Measuring Controlled-NOT and two-qubit gate operation

Accurate characterisation of two-qubit gates will be critical for any realisation of quantum computation. We discuss a range of measurements aimed at characterising a two-qubit gate, specifically the CNOT gate. These measurements are architecture-independent, and range from simple truth table measurements, to single figure measures such as the fringe visibility, parity, fidelity, and entanglement witnesses, through to whole-state and whole-gate measures achieved respectively via quantum state and process tomography. In doing so, we examine critical differences between classical and quantum gate operation.Comment: 10 pages (two-column). 1 figur

Coherent response to optical excitation in a rare-earth ion doped crystal

We investigate coherent propagation through a large optical density Tm$^{3+}$:YAG crystal. Using an ultra-stable laser, fiber filtering and site selection, we investigate the transmitted pulse temporal profile. The plane wave condition is satisfied by selection of the illuminated spot central area. We pay special attention to $\pi$-pulse transmission in the prospect of implementing optical quantum storage protocols

Noiseless Linear Amplification and Distillation of Entanglement

The idea of signal amplification is ubiquitous in the control of physical systems, and the ultimate performance limit of amplifiers is set by quantum physics. Increasing the amplitude of an unknown quantum optical field, or more generally any harmonic oscillator state, must introduce noise. This linear amplification noise prevents the perfect copying of the quantum state, enforces quantum limits on communications and metrology, and is the physical mechanism that prevents the increase of entanglement via local operations. It is known that non-deterministic versions of ideal cloning and local entanglement increase (distillation) are allowed, suggesting the possibility of non-deterministic noiseless linear amplification. Here we introduce, and experimentally demonstrate, such a noiseless linear amplifier for continuous-variables states of the optical field, and use it to demonstrate entanglement distillation of field-mode entanglement. This simple but powerful circuit can form the basis of practical devices for enhancing quantum technologies. The idea of noiseless amplification unifies approaches to cloning and distillation, and will find applications in quantum metrology and communications.Comment: Submitted 10 June 200

Spectroscopic investigations of a Ti:Tm:LiNbO3 waveguide for photon-echo quantum memory

We report the fabrication and characterization of a Ti$^{4+}$:Tm$^{3+}$:LiNbO$_3$ optical waveguide in view of photon-echo quantum memory applications. In particular, we investigated room- and cryogenic-temperature properties via absorption, spectral hole burning, photon echo, and Stark spectroscopy. We found radiative lifetimes of 82 $\mu$s and 2.4 ms for the $^3$H$_4$ and $^3$F$_4$ levels, respectively, and a 44% branching ratio from the $^3$H$_{4}$ to the $^3$F$_4$ level. We also measured an optical coherence time of 1.6 $\mu$s for the $^3$H$_6\leftrightarrow{}^3$H$_4$, 795 nm wavelength transition, and investigated the limitation of spectral diffusion to spectral hole burning. Upon application of magnetic fields of a few hundred Gauss, we observed persistent spectral holes with lifetimes up to seconds. Furthermore, we measured a linear Stark shift of 25 kHz$\cdot$cm/V. Our results are promising for integrated, electro-optical, waveguide quantum memory for photons.Comment: 11 pages, 14 figure

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/sqrt(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. 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 <= 6, 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.Comment: Published in Nature. This is the final versio

State Capacity and the Environmental Investment Gap in Authoritarian States

We construct an n-period, constrained optimization model where the authoritarian ruler maximizes expected rents subject to budget constraint of available surplus. We show that the larger state capacity is in the previous period, the worse environmental quality will be in the next period: while infrastructural investment and environmental protection increase with state capacity, the former increases at a faster rate which enlarges the gap between the two?the environmental investment gap. Given infrastructural public goods typically damage the environment, the larger this gap is the worse the environmental quality would be. This follows from rulers? optimizing logic of equating marginal returns once we assume the declining marginal productivity of factors of production of surplus. We model three types of air and water pollutants in autocracies as a function of state capacity and other relevant variables. State capacity is associated with higher levels of all three types of pollutants

Set2 methyltransferase facilitates DNA replication and promotes genotoxic stress responses through MBF-dependent transcription

Chromatin modification through histone H3 lysine 36 methylation by the SETD2 tumour suppressor plays a key role in maintaining genome stability. Here we describe a role for Set2-dependent H3K36 methylation in facilitating DNA replication and the transcriptional responses to both replication stress and DNA damage through promoting MluI Cell Cycle Box (MCB) binding factor (MBF) complex-dependent transcription in fission yeast. Set2 loss leads to reduced MBF-dependent ribonucleotide reductase (RNR) expression, reduced deoxyribonucleoside triphosphate (dNTP) synthesis, altered replication origin firing and to a checkpoint-dependent S-phase delay. Accordingly, prolonged S-phase in the absence of Set2 is suppressed by increasing dNTP synthesis. Further, H3K36 is di- and tri-methylated at these MBF gene promoters, and Set2 loss leads to reduced MBF binding and transcription in response to genotoxic stress. Together, these findings provide new insights into how H3K36 methylation facilitates DNA replication and promotes genotoxic stress responses in fission yeast

Silenced yeast chromatin is maintained by Sir2 in preference to permitting histone acetylations for efficient NER

Very little is currently known about how nucleotide excision repair (NER) functions at the ends of chromosomes. To examine this, we introduced the URA3 gene into either transcriptionally active or repressed subtelomeric regions of the yeast genome. This enabled us to examine the repair of ultraviolet (UV)-induced cyclobutane pyrimidine dimers (CPDs) in identical sequences under both circumstances. We found that NER is significantly more efficient in the non-repressed subtelomere than the repressed one. At the non-repressed subtelomere, UV radiation stimulates both histones H3 and H4 acetylation in a similar fashion to that seen at other regions of the yeast genome. These modifications occur regardless of the presence of the Sir2 histone deacetylase. On the other hand, at the repressed subtelomere, where repair is much less efficient, UV radiation is unable to stimulate histone H4 or H3 acetylation in the presence of Sir2. In the absence of Sir2 both of these UV-induced modifications are detected, resulting in a significant increase in NER efficiency in the region. Our experiments reveal that there are instances in the yeast genome where the maintenance of the existing chromatin structures dominates over the action of chromatin modifications associated with efficient NER

The role of multiple marks in epigenetic silencing and the emergence of a stable bivalent chromatin state

We introduce and analyze a minimal model of epigenetic silencing in budding yeast, built upon known biomolecular interactions in the system. Doing so, we identify the epigenetic marks essential for the bistability of epigenetic states. The model explicitly incorporates two key chromatin marks, namely H4K16 acetylation and H3K79 methylation, and explores whether the presence of multiple marks lead to a qualitatively different systems behavior. We find that having both modifications is important for the robustness of epigenetic silencing. Besides the silenced and transcriptionally active fate of chromatin, our model leads to a novel state with bivalent (i.e., both active and silencing) marks under certain perturbations (knock-out mutations, inhibition or enhancement of enzymatic activity). The bivalent state appears under several perturbations and is shown to result in patchy silencing. We also show that the titration effect, owing to a limited supply of silencing proteins, can result in counter-intuitive responses. The design principles of the silencing system is systematically investigated and disparate experimental observations are assessed within a single theoretical framework. Specifically, we discuss the behavior of Sir protein recruitment, spreading and stability of silenced regions in commonly-studied mutants (e.g., sas2, dot1) illuminating the controversial role of Dot1 in the systems biology of yeast silencing.Comment: Supplementary Material, 14 page

Genome-wide analysis of transcriptional dependence and probable target sites for Abf1 and Rap1 in Saccharomyces cerevisiae

Abf1 and Rap1 are general regulatory factors (GRFs) that contribute to transcriptional activation of a large number of genes, as well as to replication, silencing and telomere structure in yeast. In spite of their widespread roles in transcription, the scope of their functional targets genome-wide has not been previously determined. Here, we use microarrays to examine the contribution of these essential GRFs to transcription genome-wide, by using ts mutants that dissociate from their binding sites at 37°C. We then combine this data with published ChIP-chip studies and motif analysis to identify probable direct targets for Abf1 and Rap1. We also identify a substantial number of genes likely to bind Rap1 or Abf1, but not affected by loss of GRF binding. Interestingly, the results strongly suggest that Rap1 can contribute to gene activation from farther upstream than can Abf1. Also, consistent with previous work, more genes that bind Abf1 are unaffected by loss of binding than those that bind Rap1. Finally, we show for several such genes that the Abf1 C-terminal region, which contains the putative activation domain, is not needed to confer this peculiar ‘memory effect’ that allows continued transcription after loss of Abf1 binding