Dynamics of a Quantum Reference Frame

We analyze a quantum mechanical gyroscope which is modeled as a large spin and used as a reference against which to measure the angular momenta of spin-1/2 particles. These measurements induce a back-action on the reference which is the central focus of our study. We begin by deriving explicit expressions for the quantum channel representing the back-action. Then, we analyze the dynamics incurred by the reference when it is used to sequentially measure particles drawn from a fixed ensemble. We prove that the reference thermalizes with the measured particles and find that generically, the thermal state is reached in time which scales linearly with the size of the reference. This contrasts a recent conclusion of Bartlett et al. that this takes a quadratic amount of time when the particles are completely unpolarized. We now understand their result in terms of a simple physical principle based on symmetries and conservation laws. Finally, we initiate the study of the non-equilibrium dynamics of the reference. Here we find that a reference in a coherent state will essentially remain in one when measuring polarized particles, while rotating itself to ultimately align with the polarization of the particles

Private quantum decoupling and secure disposal of information

Given a bipartite system, correlations between its subsystems can be understood as information that each one carries about the other. In order to give a model-independent description of secure information disposal, we propose the paradigm of private quantum decoupling, corresponding to locally reducing correlations in a given bipartite quantum state without transferring them to the environment. In this framework, the concept of private local randomness naturally arises as a resource, and total correlations get divided into eliminable and ineliminable ones. We prove upper and lower bounds on the amount of ineliminable correlations present in an arbitrary bipartite state, and show that, in tripartite pure states, ineliminable correlations satisfy a monogamy constraint, making apparent their quantum nature. A relation with entanglement theory is provided by showing that ineliminable correlations constitute an entanglement parameter. In the limit of infinitely many copies of the initial state provided, we compute the regularized ineliminable correlations to be measured by the coherent information, which is thus equipped with a new operational interpretation. In particular, our results imply that two subsystems can be privately decoupled if their joint state is separable.Comment: Child of 0807.3594 v2: minor changes v3: presentation improved, one figure added v4: extended version with a lot of discussions and examples v5: published versio

Faithful Squashed Entanglement

Squashed entanglement is a measure for the entanglement of bipartite quantum states. In this paper we present a lower bound for squashed entanglement in terms of a distance to the set of separable states. This implies that squashed entanglement is faithful, that is, strictly positive if and only if the state is entangled. We derive the bound on squashed entanglement from a bound on quantum conditional mutual information, which is used to define squashed entanglement and corresponds to the amount by which strong subadditivity of von Neumann entropy fails to be saturated. Our result therefore sheds light on the structure of states that almost satisfy strong subadditivity with equality. The proof is based on two recent results from quantum information theory: the operational interpretation of the quantum mutual information as the optimal rate for state redistribution and the interpretation of the regularised relative entropy of entanglement as an error exponent in hypothesis testing. The distance to the set of separable states is measured by the one-way LOCC norm, an operationally-motivated norm giving the optimal probability of distinguishing two bipartite quantum states, each shared by two parties, using any protocol formed by local quantum operations and one-directional classical communication between the parties. A similar result for the Frobenius or Euclidean norm follows immediately. The result has two applications in complexity theory. The first is a quasipolynomial-time algorithm solving the weak membership problem for the set of separable states in one-way LOCC or Euclidean norm. The second concerns quantum Merlin-Arthur games. Here we show that multiple provers are not more powerful than a single prover when the verifier is restricted to one-way LOCC operations thereby providing a new characterisation of the complexity class QMA.Comment: 24 pages, 1 figure, 1 table. Due to an error in the published version, claims have been weakened from the LOCC norm to the one-way LOCC nor

Precision medicine for suicidality: from universality to subtypes and personalization

Suicide remains a clear, present and increasing public health problem, despite being a potentially preventable tragedy. Its incidence is particularly high in people with overt or un(der)diagnosed psychiatric disorders. Objective and precise identification of individuals at risk, ways of monitoring response to treatments and novel preventive therapeutics need to be discovered, employed and widely deployed. We sought to investigate whether blood gene expression biomarkers for suicide (that is, a ‘liquid biopsy’ approach) can be identified that are more universal in nature, working across psychiatric diagnoses and genders, using larger cohorts than in previous studies. Such markers may reflect and/or be a proxy for the core biology of suicide. We were successful in this endeavor, using a comprehensive stepwise approach, leading to a wealth of findings. Steps 1, 2 and 3 were discovery, prioritization and validation for tracking suicidality, resulting in a Top Dozen list of candidate biomarkers comprising the top biomarkers from each step, as well as a larger list of 148 candidate biomarkers that survived Bonferroni correction in the validation step. Step 4 was testing the Top Dozen list and Bonferroni biomarker list for predictive ability for suicidal ideation (SI) and for future hospitalizations for suicidality in independent cohorts, leading to the identification of completely novel predictive biomarkers (such as CLN5 and AK2), as well as reinforcement of ours and others previous findings in the field (such as SLC4A4 and SKA2). Additionally, we examined whether subtypes of suicidality can be identified based on mental state at the time of high SI and identified four potential subtypes: high anxiety, low mood, combined and non-affective (psychotic). Such subtypes may delineate groups of individuals that are more homogenous in terms of suicidality biology and behavior. We also studied a more personalized approach, by psychiatric diagnosis and gender, with a focus on bipolar males, the highest risk group. Such a personalized approach may be more sensitive to gender differences and to the impact of psychiatric co-morbidities and medications. We compared testing the universal biomarkers in everybody versus testing by subtypes versus personalized by gender and diagnosis, and show that the subtype and personalized approaches permit enhanced precision of predictions for different universal biomarkers. In particular, LHFP appears to be a strong predictor for suicidality in males with depression. We also directly examined whether biomarkers discovered using male bipolars only are better predictors in a male bipolar independent cohort than universal biomarkers and show evidence for a possible advantage of personalization. We identified completely novel biomarkers (such as SPTBN1 and C7orf73), and reinforced previously known biomarkers (such as PTEN and SAT1). For diagnostic ability testing purposes, we also examined as predictors phenotypic measures as apps (for suicide risk (CFI-S, Convergent Functional Information for Suicidality) and for anxiety and mood (SASS, Simplified Affective State Scale)) by themselves, as well as in combination with the top biomarkers (the combination being our a priori primary endpoint), to provide context and enhance precision of predictions. We obtained area under the curves of 90% for SI and 77% for future hospitalizations in independent cohorts. Step 5 was to look for mechanistic understanding, starting with examining evidence for the Top Dozen and Bonferroni biomarkers for involvement in other psychiatric and non-psychiatric disorders, as a mechanism for biological predisposition and vulnerability. The biomarkers we identified also provide a window towards understanding the biology of suicide, implicating biological pathways related to neurogenesis, programmed cell death and insulin signaling from the universal biomarkers, as well as mTOR signaling from the male bipolar biomarkers. In particular, HTR2A increase coupled with ARRB1 and GSK3B decreases in expression in suicidality may provide a synergistic mechanistical corrective target, as do SLC4A4 increase coupled with AHCYL1 and AHCYL2 decrease. Step 6 was to move beyond diagnostics and mechanistical risk assessment, towards providing a foundation for personalized therapeutics. Items scored positive in the CFI-S and subtypes identified by SASS in different individuals provide targets for personalized (psycho)therapy. Some individual biomarkers are targets of existing drugs used to treat mood disorders and suicidality (lithium, clozapine and omega-3 fatty acids), providing a means toward pharmacogenomics stratification of patients and monitoring of response to treatment. Such biomarkers merit evaluation in clinical trials. Bioinformatics drug repurposing analyses with the gene expression biosignatures of the Top Dozen and Bonferroni-validated universal biomarkers identified novel potential therapeutics for suicidality, such as ebselen (a lithium mimetic), piracetam (a nootropic), chlorogenic acid (a polyphenol) and metformin (an antidiabetic and possible longevity promoting drug). Finally, based on the totality of our data and of the evidence in the field to date, a convergent functional evidence score prioritizing biomarkers that have all around evidence (track suicidality, predict it, are reflective of biological predisposition and are potential drug targets) brought to the fore APOE and IL6 from among the universal biomarkers, suggesting an inflammatory/accelerated aging component that may be a targetable common denominator

Quantum geometry and quantum algorithms

Motivated by algorithmic problems arising in quantum field theories whose dynamical variables are geometric in nature, we provide a quantum algorithm that efficiently approximates the colored Jones polynomial. The construction is based on the complete solution of Chern-Simons topological quantum field theory and its connection to Wess-Zumino-Witten conformal field theory. The colored Jones polynomial is expressed as the expectation value of the evolution of the q-deformed spin-network quantum automaton. A quantum circuit is constructed capable of simulating the automaton and hence of computing such expectation value. The latter is efficiently approximated using a standard sampling procedure in quantum computation.Comment: Submitted to J. Phys. A: Math-Gen, for the special issue ``The Quantum Universe'' in honor of G. C. Ghirard

Quantum capacity under adversarial quantum noise: arbitrarily varying quantum channels

We investigate entanglement transmission over an unknown channel in the presence of a third party (called the adversary), which is enabled to choose the channel from a given set of memoryless but non-stationary channels without informing the legitimate sender and receiver about the particular choice that he made. This channel model is called arbitrarily varying quantum channel (AVQC). We derive a quantum version of Ahlswede's dichotomy for classical arbitrarily varying channels. This includes a regularized formula for the common randomness-assisted capacity for entanglement transmission of an AVQC. Quite surprisingly and in contrast to the classical analog of the problem involving the maximal and average error probability, we find that the capacity for entanglement transmission of an AVQC always equals its strong subspace transmission capacity. These results are accompanied by different notions of symmetrizability (zero-capacity conditions) as well as by conditions for an AVQC to have a capacity described by a single-letter formula. In he final part of the paper the capacity of the erasure-AVQC is computed and some light shed on the connection between AVQCs and zero-error capacities. Additionally, we show by entirely elementary and operational arguments motivated by the theory of AVQCs that the quantum, classical, and entanglement-assisted zero-error capacities of quantum channels are generically zero and are discontinuous at every positivity point.Comment: 49 pages, no figures, final version of our papers arXiv:1010.0418v2 and arXiv:1010.0418. Published "Online First" in Communications in Mathematical Physics, 201

Discrepancies between transcutaneous and estimated glomerular filtration rates in rats with chronic kidney disease

Accurate assessment of the glomerular filtration rate (GFR) is crucial for researching kidney disease in rats. Although validation of methods that assess GFR is crucial, large-scale comparisons between different methods are lacking. Both transcutaneous GFR (tGFR) and a newly developed estimated GFR (eGFR) equation by our group provide a low-invasive approach enabling repeated measurements. The tGFR is a single bolus method using FITC-labeled sinistrin to measure GFR based on half-life of the transcutaneous signal, whilst the eGFR is based on urinary sinistrin clearance. Here, we retrospectively compared tGFR, using both 1- and 3- compartment models (tGFR_1c and tGFR_3c, respectively) to the eGFR in a historic cohort of 43 healthy male rats and 84 male rats with various models of chronic kidney disease. The eGFR was on average considerably lower than tGFR-1c and tGFR-3c (mean differences 855 and 216 μL/min, respectively) and only 20 and 47% of measurements were within 30% of each other, respectively. The relative difference between eGFR and tGFR was highest in rats with the lowest GFR. Possible explanations for the divergence are problems inherent to tGFR, such as technical issues with signal measurement, description of the signal kinetics, and translation of half-life to tGFR, which depends on distribution volume. The unknown impact of isoflurane anesthesia used in determining mGFR remains a limiting factor. Thus, our study shows that there is a severe disagreement between GFR measured by tGFR and eGFR, stressing the need for more rigorous validation of the tGFR and possible adjustments to the underlying technique.</p

Discrepancies between transcutaneous and estimated glomerular filtration rates in rats with chronic kidney disease

Accurate assessment of the glomerular filtration rate (GFR) is crucial for researching kidney disease in rats. Although validation of methods that assess GFR is crucial, large-scale comparisons between different methods are lacking. Both transcutaneous GFR (tGFR) and a newly developed estimated GFR (eGFR) equation by our group provide a low-invasive approach enabling repeated measurements. The tGFR is a single bolus method using FITC-labeled sinistrin to measure GFR based on half-life of the transcutaneous signal, whilst the eGFR is based on urinary sinistrin clearance. Here, we retrospectively compared tGFR, using both 1- and 3- compartment models (tGFR_1c and tGFR_3c, respectively) to the eGFR in a historic cohort of 43 healthy male rats and 84 male rats with various models of chronic kidney disease. The eGFR was on average considerably lower than tGFR-1c and tGFR-3c (mean differences 855 and 216 μL/min, respectively) and only 20 and 47% of measurements were within 30% of each other, respectively. The relative difference between eGFR and tGFR was highest in rats with the lowest GFR. Possible explanations for the divergence are problems inherent to tGFR, such as technical issues with signal measurement, description of the signal kinetics, and translation of half-life to tGFR, which depends on distribution volume. The unknown impact of isoflurane anesthesia used in determining mGFR remains a limiting factor. Thus, our study shows that there is a severe disagreement between GFR measured by tGFR and eGFR, stressing the need for more rigorous validation of the tGFR and possible adjustments to the underlying technique.</p

Monitoring the vadose zone in fractured tuff, Yucca Mountain, Nevada

Unsaturated tuff beneath Yucca Mountain, Nevada, is being evaluated by the US Department of Energy as a host rock for a potential repository for high-level radioactive waste. As part of the Nevada Nuclear Waste Storage Investigations Project of the US Department of Energy, the US Geological Survey has been conducting hydrologic, geologic, and geophysical investigations at Yucca Mountain and the surrounding region to provide data evaluation of the potential suitability of the site. Hydrologic investigations of the unsaturated zone at this site were started in 1982. A 17.5-inch- (44.5-centimeter-) diameter borehole (USW UZ-1) was drilled by the reverse-air vacuum-drilling technique to a depth of 1269 feet (387 meters). This borehole was instrumented at 33 depth levels. At 15 of the levels, 3 well screens were embedded in coarse-sand columns. The sand columns were isolated from each other by thin layers of bentonite, columns of silica flour, and isolation plugs consisting of expansive cement. Thermocouple psychrometers and pressure transducers were installed within the screens and connected to the data-acquisition system at the land surface through thermocouple and logging cables. Two of the screens at each level were equipped with access tubes to allow collection of pore-gas samples. In addition to these instruments, 18 heat-dissipation probes were installed within the columns of silica flour, some of which also had thermocouple psychrometers. 20 refs., 13 figs., 2 tabs

Continuity of quantum channel capacities

We prove that a broad array of capacities of a quantum channel are continuous. That is, two channels that are close with respect to the diamond norm have correspondingly similar communication capabilities. We first show that the classical capacity, quantum capacity, and private classical capacity are continuous, with the variation on arguments epsilon apart bounded by a simple function of epsilon and the channel's output dimension. Our main tool is an upper bound of the variation of output entropies of many copies of two nearby channels given the same initial state; the bound is linear in the number of copies. Our second proof is concerned with the quantum capacities in the presence of free backward or two-way public classical communication. These capacities are proved continuous on the interior of the set of non-zero capacity channels by considering mutual simulation between similar channels.Comment: 12 pages, Revised according to referee's suggestion