Transverse multi-mode effects on the performance of photon-photon gates

The multi-mode character of quantum fields imposes constraints on the implementation of high-fidelity quantum gates between individual photons. So far this has only been studied for the longitudinal degree of freedom. Here we show that effects due to the transverse degrees of freedom significantly affect quantum gate performance. We also discuss potential solutions, in particular separating the two photons in the transverse direction.Comment: 5 pages, 3 figures, published versio

Direct probing of the Wigner function by time-multiplexed detection of photon statistics

We investigate the capabilities of loss-tolerant quantum state characterization using a photon-number resolving, time-multiplexed detector (TMD). We employ the idea of probing the Wigner function point-by-point in phase space via photon parity measurements and displacement operations, replacing the conventional homodyne tomography. Our emphasis lies on reconstructing the Wigner function of non-Gaussian Fock states with highly negative values in a scheme that is based on a realistic experimental setup. In order to establish the concept of loss-tolerance for state characterization we show how losses can be decoupled from the impact of other experimental imperfections, i.e. the non-unity transmittance of the displacement beamsplitter and non-ideal mode overlap. We relate the experimentally accessible parameters to effective ones that are needed for an optimised state reconstruction. The feasibility of our approach is tested by Monte Carlo simulations, which provide bounds resulting from statistical errors that are due to limited data sets. Our results clearly show that high losses can be accepted for a defined parameter range, and moreover, that (in contrast to homodyne detection) mode mismatch results in a distinct signature, which can be evaluated by analysing the photon number oscillations of the displaced Fock states.Comment: 22 pages, 13 figures, published versio

Memory for Light as a Quantum Process

We report complete characterization of an optical memory based on electromagnetically induced transparency. We recover the superoperator associated with the memory, under two different working conditions, by means of a quantum process tomography technique that involves storage of coherent states and their characterization upon retrieval. In this way, we can predict the quantum state retrieved from the memory for any input, for example, the squeezed vacuum or the Fock state. We employ the acquired superoperator to verify the nonclassicality benchmark for the storage of a Gaussian distributed set of coherent states

Pulsed squeezed light: simultaneous squeezing of multiple modes

We analyze the spectral properties of squeezed light produced by means of pulsed, single-pass degenerate parametric down-conversion. The multimode output of this process can be decomposed into characteristic modes undergoing independent squeezing evolution akin to the Schmidt decomposition of the biphoton spectrum. The main features of this decomposition can be understood using a simple analytical model developed in the perturbative regime. In the strong pumping regime, for which the perturbative approach is not valid, we present a numerical analysis, specializing to the case of one-dimensional propagation in a beta-barium borate waveguide. Characterization of the squeezing modes provides us with an insight necessary for optimizing homodyne detection of squeezing. For a weak parametric process, efficient squeezing is found in a broad range of local oscillator modes, whereas the intense generation regime places much more stringent conditions on the local oscillator. We point out that without meeting these conditions, the detected squeezing can actually diminish with the increasing pumping strength, and we expose physical reasons behind this inefficiency

Discrete Wigner functions and the phase space representation of quantum teleportation

We present a phase space description of the process of quantum teleportation for a system with an $N$ dimensional space of states. For this purpose we define a discrete Wigner function which is a minor variation of previously existing ones. This function is useful to represent composite quantum system in phase space and to analyze situations where entanglement between subsystems is relevant (dimensionality of the space of states of each subsystem is arbitrary). We also describe how a direct tomographic measurement of this Wigner function can be performed.Comment: 8 pages, 1 figure, to appear in Phys Rev

A complementarity-based approach to phase in finite-dimensional quantum systems

We develop a comprehensive theory of phase for finite-dimensional quantum systems. The only physical requirement we impose is that phase is complementary to amplitude. To implement this complementarity we use the notion of mutually unbiased bases, which exist for dimensions that are powers of a prime. For a d-dimensional system (qudit) we explicitly construct d+1 classes of maximally commuting operators, each one consisting of d-1 operators. One of this class consists of diagonal operators that represent amplitudes (or inversions). By the finite Fourier transform, it is mapped onto ladder operators that can be appropriately interpreted as phase variables. We discuss the examples of qubits and qutrits, and show how these results generalize previous approaches.Comment: 6 pages, no figure

Experimental Vacuum Squeezing in Rubidium Vapor via Self-Rotation

We report the generation of optical squeezed vacuum states by means of polarization self-rotation in rubidium vapor following a proposal by Matsko et al. [Phys. Rev. A 66, 043815 (2002)]. The experimental setup, involving in essence just a diode laser and a heated rubidium gas cell, is simple and easily scalable. A squeezing of 0.85+-0.05 dB was achieved

A high-fidelity noiseless amplifier for quantum light states

Noise is the price to pay when trying to clone or amplify arbitrary quantum states. The quantum noise associated to linear phase-insensitive amplifiers can only be avoided by relaxing the requirement of a deterministic operation. Here we present the experimental realization of a probabilistic noiseless linear amplifier that is able to amplify coherent states at the highest level of effective gain and final state fidelity ever reached. Based on a sequence of photon addition and subtraction, and characterized by a significant amplification and low distortions, this high-fidelity amplification scheme may become an essential tool for quantum communications and metrology, by enhancing the discrimination between partially overlapping quantum states or by recovering the information transmitted over lossy channels.Comment: 5 pages, 4 figure

A balanced homodyne detector for high-rate Gaussian-modulated coherent-state quantum key distribution

We discuss excess noise contributions of a practical balanced homodyne detector in Gaussian-modulated coherent-state (GMCS) quantum key distribution (QKD). We point out the key generated from the original realistic model of GMCS QKD may not be secure. In our refined realistic model, we take into account excess noise due to the finite bandwidth of the homodyne detector and the fluctuation of the local oscillator. A high speed balanced homodyne detector suitable for GMCS QKD in the telecommunication wavelength region is built and experimentally tested. The 3dB bandwidth of the balanced homodyne detector is found to be 104MHz and its electronic noise level is 13dB below the shot noise at a local oscillator level of 8.5*10^8 photon per pulse. The secure key rate of a GMCS QKD experiment with this homodyne detector is expected to reach Mbits/s over a few kilometers.Comment: 22 pages, 11 figure

The Uncertainty Relation in "Which-Way" Experiments: How to Observe Directly the Momentum Transfer using Weak Values

A which-way measurement destroys the twin-slit interference pattern. Bohr argued that distinguishing between two slits a distance s apart gives the particle a random momentum transfer \wp of order h/s. This was accepted for more than 60 years, until Scully, Englert and Walther (SEW) proposed a which-way scheme that, they claimed, entailed no momentum transfer. Storey, Tan, Collett and Walls (STCW) in turn proved a theorem that, they claimed, showed that Bohr was right. This work reviews and extends a recent proposal [Wiseman, Phys. Lett. A 311, 285 (2003)] to resolve the issue using a weak-valued probability distribution for momentum transfer, P_wv(\wp). We show that P_wv(\wp) must be wider than h/6s. However, its moments can still be zero because P_wv(\wp) is not necessarily positive definite. Nevertheless, it is measurable in a way understandable to a classical physicist. We introduce a new measure of spread for P_wv(\wp): half of the unit-confidence interval, and conjecture that it is never less than h/4s. For an idealized example with infinitely narrow slits, the moments of P_wv(\wp) and of the momentum distributions are undefined unless a process of apodization is used. We show that by considering successively smoother initial wave functions, successively more moments of both P_wv(\wp) and the momentum distributions become defined. For this example the moments of P_wv(\wp) are zero, and these are equal to the changes in the moments of the momentum distribution. We prove that this relation holds for schemes in which the moments of P_wv(\wp) are non-zero, but only for the first two moments. We also compare these moments to those of two other momentum-transfer distributions and \hat{p}_f-\hat{p}_i. We find agreement between all of these, but again only for the first two moments.Comment: 14 pages, 6 figures, submitted to J. Opt.