Publications (46)110.09 Total impact
 [Show abstract] [Hide abstract]
ABSTRACT: The question of which twoqubit states are steerable (i.e. permit a demonstration of EPRsteering) remains open. Here, a strong necessary condition is obtained for the steerability of twoqubit states having maximallymixed reduced states, via the construction of local hidden state models. It is conjectured that this condition is in fact sufficient. Two provably sufficient conditions are also obtained, via asymmetric EPRsteering inequalities. Our work uses ideas from the quantum steering ellipsoid formalism, and explicitly evaluates the integral of $\boldsymbol n/(\boldsymbol n^\intercal A\boldsymbol n)^2$ over arbitrary unit hemispheres for any positive matrix $A$.11/2014;  [Show abstract] [Hide abstract]
ABSTRACT: We propose quantum versions of the BellZivZakai lower bounds on the error in multiparameter estimation. As an application we consider measurement of a timevarying optical phase signal with stationary Gaussian prior statistics and a power law spectrum $\sim 1/\omega^p$, with $p>1$. With no other assumptions, we show that the meansquare error has a lower bound scaling as $1/{\cal N}^{2(p1)/(p+1)}$, where ${\cal N}$ is the timeaveraged mean photon flux. Moreover, we show that this accuracy is achievable by sampling and interpolation, for any $p>1$. This bound is thus a rigorous generalization of the Heisenberg limit, for measurement of a single unknown optical phase, to a stochastically varying optical phase.09/2014;  [Show abstract] [Hide abstract]
ABSTRACT: Bell nonlocality between distant quantum systemsi.e., joint correlations which violate a Bell inequalitycan be verified without trusting the measurement devices used, nor those performing the measurements. This leads to unconditionally secure protocols for quantum information tasks such as cryptographic key distribution. However, complete verification of Bell nonlocality requires high detection efficiencies, and is not robust to the typical transmission losses that occur in long distance applications. In contrast, quantum steering, a weaker form of quantum correlation, can be verified for arbitrarily low detection efficiencies and high losses. The cost is that current steeringverification protocols require complete trust in one of the measurement devices and its operator, allowing only onesided secure key distribution. We present deviceindependent steering protocols that remove this need for trust, even when Bell nonlocality is not present. We experimentally demonstrate this principle for singlet states and states that do not violate a Bell inequality.Nature communications. 08/2014; 6.  [Show abstract] [Hide abstract]
ABSTRACT: Master equations govern the time evolution of a quantum system interacting with an environment, and may be written in a variety of forms. Timeindependent or memoryless master equations, in particular, can be cast in the wellknown Lindblad form. Any timelocal master equation, Markovian or nonMarkovian, may in fact also be written in a Lindbladlike form. A diagonalisation procedure results in a unique, and in this sense canonical, representation of the equation, which may be used to fully characterize the nonMarkovianity of the time evolution. Recently, several different measures of nonMarkovianity have been presented which reflect, to varying degrees, the appearance of negative decoherence rates in the Lindbladlike form of the master equation. We therefore propose using the negative decoherence rates themselves, as they appear in the canonical form of the master equation, to completely characterize nonMarkovianity. The advantages of this are especially apparent when more than one decoherence channel is present. We show that a measure proposed by Rivas et al. is a surprisingly simple function of the canonical decoherence rates, and give an example of a master equation that is nonMarkovian for all times t > 0, but to which nearly all proposed measures are blind. We also give necessary and sufficient conditions for trace distance and volume measures to witness nonMarkovianity, in terms of the Bloch damping matrix.Physical Review A 04/2014; 89:042120. · 3.04 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We investigate whether quantum theory can be understood as the continuum limit of a mechanical theory, in which there is a huge, but finite, number of classical 'worlds', and quantum effects arise solely from a universal interaction between these worlds, without reference to any wave function. Here a `world' means an entire universe with welldefined properties, determined by the classical configuration of its particles and fields. In our approach each world evolves deterministically; probabilities arise due to ignorance as to which world a given observer occupies; and we argue that in the limit of infinitely many worlds the wave function can be recovered (as a secondary object) from the motion of these worlds. We introduce a simple model of such a 'many interacting worlds' approach and show that it can reproduce some generic quantum phenomenasuch as Ehrenfest's theorem, wavepacket spreading, barrier tunneling and zero point energyas a direct consequence of mutual repulsion between worlds. Finally, we perform numerical simulations using our approach. We demonstrate, first, that it can be used to calculate quantum ground states, and second, that it is capable of reproducing, at least qualitatively, the doubleslit interference phenomenon.02/2014;  [Show abstract] [Hide abstract]
ABSTRACT: We introduce informationtheoretic definitions for noise and disturbance in quantum measurements and prove a stateindependent noisedisturbance tradeoff relation that these quantities have to satisfy in any conceivable setup. Contrary to previous approaches, the informationtheoretic quantities we define are invariant under the relabelling of outcomes and allow for the possibility of using quantum or classical operations to "correct" for the disturbance. We also show how our bound implies strong tradeoff relations for mean square deviations.Physical Review Letters 02/2014; 112(5):050401. · 7.73 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: The ultimate limits to estimating a fluctuating phase imposed on an optical beam can be found using the recently derived continuous quantum CramérRao bound. For Gaussian stationary statistics, and a phase spectrum scaling asymptotically as ω^{p} with p>1, the minimum meansquare error in any (singletime) phase estimate scales as N^{2(p1)/(p+1)}, where N is the photon flux. This gives the usual Heisenberg limit for a constant phase (as the limit p→∞) and provides a stochastic Heisenberg limit for fluctuating phases. For p=2 (Brownian motion), this limit can be attained by phase tracking.Physical Review Letters 09/2013; 111(11):113601. · 7.73 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: There has been much interest in developing phase estimation schemes which beat the socalled Heisenberg limit, i.e., for which the phase resolution scales better than 1/n, where n is a measure of resources such as the average photon number or the number of atomic qubits. In particular, a number of nonlinear schemes have been proposed for which the resolution appears to scale as 1/n^k or even exp(n), based on optimising the quantum CramerRao bound. Such schemes include the use of entangled coherent states. However, it may be shown that the average root mean square errors of the proposed schemes (averaged over any prior distribution of phase shifts), cannot beat the Heisenberg limit, and that simple estimation schemes based on entangled coherent states cannot scale better than 1/n^{1/4}. This paradox is related to the role of 'bias' in CramerRao bounds, and is only partially ameliorated via iterative implementations of the proposed schemes. The results are based on new informationtheoretic bounds for the average information gain and error of any phase estimation scheme, and generalise to estimates of shifts generated by any operator having discrete eigenvalues.07/2013;  [Show abstract] [Hide abstract]
ABSTRACT: Complementarity restricts the accuracy with which incompatible quantum observables can be jointly measured. Despite popular conception, the Heisenberg uncertainty relation does not quantify this principle. We report the experimental verification of universally valid complementarity relations, including an improved relation derived here. We exploit EinsteinPoldolskyRosen correlations between two photonic qubits to jointly measure incompatible observables of one. The product of our measurement inaccuracies is low enough to violate the widely used, but not universally valid, ArthursKelly relation.Physical Review Letters 05/2013; 110(22):220402. · 7.73 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: Various protocols exist by which a referee can be convinced that two observers share an entangled resource. Such protocols typically specify the types of communication allowed, and the degrees of trust required, between the referee and each observer. Here it is shown that the need for any degree of trust of the observers by the referee can be completely removed, allowing device independent verification of entanglement, via the referee using classical and quantum communication channels appropriately. In particular, trustfree verification of Bell nonlocality, EPRsteering, and entanglement, respectively, requires two classical channels, one classical and one quantum channel, and two quantum channels. These channels correspond to suitable inputs of quantum randomness by the referee, which prevent the observers from mimicking entanglement using shared classical randomness. Our results generalize recent work by F. Buscemi [Phys. Rev. Lett. {\bf 108}, 200401 (2012)], and offer a perspective on the operational significance of that work. They also offer the possibility of simpler experimental demonstrations of the basic idea of quantumrefereed nonlocality tests.Physical Review A 10/2012; 87(3). · 2.99 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: With the advent of quantum information, the violation of a Bell inequality is used to witness the absence of an eavesdropper in cryptographic scenarios such as key distribution and randomness expansion. One of the key assumptions of Bell's theorem is the existence of experimental "free will," meaning that measurement settings can be chosen at random and independently by each party. The relaxation of this assumption potentially shifts the balance of power towards an eavesdropper. We consider a nosignaling model with reduced "free will" and bound the adversary’s capabilities in the task of randomness expansion.Physical Review Letters 10/2012; 109(16):160404. · 7.73 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: The ultimate bound to the accuracy of phase estimates is often assumed to be given by the Heisenberg limit. Recent work seemed to indicate that this bound can be violated, yielding measurements with much higher accuracy than was previously expected. The Heisenberg limit can be restored as a rigorous bound to the accuracy provided one considers the accuracy averaged over the possible values of the unknown phase, as we have recently shown [Phys. Rev. A 85, 041802(R) (2012)]. Here we present an expanded proof of this result together with a number of additional results, including the proof of a previously conjectured stronger bound in the asymptotic limit. Other measures of the accuracy are examined, as well as other restrictions on the generator of the phase shifts. We provide expanded numerical results for the minimum error and asymptotic expansions. The significance of the results claiming violation of the Heisenberg limit is assessed, followed by a detailed discussion of the limitations of the CramerRao bound.Physical Review A 09/2012; 86(5). · 2.99 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We consider a system with a discrete configuration space. We show that the geometrical structures associated with such a system provide the tools necessary for a reconstruction of discrete quantum mechanics once dynamics is brought into the picture. We do this in three steps. Our starting point is information geometry, the natural geometry of the space of probability distributions. Dynamics requires additional structure. To evolve the probabilities P^k, we introduce coordinates S^k canonically conjugate to the P^k and a symplectic structure. We then seek to extend the metric structure of information geometry, to define a geometry over the full space of the P^k and S^k. Consistency between the metric tensor and the symplectic form forces us to introduce a K\"ahler geometry. The construction has notable features. A complex structure is obtained in a natural way. The canonical coordinates of the K\"ahler space are precisely the wave functions of quantum mechanics. The full group of unitary transformations is obtained. Finally, one may associate a Hilbert space with the K\"ahler space, which leads to the standard version of quantum theory. We also show that the metric that we derive here using purely geometrical arguments is precisely the one that leads to Wootters' expression for the statistical distance for quantum systems.07/2012;  [Show abstract] [Hide abstract]
ABSTRACT: When interactions are turned off, the theory of interacting quantum and classical ensembles due to Hall and Reginatto is shown to suffer from a nonlocal signaling effect that is effectively action at a distance. This limits the possible applicability of the theory. In its present form, it is restricted to those situations in which interactions are always on, such as classical gravity interacting with quantized matter.Physical Review A 07/2012; 86(5). · 2.99 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: A construction of covariant quantum phase observables, for Hamiltonians with a finite number of energy eigenvalues, has been recently given by D. Arsenovic et al. [Phys. Rev. A 85, 044103 (2012)]. For Hamiltonians generating periodic evolution, we show that this construction is just a simple rescaling of the known canonical 'time' or 'age' observable, with the period T rescaled to 2\pi. Further, for Hamiltonians generating quasiperiodic evolution, we note that the construction leads to a phase observable having several undesirable features, including (i) having a trivially uniform probability density for any state of the system, (ii) not reducing to the periodic case in an appropriate limit, and (iii) not having any clear generalisation to an infinite energy spectrum. In contrast, we note that a covariant time observable has been previously defined for such Hamiltonians, which avoids these features. We also show how this 'quasiperiodic' time observable can be represented as the welldefined limit of a sequence of periodic time observables.Physical Review A 06/2012; 86(5). · 2.99 Impact Factor 
Article: Does nonlinear metrology offer improved resolution? Answers from quantum information theory
[Show abstract] [Hide abstract]
ABSTRACT: A number of authors have suggested that nonlinear interactions can enhance resolution of phase shifts beyond the usual Heisenberg scaling of 1/n, where n is a measure of resources such as the number of subsystems of the probe state or the mean photon number of the probe state. These suggestions are based on calculations of `local precision' for particular nonlinear schemes. However, we show that there is no simple connection between the local precision and the average estimation error for these schemes, leading to a scaling puzzle. This puzzle is partially resolved by a careful analysis of iterative implementations of the suggested nonlinear schemes. However, it is shown that the suggested nonlinear schemes are still limited to an exponential scaling in \sqrt{n}. (This scaling may be compared to the exponential scaling in n which is achievable if multiple passes are allowed, even for linear schemes.) The question of whether nonlinear schemes may have a scaling advantage in the presence of loss is left open. Our results are based on a new bound for average estimation error that depends on (i) an entropic measure of the degree to which the probe state can encode a reference phase value, called the Gasymmetry, and (ii) any prior information about the phase shift. This bound is asymptotically stronger than bounds based on the variance of the phase shift generator. The Gasymmetry is also shown to directly bound the average information gained per estimate. Our results hold for any prior distribution of the shift parameter, and generalise to estimates of any shift generated by an operator with discrete eigenvalues.Physical Review X 05/2012; 2(4). · 8.39 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: We investigate the effect of dissipation on indirectly coupled harmonic oscillators and show that the degree of entanglement of initially separable states, caused by squeezing, is enhanced by dissipation. This counterintuitive enhancement is generic, since it arises generally when squeezing is present, and squeezing is always present when the rotatingwave approximation is not made. The effect vanishes if all the oscillators are coupled to identical heat baths, suggesting that "heat flow" may be a necessary condition for dissipationboosted quantum correlations in coupled harmonic oscillators.03/2012; 
Article: The effects of reduced
[Show abstract] [Hide abstract]
ABSTRACT: With the advent of quantum information, the violation of a Bell inequality is used as evidence of the absence of an eavesdropper in cryptographic scenarios such as key distribution and randomness expansion. One of the key assumptions of Bell's Theorem is the existence of experimental "free will", meaning that measurement settings can be chosen at random and independently by each party. The relaxation of this assumption potentially shifts the balance of power towards an eavesdropper. We consider a nosignalling model with reduced "free will" and bound the adversary's capabilities in the task of randomness expansion.02/2012; 
Article: Heisenbergstyle bounds for arbitrary estimates of shift parameters including prior information
[Show abstract] [Hide abstract]
ABSTRACT: A rigorous lower bound is obtained for the average resolution of any estimate of a shift parameter, such as an optical phase shift or a spatial translation. The bound has the asymptotic form k_I/<2G> where G is the generator of the shift (with an arbitrary discrete or continuous spectrum), and hence establishes a universally applicable bound of the same form as the usual Heisenberg limit. The scaling constant k_I depends on prior information about the shift parameter. For example, in phase sensing regimes, where the phase shift is confined to some small interval of length L, the relative resolution \delta\hat{\Phi}/L has the strict lower bound (2\pi e^3)^{1/2}/<2m G_1 +1>, where m is the number of probes, each with generator G_1, and entangling joint measurements are permitted. Generalisations using other resource measures and including noise are briefly discussed. The results rely on the derivation of general entropic uncertainty relations for continuous observables, which are of interest in their own right.New Journal of Physics 01/2012; 14(3). · 3.67 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: The Heisenberg limit traditionally provides a lower bound on the phase uncertainty scaling as 1/ , where is the mean number of photons in the probe. However, this limit has a number of loopholes which potentially might be exploited, to achieve measurements with even greater accuracy. Here we close these loopholes by proving a completely rigorous form of the Heisenberg limit for the average error over all phase shifts. Our result gives the first completely general, constraintfree and nonasymptotic statement of the Heisenberg limit. It holds for all phase estimation schemes, including multiple passes, nonlinear phase shifts, multimode probes, and arbitrary measurements.Physical Review A 11/2011; · 2.99 Impact Factor
Publication Stats
884  Citations  
110.09  Total Impact Points  
Top Journals
Institutions

2011–2014

Griffith University
 Centre for Quantum Dynamics
Southport, Queensland, Australia


2013

Macquarie University
 Department of Physics and Astronomy
Sydney, New South Wales, Australia


1997–2011

Australian National University
 Department of Theoretical Physics
Canberra, Australian Capital Territory, Australia


2002–2008

Institute for Advanced Study
Princeton Junction, New Jersey, United States
