Showing papers by "Jeffrey H. Shapiro published in 2009"

The Quantum Theory of Optical Communications

Abstract: Communication theory applied to lightwave channels is ordinarily carried out using the semiclassical theory of photodetection. Recent development of nonclassical light sources-whose photodetection statistics require the use of quantum theory-plus increasing interest in optics-based approaches to quantum information processing necessitates a thorough understanding of the similarities and distinctions between the semiclassical and quantum theories of optical communications. This paper is addressed to that need, focusing, for convenience, on the free-space communication channel using Gaussian states of light. The quantum version of the Huygens-Fresnel diffraction integral is reviewed, along with the semiclassical and quantum theories of direct, homodyne, and heterodyne detection. Maximally entangled Gaussian state light is used, in conjunction with quantum photodetection theory, to explain the nonclassical effects seen in Hong-Ou-Mandel interferometry and violation of the Clauser-Horne-Shimony-Holt form of Bell's inequality. The classical information capacities of several bosonic channels are reviewed, and shown to exceed what can be achieved using conventional optical receivers.

Quantum illumination versus coherent-state target detection

Abstract: Entanglement is arguably the key quantum-mechanical resource for improving the performance of communication, precision measurement and computing systems beyond their classical-physics limits. Yet entanglement is fragile, being very susceptible to destruction by the decoherence arising from loss and noise. Surprisingly, Lloyd (2008 Science 321 1463) recently proved that a very large performance gain accrues from use of entanglement in single-photon target detection within an entanglement-destroying lossy, noisy environment when compared to what can be achieved with unentangled single-photon states. We extend Lloyd's analysis to the full multiphoton input Hilbert space. We show that the performance of Lloyd's single-photon'quantum illumination' system is, at best, equal to that of a coherent-state transmitter of the same average photon number, and may be substantially worse. We demonstrate that the coherent-state system derives its advantage from the coherence between a sequence of weak—single photon on average—transmissions, a possibility that was not allowed for in Lloyd's work. Nevertheless, as shown by Tan et al (2008 Phys. Rev. Lett. 101 253601), quantum illumination may offer a significant, although more modest, performance gain when operation is not limited to the single-photon regime.

Computational ghost imaging

Abstract: A computational ghost-imaging arrangement that uses only a single-pixel detector is described. It affords a new 3D sectioning capability and matches the resolution of pseudothermal ghost imaging.

Reverse coherent information.

Abstract: In this Letter we define a family of entanglement distribution protocols assisted by feedback classical communication that gives an operational interpretation to reverse coherent information, i.e., the symmetric counterpart of the well-known coherent information. This leads to the definition of a new entanglement distribution capacity that exceeds the unassisted capacity for some interesting channels.

Sub-Rayleigh-diffraction-bound quantum imaging

Abstract: The spatial resolution of an imaging apparatus is limited by the Rayleigh diffraction bound, a consequence of the imager's finite spatial extent. We show some $N$-photon strategies that permit resolution of details that are smaller than this bound, attaining either a $1∕\sqrt{N}$ enhancement (standard quantum limit) or a $1∕N$ enhancement (Heisenberg-like scaling) over standard techniques. In the incoherent imaging regime, the methods presented are loss resistant, since classical light sources suffice. Our results may be of importance in many applications: microscopy, telescopy, lithography, metrology, etc.

Signal-to-noise ratio of Gaussian-state ghost imaging

Abstract: The signal-to-noise ratios (SNRs) of three Gaussian-state ghost-imaging configurations---distinguished by the nature of their light sources---are derived. Two use classical-state light, specifically a joint signal-reference field state that has either the maximum phase-insensitive or the maximum phase-sensitive cross correlation consistent with having a proper $P$ representation. The third uses nonclassical light, in particular an entangled signal-reference field state with the maximum phase-sensitive cross correlation permitted by quantum mechanics. Analytic SNR expressions are developed for the near-field and far-field regimes, within which simple asymptotic approximations are presented for low-brightness and high-brightness sources. A high-brightness thermal-state (classical phase-insensitive state) source will typically achieve a higher SNR than a biphoton-state (low-brightness, low-flux limit of the entangled-state) source, when all other system parameters are equal for the two systems. With high efficiency photon-number-resolving detectors, a low-brightness, high-flux entangled-state source may achieve a higher SNR than that obtained with a high-brightness thermal-state source.

Defeating passive eavesdropping with quantum illumination

Abstract: A two-way protocol for defeating passive eavesdropping is proposed. For each information bit, Alice sends Bob $T$ sec of signal-beam output from a spontaneous parametric down-converter over a pure-loss channel while retaining the idler beam with which it is maximally entangled. Bob imposes a single information bit on the light he receives from Alice via binary phase-shift keying. He then amplifies the modulated beam and sends the resulting light back to Alice over the same pure-loss channel. Even though the loss and amplifier noise destroy any entanglement between the light that Alice receives from Bob and the idler she has retained, she can decode Bob's bit with an error probability that can be orders of magnitude lower than what is achieved by a passive eavesdropper who receives all the photons that are lost en route from Alice to Bob and from Bob to Alice. In particular, Alice and Bob can communicate at 50 Mbit/s over 50 km of low-loss fiber with an error probability of less than ${10}^{\ensuremath{-}6}$ while the passive eavesdropper's error probability must exceed 0.28.

Ghost imaging: from quantum to classical to computational

Abstract: Ghost‐imaging experiments correlate the outputs from two photodetectors: a high spatial‐resolution (scanning pinhole or CCD camera) detector that measures a field which has not interacted with the object to be imaged, and a bucket (single‐pixel) detector that collects a field that has interacted with the object. We review the Gaussian‐state framework for ghost imaging setups that rely on biphoton states or pseudothermal states. The understanding derived therefrom leads to two new ghost imaging configurations, employing spatial light modulators to impose controlled spatial incoherence at the source, one of which uses only a single‐pixel detector.

Quantum theory of optical temporal phase and instantaneous frequency. II. Continuous-time limit and state-variable approach to phase-locked loop design

Abstract: We consider the continuous-time version of our recently proposed quantum theory of optical temporal phase and instantaneous frequency [M. Tsang et al., Phys. Rev. A 78, 053820 (2008)]. Using a state-variable approach to estimation, we design homodyne phase-locked loops that can measure the temporal phase with quantum-limited accuracy. We show that postprocessing can further improve the estimation performance if delay is allowed in the estimation. We also investigate the fundamental uncertainties in the simultaneous estimation of harmonic-oscillator position and momentum via continuous optical phase measurements from the classical estimation theory perspective. In the case of delayed estimation, we find that the inferred uncertainty product can drop below that allowed by the Heisenberg uncertainty relation. Although this result seems counterintuitive, we argue that it does not violate any basic principle of quantum mechanics.

Computational ghost imaging

Abstract: A computational ghost-imaging arrangement that uses only a single-pixel detector is described. It affords a new 3D sectioning capability and matches the resolution of pseudothermal ghost imaging.

Signal-to-noise ratio of Gaussian-state ghost imaging

Abstract: The signal-to-noise ratios of pseudothermal and biphoton ghost imagers are derived and compared by means of a unified Gaussian-state analysis.

Quantum illumination versus coherent-state target detection

Abstract: Lloyd [1] proved that a large performance gain accrues from use of entanglement in single-photon target detection within a lossy, noisy environment when compared to what can be achieved with unentangled single-photon states. We show that the performance of Lloyd's "quantum illumination" system is, at best, equal to that of a coherent-state transmitter, and may be substantially worse. Nevertheless, as shown in [2], quantum illumination may offer a significant performance gain when operation is not limited to the single-photon regime.

Classical low-coherence interferometry based on broadband parametric fluorescence and amplification.

Abstract: We demonstrate that single-mode broadband amplified spontaneous parametric downconversion, combined with optical parametric amplification, can be used as a classical source of phase-sensitive cross-correlated beams. We first study the single spatial mode emission and the spectral brightness properties of the parametric fluorescence, produced in periodically poled MgO-doped lithium niobate. Using the same single-pass bulk-crystal configuration for a pulsed optical parametric amplifier, we achieve a gain of approximately 20 dB at an average pump power of 2W, and explain the pulse narrowing observed at the output of both parametric fluorescence and amplification in the regime of high gain. Combining these two nonlinear processes, we measured optical coherence tomography signals with standard InGaAs photodiodes, thus realizing the first classical interferometer based on amplified parametric fluorescence. The results suggest their utility for demonstrating phase-conjugate optical coherence tomography.

The bosonic minimum output entropy conjecture and Lagrangian minimization

Abstract: We introduce a new form for the bosonic channel minimal output entropy conjecture, namely that among states with equal input entropy, the thermal states are the ones that have slightest increase in entropy when sent through a infinitesimal thermalizing channel. We then detail a strategy to prove the conjecture through variational techniques. This would lead to the calculation of the classical capacity of a communication channel subject to thermal noise. Our strategy detects input thermal ensembles as possible solutions for the optimal encoding of the channel, lending support to the conjecture. However, it does not seem to be able to exclude the possibility that other input ensembles can attain the channel capacity.

Signal-to-noise ratio of Gaussian-state ghost imaging

Abstract: The signal-to-noise ratios of pseudothermal and biphoton ghost imagers are derived and compared by means of a unified Gaussian-state analysis.

Sub-Rayleigh-diffraction-bound quantum imaging

Abstract: The spatial resolution of an imaging apparatus is limited by the Rayleigh diffraction bound, a consequence of the imager's finite spatial extent. We show some $N$-photon strategies that permit resolution of details that are smaller than this bound, attaining either a $1∕\sqrt{N}$ enhancement (standard quantum limit) or a $1∕N$ enhancement (Heisenberg-like scaling) over standard techniques. In the incoherent imaging regime, the methods presented are loss resistant, since classical light sources suffice. Our results may be of importance in many applications: microscopy, telescopy, lithography, metrology, etc.

Proof of the bosonic minimum output entropy conjecture

Abstract: We introduce a new form for the bosonic channel minimal output entropy conjecture, namely that among states with equal input entropy, the thermal states are the ones that have slightest increase in entropy when sent through a infinitesimal thermalizing channel We then detail a strategy to prove the conjecture through variational techniques This would lead to the calculation of the classical capacity of a communication channel subject to thermal noise Our strategy detects input thermal ensembles as possible solutions for the optimal encoding of the channel, lending support to the conjecture However, it does not seem to be able to exclude the possibility that other input ensembles can attain the channel capacity

Defeating Passive Eavesdropping with Quantum Illumination

Abstract: Quantum illumination permits Alice and Bob to communicate at 50 Mbit/s over 50 km of low-loss fiber with error probability less than 10-6while the optimum passive eavesdropper's error probability must exceed 0.28.

Secure Communication using Gaussian-State Quantum Illumination

Abstract: A new paradigm for secure communication, based on quantum illumination, is proposed. Alice uses spontaneous parametric down-conversion to send Bob a set of signal modes over a pure-loss channel while retaining the set of idler modes with which they are maximally entangled. Bob imposes a single information bit on the modes he receives from Alice via binary phase-shift keying. He then adds classical Gaussian noise and sends the noisy modulated modes back to Alice over the same pure-loss channel. Even though the loss and noise destroy any entanglement between the modes that Alice receives from Bob and the idler modes she has retained, she can decode Bob's bit with an error probability that can be orders of magnitude lower than what is achieved by a passive eavesdropper who receives all the photons that are lost en route from Alice to Bob and from Bob to Alice.

Optical coherence tomography based on intensity correlations of quasi-thermal light

Abstract: We show theoretically that the longitudinal resolution of conventional optical coherence tomography can be improved by a factor of √2 when a two-photon (as opposed to a single-photon) sensitive detector is used, and we present preliminary supporting results.

Reverse Coherent Information

Abstract: We define a family of entanglement distribution protocols assisted by classical feedback communication that gives an operational interpretation to reverse coherent information, i.e., the symmetric counterpart of the well‐known coherent information. This protocol family leads to the definition of a new entanglement distribution capacity that exceeds the unassisted entanglement distribution capacity for some interesting channels.

Defeating passive eavesdropping with quantum illumination

Abstract: Quantum illumination permits Alice and Bob to communicate at 50 Mbit/s over 50 km of low-loss fiber with error probability less than 10-6while the optimum passive eavesdropper's error probability must exceed 0.28.

Quantum optical temporal phase estimation by homodyne phase-locked loops

Abstract: Using classical estimation techniques, we design homodyne phase-locked loops for optical temporal phase and instantaneous frequency measurements at the quantum limit.

Phase-conjugate optical coherence tomography

Abstract: We demonstrate a new type of optical coherence tomography using only classical resources to achieve results that are typically associated with quantum-enhancedmetrology: factor-of-two axial resolution enhancement and even-order dispersion cancellation.

Reverse Coherent Information

Abstract: In this Letter we define a family of entanglement distribution protocols assisted by feedback classical communication that gives an operational interpretation to reverse coherent information, i.e., the symmetric counterpart of the well-known coherent information. This leads to the definition of a new entanglement distribution capacity that exceeds the unassisted capacity for some interesting channels.

LADAR resolution improvement using squeezed‐vacuum injection

Abstract: We evaluate the signal‐to‐noise ratio (SNR) dependence of LADAR spatial resolution, and the improvement afforded by squeezed‐vacuum injection at the receiver. We define spatial resolution as the ability to distinguish two point targets from a single point target. For speckle returns and a soft‐aperture homodyne receiver, the resolution scales as SNR−3/10 at high SNR, and exhibits a threshold SNR below which targets are unresolvable. Injecting a 15 dB squeezed vacuum improves the resolution by a factor of about 2 at high SNR, and provides approximately 3.5 dB of threshold extension, which permits some classically‐unresolvable targets to become distinguishable.

Improved resolution in imaging through quantum post‐selection

Abstract: We show how we can obtain improved resolution when imaging an object by filtering “high‐resolution” quantum states from impinging classical radiation The method allows one to beat the Rayleigh diffraction bound that is intrinsic in any imaging apparatus It is based on using focused classical illumination sources and N‐photon coincidence detection