arXiv subjects

Jeffrey H. Shapiro

Publications and source records attributed to Jeffrey H. Shapiro.

At least 109 records · Page 6Linked to original sources

arXiv2009

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

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.

quant-ph↗

arXiv2008

Quantum theory of optical temporal phase and instantaneous frequency

We propose a general quantum theory of optical phase and instantaneous frequency in the time domain for slowly varying optical signals. Guided by classical estimation theory, we design homodyne phase-locked loops that enable quantum-limited measurements of temporal phase and instantaneous frequency. Standard and Heisenberg quantum limits to such measurements are then derived. For optical sensing applications, we propose multipass and Fabry-Pérot position and velocity sensors that take advantage of the signal-to-noise-ratio enhancement effect of wideband angle modulation without requiring nonclassical light. We also generalize our theory to three spatial dimensions for nonrelativistic bosons and define an Hermitian fluid velocity operator, which provides a theoretical underpinning to the current-algebra approach of quantum hydrodynamics.

quant-ph↗

arXiv2008

The Poisson Channel at Low Input Powers

The asymptotic capacity at low input powers of an average-power limited or an average- and peak-power limited discrete-time Poisson channel is considered. For a Poisson channel whose dark current is zero or decays to zero linearly with its average input power $E$, capacity scales like $E\log\frac{1}{E}$ for small $E$. For a Poisson channel whose dark current is a nonzero constant, capacity scales, to within a constant, like $E\log\log\frac{1}{E}$ for small $E$.

cs.IT↗

arXiv2008

Quantum Illumination with Gaussian States

An optical transmitter irradiates a target region containing a bright thermal-noise bath in which a low-reflectivity object might be embedded. The light received from this region is used to decide whether the object is present or absent. The performance achieved using a coherent-state transmitter is compared with that of a quantum illumination transmitter, i.e., one that employs the signal beam obtained from spontaneous parametric downconversion (SPDC). By making the optimum joint measurement on the light received from the target region together with the retained SPDC idler beam, the quantum illumination system realizes a 6 dB advantage in error probability exponent over the optimum reception coherent-state system. This advantage accrues despite there being no entanglement between the light collected from the target region and the retained idler beam.

quant-ph↗

arXiv2008

Sub-Rayleigh Quantum Imaging

No imaging apparatus can produce perfect images: spatial resolution is limited by the Rayleigh diffraction bound that is 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 limit) over standard techniques. In the incoherent imaging regime, the methods presented are loss resistant, because they can be implemented with classical-state light sources. Our results may be of importance in many applications: microscopy, telescopy, lithography, metrology, etc.

quant-ph↗

arXiv2008

Gaussian-State Theory of Two-Photon Imaging

Biphoton states of signal and idler fields--obtained from spontaneous parametric downconversion (SPDC) in the low-brightness, low-flux regime--have been utilized in several quantum imaging configurations to exceed the resolution performance of conventional imagers that employ coherent-state or thermal light. Recent work--using the full Gaussian-state description of SPDC--has shown that the same resolution performance seen in quantum optical coherence tomography and the same imaging characteristics found in quantum ghost imaging can be realized by classical-state imagers that make use of phase-sensitive cross correlations. This paper extends the Gaussian-state analysis to two additional biphoton-state quantum imaging scenarios: far field diffraction-pattern imaging; and broadband thin-lens imaging. It is shown that the spatial resolution behavior in both cases is controlled by the nonzero phase-sensitive cross correlation between the signal and idler fields. Thus, the same resolution can be achieved in these two configurations with classical-state signal and idler fields possessing a nonzero phase-sensitive cross correlation.

quant-ph↗

arXiv2008

Capacity of the Bosonic Wiretap Channel and the Entropy Photon-Number Inequality

Determining the ultimate classical information carrying capacity of electromagnetic waves requires quantum-mechanical analysis to properly account for the bosonic nature of these waves. Recent work has established capacity theorems for bosonic single-user and broadcast channels, under the presumption of two minimum output entropy conjectures. Despite considerable accumulated evidence that supports the validity of these conjectures, they have yet to be proven. In this paper, it is shown that the second conjecture suffices to prove the classical capacity of the bosonic wiretap channel, which in turn would also prove the quantum capacity of the lossy bosonic channel. The preceding minimum output entropy conjectures are then shown to be simple consequences of an Entropy Photon-Number Inequality (EPnI), which is a conjectured quantum-mechanical analog of the Entropy Power Inequality (EPI) form classical information theory.

quant-ph↗

arXiv2007

Unified Theory of Ghost Imaging with Gaussian-State Light

The theory of ghost imaging is developed in a Gaussian-state framework that both encompasses prior work - on thermal-state and biphoton-state imagers - and provides a complete understanding of the boundary between classical and quantum behavior in such systems. The core of this analysis is the expression derived for the photocurrent-correlation image obtained using a general Gaussian-state source. This image is expressed in terms of the phase-insensitive and phase-sensitive cross-correlations between the two detected fields, plus a background. Because any pair of cross-correlations is obtainable with classical Gaussian states, the image does not carry a quantum signature per se. However, if the image characteristics of classical and nonclassical Gaussian-state sources with identical auto-correlation functions are compared, the nonclassical source provides resolution improvement in its near field and field-of-view improvement in its far field.

quant-ph↗

arXiv2007

The Entropy Photon-Number Inequality and its Consequences

Determining the ultimate classical information carrying capacity of electromagnetic waves requires quantum-mechanical analysis to properly account for the bosonic nature of these waves. Recent work has established capacity theorems for bosonic single-user, broadcast, and wiretap channels, under the presumption of two minimum output entropy conjectures. Despite considerable accumulated evidence that supports the validity of these conjectures, they have yet to be proven. Here we show that the preceding minimum output entropy conjectures are simple consequences of an Entropy Photon-Number Inequality, which is a conjectured quantum-mechanical analog of the Entropy Power Inequality (EPI) from classical information theory.

quant-ph↗

arXiv2007

Classical capacity of bosonic broadcast communication and a new minimum output entropy conjecture

Previous work on the classical information capacities of bosonic channels has established the capacity of the single-user pure-loss channel, bounded the capacity of the single-user thermal-noise channel, and bounded the capacity region of the multiple-access channel. The latter is a multi-user scenario in which several transmitters seek to simultaneously and independently communicate to a single receiver. We study the capacity region of the bosonic broadcast channel, in which a single transmitter seeks to simultaneously and independently communicate to two different receivers. It is known that the tightest available lower bound on the capacity of the single-user thermal-noise channel is that channel's capacity if, as conjectured, the minimum von Neumann entropy at the output of a bosonic channel with additive thermal noise occurs for coherent-state inputs. Evidence in support of this minimum output entropy conjecture has been accumulated, but a rigorous proof has not been obtained. In this paper, we propose a new minimum output entropy conjecture that, if proved to be correct, will establish that the capacity region of the bosonic broadcast channel equals the inner bound achieved using a coherent-state encoding and optimum detection. We provide some evidence that supports this new conjecture, but again a full proof is not available.

quant-ph↗

arXiv2007

Classical Information Capacity of the Bosonic Broadcast Channel

We show that when coherent-state encoding is employed in conjunction with coherent detection, the Bosonic broadcast channel is equivalent to a classical degraded Gaussian broadcast channel whose capacity region is dual to that of the classical Gaussian multiple-access channel. We further show that if a minimum output-entropy conjecture holds true, then the ultimate classical information capacity of the Bosonic broadcast channel can be achieved by a coherent-state encoding. We provide some evidence in support of the conjecture.

quant-ph↗

arXiv2007

Continuous-time cross-phase modulation and quantum computation

The weak nonlinear Kerr interaction between single photons and intense laser fields has been recently proposed as a basis for distributed optics-based solutions to few-qubit applications in quantum communication and computation. Here, we analyze the above Kerr interaction by employing a continuous-time multi-mode model for the input/output fields to/from the nonlinear medium. In contrast to previous single-mode treatments of this problem, our analysis takes into account the full temporal content of the free-field input beams as well as the non-instantaneous response of the medium. The main implication of this model, in which the cross-Kerr phase shift on one input is proportional to the photon flux of the other input, is the existence of phase noise terms at the output. We show that these phase noise terms will preclude satisfactory performance of the parity gate proposed by Munro, Nemoto, and Spiller [New J. Phys. 7, 137 (2005)].

quant-ph↗

arXiv2007

A non-adiabatic approach to entanglement distribution over long distances

Entanglement distribution between trapped-atom quantum memories, viz. single atoms in optical cavities, is addressed. In most scenarios, the rate of entanglement distribution depends on the efficiency with which the state of traveling single photons can be transferred to trapped atoms. This loading efficiency is analytically studied for two-level, $V$-level, $Λ$-level, and double-$Λ$-level atomic configurations by means of a system-reservoir approach. An off-resonant non-adiabatic approach to loading $Λ$-level trapped-atom memories is proposed, and the ensuing trade-offs between the atom-light coupling rate and input photon bandwidth for achieving a high loading probability are identified. The non-adiabatic approach allows a broad class of optical sources to be used, and in some cases it provides a higher system throughput than what can be achieved by adiabatic loading mechanisms. The analysis is extended to the case of two double-$Λ$ trapped-atom memories illuminated by a polarization-entangled biphoton.

quant-ph↗

arXiv2006

Ghost Imaging: What is quantum, what is not

We provide a unified treatment of classical and quantum Gaussian-state sources that unambiguously identifies which features of ghost imaging are strictly quantum mechanical. We show that ghost-image formation is fundamentally classical, with the image being expressible in terms of the phase-insensitive and phase-sensitive cross correlations between the detected fields. We then consider ghost-imaging scenarios with either phase-insensitive or phase-sensitive sources, where the former are always classical but the latter may be classical or quantum mechanical. We show that if their auto-correlations are identical, then a quantum source provides resolution improvement in its near-field and field-of-view improvement in its far field when compared to a classical source.

quant-ph↗

arXiv2006

Complete physical simulation of the entangling-probe attack on the BB84 protocol

We have used deterministic single-photon two qubit (SPTQ) quantum logic to implement the most powerful individual-photon attack against the Bennett-Brassard 1984 (BB84) quantum key distribution protocol. Our measurement results, including physical source and gate errors, are in good agreement with theoretical predictions for the Renyi information obtained by Eve as a function of the errors she imparts to Alice and Bob's sifted key bits. The current experiment is a physical simulation of a true attack, because Eve has access to Bob's physical receiver module. This experiment illustrates the utility of an efficient deterministic quantum logic for performing realistic physical simulations of quantum information processing functions.

quant-ph↗

arXiv2006

Phase-conjugate optical coherence tomography

Quantum optical coherence tomography (Q-OCT) offers a factor-of-two improvement in axial resolution and the advantage of even-order dispersion cancellation when it is compared to conventional OCT (C-OCT). These features have been ascribed to the non-classical nature of the biphoton state employed in the former, as opposed to the classical state used in the latter. Phase-conjugate OCT (PC-OCT), introduced here, shows that non-classical light is not necessary to reap Q-OCT's advantages. PC-OCT uses classical-state signal and reference beams, which have a phase-sensitive cross-correlation, together with phase conjugation to achieve the axial resolution and even-order dispersion cancellation of Q-OCT with a signal-to-noise ratio that can be comparable to that of C-OCT.

quant-ph↗

arXiv2006

Time-bin modulated polarization-entangled biphotons from cavity-enhanced down-conversion

We have generated a new type of biphoton state by cavity-enhanced down-conversion in a type-II phase-matched, periodically-poled KTiOPO_4 (PPKTP) crystal. By introducing a weak intracavity birefringence, the polarization-entangled output was modulated between the singlet and triplet states according to the arrival-time difference of the signal and idler photons. This cavity-enhanced biphoton source is spectrally bright, yielding a single-mode fiber-coupled coincidence rate of 0.7 pairs/s per mW of pump power per MHz of down-conversion bandwidth. Its novel biphoton behavior may be utilized in sensitive measurements of weak intracavity birefringence.

quant-ph↗

arXiv2005

Long-Distance Quantum Communication with Neutral Atoms

The architecture proposed by Duan, Lukin, Cirac, and Zoller (DLCZ) for long-distance quantum communication with atomic ensembles is analyzed. Its fidelity and throughput in entanglement distribution, entanglement swapping, and quantum teleportation is derived within a framework that accounts for multiple excitations in the ensembles as well as loss and asymmetries in the channel. The DLCZ performance metrics that are obtained are compared to the corresponding results for the trapped-atom quantum communication architecture that has been proposed by a team from the Massachusetts Institute of Technology and Northwestern University (MIT/NU). Both systems are found to be capable of high-fidelity entanglement distribution. However, the DLCZ scheme only provides conditional teleportation and repeater operation, whereas the MIT/NU architecture affords full Bell-state measurements on its trapped atoms. Moreover, it is shown that achieving unity conditional fidelity in DLCZ teleportation and repeater operation requires ideal photon-number resolving detectors. The maximum conditional fidelities for DLCZ teleportation and repeater operation that can be realized with non-resolving detectors are 1/2 and 2/3, respectively.

quant-ph↗