No Tradeoff between Coherence and Sub-Poissonianity for Heisenberg-Limited Lasers.

The Heisenberg limit to laser coherence C-the number of photons in the maximally populated mode of the laser beam-is the fourth power of the number of excitations inside the laser. We generalize the previous proof of this upper bound scaling by dropping the requirement that the beam photon statistics be Poissonian (i.e., Mandel's Q=0). We then show that the relation between C and sub-Poissonianity (Q<0) is win-win, not a tradeoff. For both regular (non-Markovian) pumping with semiunitary gain (which allows Q→-1), and random (Markovian) pumping with optimized gain, C is maximized when Q is minimized.

Quantum optical waveform conversion.

Proposals for long-distance quantum communication rely on the entanglement of matter-based quantum nodes through optical communications channels, but the entangling light pulses have poor temporal behavior in current experiments. Here we show that nonlinear mixing of a quantum light pulse with a spectrally tailored classical field can compress the quantum pulse by more than a factor of 100 and flexibly reshape its temporal waveform while preserving all quantum properties, including entanglement. Our scheme paves the way for quantum communication at the full data rate of optical telecommunications.

How many bits does it take to track an open quantum system?

A D-dimensional Markovian open quantum system will undergo quantum jumps between pure states, if we can monitor the bath to which it is coupled with sufficient precision. In general, these jumps, plus the between-jump evolution, create a trajectory which passes through infinitely many different pure states. Here we show that, for any ergodic master equation, one can expect to find an adaptive monitoring scheme on the bath that can confine the system state to jumping between only K states, for some K ≥ (D - 1)(2) + 1. For D = 2 we explicitly construct a two-state ensemble for any ergodic master equation, showing that one bit is always sufficient to track a qubit.

Adaptive optical phase estimation using time-symmetric quantum smoothing.

Quantum parameter estimation has many applications, from gravitational wave detection to quantum key distribution. The most commonly used technique for this type of estimation is quantum filtering, using only past observations. We present the first experimental demonstration of quantum smoothing, a time-symmetric technique that uses past and future observations, for quantum parameter estimation. We consider both adaptive and nonadaptive quantum smoothing, and show that both are better than their filtered counterparts. For the problem of estimating a stochastically varying phase shift on a coherent beam, our theory predicts that adaptive quantum smoothing (the best scheme) gives an estimate with a mean-square error up to 2sqrt[2] times smaller than nonadaptive filtering (the standard quantum limit). The experimentally measured improvement is 2.24+/-0.14.

A model for measurement of the states in a coupled-dot qubit.

We propose a quantum trajectory analysis of a scheme to measure the states of a coupled-dot device (qubit) where there is a fluctuating energy gap Δ between the two states. The system consists of the qubit and a readout dot coupled to source and drain leads. The tunnel rate through the detector is conditioned by the occupation number of the nearer quantum dot (target) of the qubit and therefore probes the states of the qubit. We derive a Lindblad-form master equation to calculate the unconditional evolution of the qubit and a conditional stochastic master equation calculating the conditional evolution for different tunneling rates. The results show the effects of various device parameters and provide the optimum selection and combination of the system structure.

Mixed state discrimination using optimal control.

We present theory and experiment for the task of discriminating two nonorthogonal states, given multiple copies. We implement several local measurement schemes, on both pure states and states mixed by depolarizing noise. We find that schemes which are optimal (or have optimal scaling) without noise perform worse with noise than simply repeating the optimal single-copy measurement. Applying optimal control theory, we derive the globally optimal local measurement strategy, which outperforms all other local schemes, and experimentally implement it for various levels of noise.

Entanglement-free Heisenberg-limited phase estimation.

Measurement underpins all quantitative science. A key example is the measurement of optical phase, used in length metrology and many other applications. Advances in precision measurement have consistently led to important scientific discoveries. At the fundamental level, measurement precision is limited by the number N of quantum resources (such as photons) that are used. Standard measurement schemes, using each resource independently, lead to a phase uncertainty that scales as 1/square root N-known as the standard quantum limit. However, it has long been conjectured that it should be possible to achieve a precision limited only by the Heisenberg uncertainty principle, dramatically improving the scaling to 1/N (ref. 3). It is commonly thought that achieving this improvement requires the use of exotic quantum entangled states, such as the NOON state. These states are extremely difficult to generate. Measurement schemes with counted photons or ions have been performed with N < or = 6 (refs 6-15), but few have surpassed the standard quantum limit and none have shown Heisenberg-limited scaling. Here we demonstrate experimentally a Heisenberg-limited phase estimation procedure. We replace entangled input states with multiple applications of the phase shift on unentangled single-photon states. We generalize Kitaev's phase estimation algorithm using adaptive measurement theory to achieve a standard deviation scaling at the Heisenberg limit. For the largest number of resources used (N = 378), we estimate an unknown phase with a variance more than 10 dB below the standard quantum limit; achieving this variance would require more than 4,000 resources using standard interferometry. Our results represent a drastic reduction in the complexity of achieving quantum-enhanced measurement precision.

Steering, entanglement, nonlocality, and the Einstein-Podolsky-Rosen paradox.

The concept of steering was introduced by Schrödinger in 1935 as a generalization of the Einstein-Podolsky-Rosen paradox for arbitrary pure bipartite entangled states and arbitrary measurements by one party. Until now, it has never been rigorously defined, so it has not been known (for example) what mixed states are steerable (that is, can be used to exhibit steering). We provide an operational definition, from which we prove (by considering Werner states and isotropic states) that steerable states are a strict subset of the entangled states, and a strict superset of the states that can exhibit Bell nonlocality. For arbitrary bipartite Gaussian states we derive a linear matrix inequality that decides the question of steerability via Gaussian measurements, and we relate this to the original Einstein-Podolsky-Rosen paradox.

Measurement of quantum weak values of photon polarization.

We experimentally determine weak values for a single photon's polarization, obtained via a weak measurement that employs a two-photon entangling operation, and postselection. The weak values cannot be explained by a semiclassical wave theory, due to the two-photon entanglement. We observe the variation in the size of the weak value with measurement strength, obtaining an average measurement of the S1 Stokes parameter more than an order of magnitude outside of the operator's spectrum for the smallest measurement strengths.

Optimal unravellings for feedback control in linear quantum systems.

For quantum systems with linear dynamics in phase space much of classical feedback control theory applies. However, there are some questions that are sensible only for the quantum case: Given a fixed interaction between the system and the environment what is the optimal measurement on the environment for a particular control problem? We show that for a broad class of optimal (state-based) control problems (the stationary linear-quadratic-Gaussian class), this question is a semidefinite program. Moreover, the answer also applies to Markovian (current-based) feedback.

Entanglement of indistinguishable particles shared between two parties.

Using an operational definition we quantify the entanglement, E(P), between two parties who share an arbitrary pure state of N indistinguishable particles. We show that E(P)< or =E(M), where E(M) is the bipartite entanglement calculated from the mode-occupation representation. Unlike E(M), E(P) is superadditive. For example, E(P)=0 for any single-particle state, but the state |1>|1>, where both modes are split between the two parties, has E(P)=1/2. We discuss how this relates to quantum correlations between particles, for both fermions and bosons.

Entanglement constrained by superselection rules.

Bipartite entanglement may be reduced if there are restrictions on allowed local operations. We introduce the concept of a generalized superselection rule to describe such restrictions, and quantify the entanglement constrained by it. We show that ensemble quantum information processing, where elements in the ensemble are not individually addressable, is subject to the superselection rule associated with the symmetric group (the group of permutations of elements). We prove that even for an ensemble comprising many pairs of qubits, each pair described by a pure Bell state, the entanglement per element constrained by this superselection rule goes to zero for a large number of elements.

Capture and release of a conditional state of a cavity QED system by quantum feedback.

Detection of a single photon escaping an optical cavity QED system prepares a nonclassical state of the electromagnetic field. The evolution of the state can be modified by changing the drive of the cavity. For the appropriate feedback, the conditional state can be captured (stabilized) and then released. This is observed by a conditional intensity measurement that shows suppression of vacuum Rabi oscillations for the length of the feedback pulse and their subsequent return.

Inequivalence of pure state ensembles for open quantum systems: the preferred ensembles are those that are physically realizable.

An open quantum system in steady state rho(ss) can be represented by a weighted ensemble of pure states rho(ss) = [equation: see text] in infinitely many ways. A physically realizable (PR) ensemble is one for which some continuous measurement of the environment will collapse the system into a pure state /psi(t)>, stochastically evolving such that the proportion of time for which /psi(t)> = /psi(k)> equals Weierstrass p(k). Some, but not all, ensembles are PR. This constitutes the preferred ensemble fact. We present the necessary and sufficient conditions for a given ensemble to be PR, and illustrate the method by showing that the coherent state ensemble is not PR for an atom laser.

Reducing the linewidth of an atom laser by feedback.

A continuous atom laser will almost certainly have a linewidth dominated by the effect of the atomic interaction energy, which turns fluctuations in the condensate atom number into fluctuations in the condensate frequency. These correlated fluctuations mean that information about the atom number could be used to reduce the frequency fluctuations, by controlling a spatially uniform potential. We show that feedback based on a physically reasonable quantum nondemolition measurement of the atom number of the condensate in situ can reduce the linewidth enormously.