A Quantum Rosetta Stone for Interferometry

Heisenberg-limited measurement protocols can be used to gain an increase in measurement precision over classical protocols. Such measurements can be implemented using, e.g., optical Mach-Zehnder interferometers and Ramsey spectroscopes. We address the formal equivalence between the Mach-Zehnder interferometer, the Ramsey spectroscope, and the discrete Fourier transform. Based on this equivalence we introduce the ``quantum Rosetta stone'', and we describe a projective-measurement scheme for generating the desired correlations between the interferometric input states in order to achieve Heisenberg-limited sensitivity. The Rosetta stone then tells us the same method should work in atom spectroscopy.Comment: 8 pages, 4 figure

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.Comment: 5 pages, 4 figures; submitted to IEEE Journal of Selected Topics in Quantum Electronics, special issue on "Quantum Internet Technologies

From Linear Optical Quantum Computing to Heisenberg-Limited Interferometry

The working principles of linear optical quantum computing are based on photodetection, namely, projective measurements. The use of photodetection can provide efficient nonlinear interactions between photons at the single-photon level, which is technically problematic otherwise. We report an application of such a technique to prepare quantum correlations as an important resource for Heisenberg-limited optical interferometry, where the sensitivity of phase measurements can be improved beyond the usual shot-noise limit. Furthermore, using such nonlinearities, optical quantum nondemolition measurements can now be carried out at the single-photon level.Comment: 10 pages, 5 figures; Submitted to a Special Issue of J. Opt. B on "Fluctuations and Noise in Photonics and Quantum Optics" (Herman Haus Memorial Issue); v2: minor change

Photon number resolution using a time-multiplexed single-photon detector

Photon number resolving detectors are needed for a variety of applications including linear-optics quantum computing. Here we describe the use of time-multiplexing techniques that allows ordinary single photon detectors, such as silicon avalanche photodiodes, to be used as photon number-resolving detectors. The ability of such a detector to correctly measure the number of photons for an incident number state is analyzed. The predicted results for an incident coherent state are found to be in good agreement with the results of a proof-of-principle experimental demonstration.Comment: REVTeX4, 6 pages, 8 eps figures, v2: minor changes, v3: changes in response to referee report, appendix added, 1 reference adde

Nano-displacement measurements using spatially multimode squeezed light

We demonstrate the possibility of surpassing the quantum noise limit for simultaneous multi-axis spatial displacement measurements that have zero mean values. The requisite resources for these measurements are squeezed light beams with exotic transverse mode profiles. We show that, in principle, lossless combination of these modes can be achieved using the non-degenerate Gouy phase shift of optical resonators. When the combined squeezed beams are measured with quadrant detectors, we experimentally demonstrate a simultaneous reduction in the transverse x- and y- displacement fluctuations of 2.2 dB and 3.1 dB below the quantum noise limit.Comment: 21 pages, 9 figures, submitted to "Special Issue on Fluctuations & Noise in Photonics & Quantum Optics" of J. Opt.

Creation of maximally entangled photon-number states using optical fiber multiports

We theoretically demonstrate a method for producing the maximally path-entangled state (1/Sqrt[2]) (|N,0> + exp[iN phi] |0,N>) using intensity-symmetric multiport beamsplitters, single photon inputs, and either photon-counting postselection or conditional measurement. The use of postselection enables successful implementation with non-unit efficiency detectors. We also demonstrate how to make the same state more conveniently by replacing one of the single photon inputs by a coherent state.Comment: 4 pages, 1 figure. REVTeX4. Replaced with published versio

Review article: Linear optical quantum computing

Linear optics with photon counting is a prominent candidate for practical quantum computing. The protocol by Knill, Laflamme, and Milburn [Nature 409, 46 (2001)] explicitly demonstrates that efficient scalable quantum computing with single photons, linear optical elements, and projective measurements is possible. Subsequently, several improvements on this protocol have started to bridge the gap between theoretical scalability and practical implementation. We review the original theory and its improvements, and we give a few examples of experimental two-qubit gates. We discuss the use of realistic components, the errors they induce in the computation, and how these errors can be corrected.Comment: 41 pages, 37 figures, many small changes, added references, and improved discussion on error correction and fault toleranc

Conditional generation of arbitrary multimode entangled states of light with linear optics

We propose a universal scheme for the probabilistic generation of an arbitrary multimode entangled state of light with finite expansion in Fock basis. The suggested setup involves passive linear optics, single photon sources, strong coherent laser beams, and photodetectors with single-photon resolution. The efficiency of this setup may be greatly enhanced if, in addition, a quantum memory is available.Comment: 7 pages, 5 figure