All our former experience with application of quantum theory seems to say:
{\it what is predicted by quantum formalism must occur in laboratory} But the
essence of quantum formalism - entanglement, recognized by Einstein, Podolsky,
Rosen and Schr\"odinger - waited over 70 years to enter to laboratories as a
new resource as real as energy This holistic property of compound quantum systems, which involves
nonclassical correlations between subsystems, is a potential for many quantum
processes, including ``canonical'' ones: quantum cryptography, quantum
teleportation and dense coding However, it appeared that this new resource is
very complex and difficult to detect Being usually fragile to environment, it
is robust against conceptual and mathematical tools, the task of which is to
decipher its rich structure This article reviews basic aspects of entanglement including its
characterization, detection, distillation and quantifying In particular, the
authors discuss various manifestations of entanglement via Bell inequalities,
entropic inequalities, entanglement witnesses, quantum cryptography and point
out some interrelations They also discuss a basic role of entanglement in
quantum communication within distant labs paradigm and stress some
peculiarities such as irreversibility of entanglement manipulations including
its extremal form - bound entanglement phenomenon A basic role of entanglement
witnesses in detection of entanglement is emphasized

Quantum entanglement

Quantum computers promise to increase greatly the efficiency of solving problems such as factoring large integers, combinatorial optimization and quantum physics simulation. One of the greatest challenges now is to implement the basic quantum-computational elements in a physical system and to demonstrate that they can be reliably and scalably controlled. One of the earliest proposals for quantum computation is based on implementing a quantum bit with two optical modes containing one photon. The proposal is appealing because of the ease with which photon interference can be observed. Until now, it suffered from the requirement for non-linear couplings between optical modes containing few photons. Here we show that efficient quantum computation is possible using only beam splitters, phase shifters, single photon sources and photo-detectors. Our methods exploit feedback from photo-detectors and are robust against errors from photon loss and detector inefficiency. The basic elements are accessible to experimental investigation with current technology.

A scheme for efficient quantum computation with linear optics.

The statistical error in any estimation can be reduced by repeating the measurement and averaging the results. The central limit theorem implies that the reduction is proportional to the square root of the number of repetitions. Quantum metrology is the use of quantum techniques such as entanglement to yield higher statistical precision than purely classical approaches. In this Review, we analyse some of the most promising recent developments of this research field and point out some of the new experiments. We then look at one of the major new trends of the field: analyses of the effects of noise and experimental imperfections.

Advances in quantum metrology

Quantum key distribution (QKD) is the first quantum information task to reach the level of mature technology, already fit for commercialization. It aims at the creation of a secret key between authorized partners connected by a quantum channel and a classical authenticated channel. The security of the key can in principle be guaranteed without putting any restriction on an eavesdropper's power. This article provides a concise up-to-date review of QKD, biased toward the practical side. Essential theoretical tools that have been developed to assess the security of the main experimental platforms are presented (discrete-variable, continuous-variable, and distributed-phase-reference protocols).

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The security of practical quantum key distribution

Linear optics with photon counting is a prominent candidate for practical quantum computing. The protocol by Knill, Laflamme, and Milburn [2001, Nature (London) 409, 46] 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. The original theory and its improvements are reviewed, and a few examples of experimental two-qubit gates are given. The use of realistic components, the errors they induce in the computation, and how these errors can be corrected is discussed.

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Linear optical quantum computing with photonic qubits

Precision measurements are important across all fields of science In particular, optical phase measurements can be used to measure distance, position, displacement, acceleration, and optical path length Quantum entanglement enables higher precision than would otherwise be possible We demonstrated an optical phase measurement with an entangled four-photon interference visibility greater than the threshold to beat the standard quantum limit-the limit attainable without entanglement These results open the way for new high-precision measurement applications

Beating the Standard Quantum Limit with Four-Entangled Photons

Entangled states represent correlations between two separate systems that are too precise to be represented by products of local quantum states. We show that this limit of precision for the local quantum states of a pair of N-level systems can be defined by an appropriate class of uncertainty relations. The violation of such local uncertainty relations may be used as an experimental test of entanglement generation.

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Violation of local uncertainty relations as a signature of entanglement

Visible light photon counters feature noise-free avalanche multiplication and narrow pulse height distribution for single photon detection events. Such a well-defined pulse height distribution for a single photon detection event, combined with the fact that the avalanche multiplication is confined to a small area of the whole detector, opens up the possibility for the simultaneous detection of two photons. In this letter, we investigated this capability using twin photons generated by parametric down conversion, and present a high quantum efficiency (∼47%) detection of two photons with good time resolution (∼2 ns), which can be distinguished from a single-photon incidence with a small bit-error rate (∼0.63%).

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Multiphoton detection using visible light photon counter

Among the applications of optical phase measurement, the differential interference contrast microscope is widely used for the evaluation of opaque materials or biological tissues. However, the signal-to-noise ratio for a given light intensity is limited by the standard quantum limit, which is critical for measurements where the probe light intensity is limited to avoid damaging the sample. The standard quantum limit can only be beaten by using N quantum correlated particles, with an improvement factor of √N. Here we report the demonstration of an entanglement-enhanced microscope, which is a confocal-type differential interference contrast microscope where an entangled photon pair (N=2) source is used for illumination. An image of a Q shape carved in relief on the glass surface is obtained with better visibility than with a classical light source. The signal-to-noise ratio is 1.35±0.12 times better than that limited by the standard quantum limit.

An entanglement-enhanced microscope.

We report the first experimental demonstration of an optical quantum controlled-NOT gate without any path interference, where the two interacting path interferometers of the original proposals have been replaced by three partially polarizing beam splitters with suitable polarization dependent transmittance and reflectance. The performance of the device is evaluated using a recently proposed method, by which the quantum process fidelity and the entanglement capability can be estimated from the 32 measurement results of two classical truth tables, significantly less than the 256 measurement results required for full quantum tomography.

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Shigeki Takeuchi

Papers

Beating the Standard Quantum Limit with Four-Entangled Photons

Violation of local uncertainty relations as a signature of entanglement

Multiphoton detection using visible light photon counter

An entanglement-enhanced microscope.

Demonstration of an Optical Quantum Controlled-NOT Gate without Path Interference