Two-dimensional Site-Bond Percolation as an Example of Self-Averaging System

The Harris-Aharony criterion for a statistical model predicts, that if a specific heat exponent $\alpha \ge 0$, then this model does not exhibit self-averaging. In two-dimensional percolation model the index $\alpha=-{1/2}$. It means that, in accordance with the Harris-Aharony criterion, the model can exhibit self-averaging properties. We study numerically the relative variances $R_{M}$ and $R_{\chi}$ for the probability $M$ of a site belongin to the "infinite" (maximum) cluster and the mean finite cluster size $\chi$. It was shown, that two-dimensional site-bound percolation on the square lattice, where the bonds play the role of impurity and the sites play the role of the statistical ensemble, over which the averaging is performed, exhibits self-averaging properties.Comment: 15 pages, 5 figure

Measuring measurement--disturbance relationships with weak values

Using formal definitions for measurement precision {\epsilon} and disturbance (measurement backaction) {\eta}, Ozawa [Phys. Rev. A 67, 042105 (2003)] has shown that Heisenberg's claimed relation between these quantities is false in general. Here we show that the quantities introduced by Ozawa can be determined experimentally, using no prior knowledge of the measurement under investigation --- both quantities correspond to the root-mean-squared difference given by a weak-valued probability distribution. We propose a simple three-qubit experiment which would illustrate the failure of Heisenberg's measurement--disturbance relation, and the validity of an alternative relation proposed by Ozawa

On quantum error-correction by classical feedback in discrete time

We consider the problem of correcting the errors incurred from sending quantum information through a noisy quantum environment by using classical information obtained from a measurement on the environment. For discrete time Markovian evolutions, in the case of fixed measurement on the environment, we give criteria for quantum information to be perfectly corrigible and characterize the related feedback. Then we analyze the case when perfect correction is not possible and, in the qubit case, we find optimal feedback maximizing the channel fidelity.Comment: 11 pages, 1 figure, revtex

A personalised medicine approach for ponatinib-resistant chronic myeloid leukaemia.

BACKGROUND: Chronic myeloid leukaemia (CML) is characterised by the presence of a fusion driver oncogene, BCR-ABL1, which is a constitutive tyrosine kinase. Tyrosine kinase inhibitors (TKIs) are the central treatment strategy for CML patients and have significantly improved survival rates, but the T315I mutation in the kinase domain of BCR-ABL1 confers resistance to all clinically approved TKIs, except ponatinib. However, compound mutations can mediate resistance even to ponatinib and remain a clinical challenge in CML therapy. Here, we investigated a ponatinib-resistant CML patient through whole-genome sequencing (WGS) to identify the cause of resistance and to find alternative therapeutic targets. PATIENTS AND METHODS: We carried out WGS on a ponatinib-resistant CML patient and demonstrated an effective combination therapy against the primary CML cells derived from this patient in vitro. RESULTS: Our findings demonstrate the emergence of compound mutations in the BCR-ABL1 kinase domain following ponatinib treatment, and chromosomal structural variation data predicted amplification of BCL2. The primary CD34(+) CML cells from this patient showed increased sensitivity to the combination of ponatinib and ABT-263, a BCL2 inhibitor with a negligible effect against the normal CD34(+) cells. CONCLUSION: Our results show the potential of personalised medicine approaches in TKI-resistant CML patients and provide a strategy that could improve clinical outcomes for these patients

Adaptive single-shot phase measurements: The full quantum theory

The phase of a single-mode field can be measured in a single-shot measurement by interfering the field with an effectively classical local oscillator of known phase. The standard technique is to have the local oscillator detuned from the system (heterodyne detection) so that it is sometimes in phase and sometimes in quadrature with the system over the course of the measurement. This enables both quadratures of the system to be measured, from which the phase can be estimated. One of us [H.M. Wiseman, Phys. Rev. Lett. 75, 4587 (1995)] has shown recently that it is possible to make a much better estimate of the phase by using an adaptive technique in which a resonant local oscillator has its phase adjusted by a feedback loop during the single-shot measurement. In Ref.~[H.M. Wiseman and R.B. Killip, Phys. Rev. A 56, 944] we presented a semiclassical analysis of a particular adaptive scheme, which yielded asymptotic results for the phase variance of strong fields. In this paper we present an exact quantum mechanical treatment. This is necessary for calculating the phase variance for fields with small photon numbers, and also for considering figures of merit other than the phase variance. Our results show that an adaptive scheme is always superior to heterodyne detection as far as the variance is concerned. However the tails of the probability distribution are surprisingly high for this adaptive measurement, so that it does not always result in a smaller probability of error in phase-based optical communication.Comment: 17 pages, LaTeX, 8 figures (concatenated), Submitted to Phys. Rev.

Multiple-copy state discrimination: Thinking globally, acting locally

We theoretically investigate schemes to discriminate between two nonorthogonal quantum states given multiple copies. We consider a number of state discrimination schemes as applied to nonorthogonal, mixed states of a qubit. In particular, we examine the difference that local and global optimization of local measurements makes to the probability of obtaining an erroneous result, in the regime of finite numbers of copies $N$, and in the asymptotic limit as $N \rightarrow \infty$. Five schemes are considered: optimal collective measurements over all copies, locally optimal local measurements in a fixed single-qubit measurement basis, globally optimal fixed local measurements, locally optimal adaptive local measurements, and globally optimal adaptive local measurements. Here, adaptive measurements are those for which the measurement basis can depend on prior measurement results. For each of these measurement schemes we determine the probability of error (for finite $N$) and scaling of this error in the asymptotic limit. In the asymptotic limit, adaptive schemes have no advantage over the optimal fixed local scheme, and except for states with less than 2% mixture, the most naive scheme (locally optimal fixed local measurements) is as good as any noncollective scheme. For finite $N$, however, the most sophisticated local scheme (globally optimal adaptive local measurements) is better than any other noncollective scheme, for any degree of mixture.Comment: 11 pages, 14 figure

Atom laser coherence and its control via feedback

We present a quantum-mechanical treatment of the coherence properties of a single-mode atom laser. Specifically, we focus on the quantum phase noise of the atomic field as expressed by the first-order coherence function, for which we derive analytical expressions in various regimes. The decay of this function is characterized by the coherence time, or its reciprocal, the linewidth. A crucial contributor to the linewidth is the collisional interaction of the atoms. We find four distinct regimes for the linewidth with increasing interaction strength. These range from the standard laser linewidth, through quadratic and linear regimes, to another constant regime due to quantum revivals of the coherence function. The laser output is only coherent (Bose degenerate) up to the linear regime. However, we show that application of a quantum nondemolition measurement and feedback scheme will increase, by many orders of magnitude, the range of interaction strengths for which it remains coherent.Comment: 15 pages, 6 figures, revtex

State and dynamical parameter estimation for open quantum systems

Following the evolution of an open quantum system requires full knowledge of its dynamics. In this paper we consider open quantum systems for which the Hamiltonian is ``uncertain''. In particular, we treat in detail a simple system similar to that considered by Mabuchi [Quant. Semiclass. Opt. 8, 1103 (1996)]: a radiatively damped atom driven by an unknown Rabi frequency $\Omega$ (as would occur for an atom at an unknown point in a standing light wave). By measuring the environment of the system, knowledge about the system state, and about the uncertain dynamical parameter, can be acquired. We find that these two sorts of knowledge acquisition (quantified by the posterior distribution for $\Omega$, and the conditional purity of the system, respectively) are quite distinct processes, which are not strongly correlated. Also, the quality and quantity of knowledge gain depend strongly on the type of monitoring scheme. We compare five different detection schemes (direct, adaptive, homodyne of the $x$ quadrature, homodyne of the $y$ quadrature, and heterodyne) using four different measures of the knowledge gain (Shannon information about $\Omega$, variance in $\Omega$, long-time system purity, and short-time system purity).Comment: 14 pages, 18 figure

Adiabatic Elimination in Compound Quantum Systems with Feedback

Feedback in compound quantum systems is effected by using the output from one sub-system (``the system'') to control the evolution of a second sub-system (``the ancilla'') which is reversibly coupled to the system. In the limit where the ancilla responds to fluctuations on a much shorter time scale than does the system, we show that it can be adiabatically eliminated, yielding a master equation for the system alone. This is very significant as it decreases the necessary basis size for numerical simulation and allows the effect of the ancilla to be understood more easily. We consider two types of ancilla: a two-level ancilla (e.g. a two-level atom) and an infinite-level ancilla (e.g. an optical mode). For each, we consider two forms of feedback: coherent (for which a quantum mechanical description of the feedback loop is required) and incoherent (for which a classical description is sufficient). We test the master equations we obtain using numerical simulation of the full dynamics of the compound system. For the system (a parametric oscillator) and feedback (intensity-dependent detuning) we choose, good agreement is found in the limit of heavy damping of the ancilla. We discuss the relation of our work to previous work on feedback in compound quantum systems, and also to previous work on adiabatic elimination in general.Comment: 18 pages, 12 figures including two subplots as jpeg attachment