. The memory device utilized a simple free-space storage loop, providing a cyclical read-out that could be synchronized with the cycle time of a quantum computer. The coherence of the photonic qubits was maintained during switching operations by using a high-speed polarizing Sagnac interferometer switch.
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Single Photons on Pseudo-Demand from Stored Parametric Down-Conversion
We describe the results of a parametric down-conversion experiment in which the detection of one photon of a pair causes the other photon to be switched into a storage loop. The stored photon can then be switched out of the loop at a later time chosen by the user, providing a single photon for potential use in a variety of quantum information processing applications. Although the stored single photon is only available at periodic time intervals, those times can be chosen to match the cycle time of a quantum computer by using pulsed down-conversion. The potential use of the storage loop as a photonic quantum memory device is also discussed.
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Quantum relays and noise suppression using linear optics
Probabilistic quantum non-demolition (QND) measurements can be performed using linear optics and post-selection. Here we show how QND devices of this kind can be used in a straightforward way to implement a quantum relay, which is capable of extending the range of a quantum cryptography system by suppressing the effects of detector noise. Unlike a quantum repeater, a quantum relay system does not require entanglement purification or the ability to store photons.
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Demonstration of Feed-Forward Control for Linear Optics Quantum Computation
One of the main requirements in linear optics quantum computing is the ability to perform single-qubit operations that are controlled by classical information fed forward from the output of single photon detectors. These operations correspond to pre-determined combinations of phase corrections and bit-flips that are applied to the post-selected output modes of non-deterministic quantum logic devices. Corrections of this kind are required in order to obtain the correct logical output for certain detection events, and their use can increase the overall success probability of the devices. In this paper, we report on the experimental demonstration of the use of this type of feed-forward system to increase the probability of success of a simple non-deterministic quantum logic operation from approximately 1/4 to 1/2. This logic operation involves the use of one target qubit and one ancilla qubit which, in this experiment, are derived from a parametric down-conversion photon pair. Classical information describing the detection of the ancilla photon is fed-forward in real-time and used to alter the quantum state of the output photon. A fiber optic delay line is used to store the output photon until a polarization-dependent phase shift can be applied using a high speed Pockels cell.
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High-fidelity quantum logic operations using linear optical elements
Knill, Laflamme, and Milburn [Nature 409, 46 (2001)] have shown that quantum logic operations can be performed using linear optical elements and additional ancilla photons. Their approach is probabilistic in the sense that the logic devices fail to produce an output with a failure rate that scales as 1/n, where n is the number of ancilla. Here we present an alternative approach in which the logic devices always produce an output with an intrinsic error rate that scales as 1/n^2,which may have several advantages in quantum computing applications.
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Dispersion cancellation and non-classical noise reduction for large photon-number states
Nonlocal dispersion cancellation is generalized to frequency-entangled states with large photon number N. We show that the same entangled states can simultaneously exhibit a factor of 1/sqrt(N) reduction in noise below the classical shot noise limit in precise timing applications, as was previously suggested by Giovannetti, Lloyd and Maccone (Nature v412 (2001) p417). The quantum-mechanical noise reduction can be destroyed by a relatively small amount of uncompensated dispersion and entangled states of this kind have larger timing uncertainties than the corresponding classical states in that case. Similar results were obtained for correlated states, anti-correlated states, and frequency-entangled coherent states, which shows that these effects are a fundamental result of entanglement.
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Perturbation theory for quantum-mechanical observables
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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Demonstration of Non-Deterministic Quantum Logic Operations using Linear Optical Elements
Knill, Laflamme, and Milburn recently showed that non-deterministic quantum logic operations could be performed using linear optical elements, additional photons (ancilla), and post-selection based on the output of single-photon detectors [Nature 409, 46 (2001)]. Here we report the experimental demonstration of two logic devices of this kind, a destructive controlled-NOT (CNOT) gate and a quantum parity check. These two devices can be combined with a pair of entangled photons to implement a conventional (non-destructive) CNOT that succeeds with a probability of 1/4.
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Probabilistic Quantum Logic Operations Using Polarizing Beam Splitters
It has previously been shown that probabilistic quantum logic operations can be performed using linear optical elements, additional photons (ancilla), and post-selection based on the output of single-photon detectors. Here we describe the operation of several quantum logic operations of an elementary nature, including a quantum parity check and a quantum encoder, and we show how they can be combined to implement a controlled-NOT (CNOT) gate. All of these gates can be constructed using polarizing beam splitters that completely transmit one state of polarization and totally reflect the orthogonal state of polarization, which allows a simple explanation of each operation. We also describe a polarizing beam splitter implementation of a CNOT gate that is closely analogous to the quantum teleportation technique previously suggested by Gottesman and Chuang [Nature 402, p.390 (1999)]. Finally, our approach has the interesting feature that it makes practical use of a quantum-eraser technique.
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Reply to a review of photon-exchange interactions by Opatrny and Kurizki
In a recent review article, Opatrny and Kurizki [submitted to Fortschr. Phys., e-print quant-ph/0003010] discussed a number of issues related to the feasibility of quantum computation based on photon-exchange interactions. This Reply summarizes my view of each of the issues and the overall prospects for quantum computing based on photon-exchange interactions.
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Maxwell Duality, Lorentz Invariance, and Topological Phase
We discuss the Maxwell electromagnetic duality relations between the Aharonov-Bohm, Aharonov-Casher, and He-McKellar-Wilkens topological phases, which allows a unified description of all three phenomena. We also elucidate Lorentz transformations that allow these effects to be understood in an intuitive fashion in the rest frame of the moving quantum particle. Finally, we propose two experimental schemes for measuring the He-McKellar-Wilkens phase.
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