Precision Calibration of Radio Interferometers Using Redundant Baselines

Growing interest in 21 cm tomography has led to the design and construction of broadband radio interferometers with low noise, moderate angular resolution, high spectral resolution, and wide fields of view. With characteristics somewhat different from traditional radio instruments, these interferometers may require new calibration techniques in order to reach their design sensitivities. Self-calibration or redundant calibration techniques that allow an instrument to be calibrated off complicated sky emission structures are ideal. In particular, the large number of redundant baselines possessed by these new instruments makes redundant calibration an especially attractive option. In this paper, we explore the errors and biases in existing redundant calibration schemes through simulations, and show how statistical biases can be eliminated. We also develop a general calibration formalism that includes both redundant baseline methods and basic point source calibration methods as special cases, and show how slight deviations from perfect redundancy and coplanarity can be taken into account.Comment: 18 pages, 13 figures; Replaced to match accepted MNRAS versio

Quantum money from knots

Quantum money is a cryptographic protocol in which a mint can produce a quantum state, no one else can copy the state, and anyone (with a quantum computer) can verify that the state came from the mint. We present a concrete quantum money scheme based on superpositions of diagrams that encode oriented links with the same Alexander polynomial. We expect our scheme to be secure against computationally bounded adversaries.Comment: 22 pages, 5 figure

Quantum money and scalable 21-cm cosmology

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2011.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from student-submitted PDF version of thesis.Includes bibliographical references (p. 165-170).This thesis covers two unrelated topics. The first part of my thesis is about quantum money, a cryptographic protocol in which a mint can generate a quantum state that no one can copy. In public-key quantum money, anyone can verify that a given quantum state came from the mint, and in collision-free quantum money, even the mint cannot generate two valid quantum bills with the same serial number. I present quantum state restoration, a new quantum computing technique that can be used to counterfeit several designs for quantum money. I describe a few other approaches to quantum money, one of which is published, that do not work. I then present a technique that seems to be secure based on a new mathematical object called a component mixer, and I give evidence money using this technique is hard to counterfeit. I describe a way to implement a component mixer and the corresponding quantum money using techniques from knot theory. The second part of my thesis is about 21-cm cosmology and the Fast Fourier transform telescope. With the FFT telescope group at MIT, I worked on a design for a radio telescope that operates between 120 and 200 MHz and will scale to an extremely large number of antennas N. We use an aperture synthesis technique based on Fast Fourier transforms with computational costs proportional toN logN instead of N2. This eliminates the cost of computers as the main limit on the size of a radio interferometer. In this type of telescope, the cost of each antenna matters regardless of how large the telescope becomes, so we focus on reducing the cost of each antenna as much as possible. I discuss the FFT aperture synthesis technique and its equivalence to standard techniques on an evenly spaced grid. I describe analog designs that can reduce the cost per antenna. I give algorithms to analyze raw data from our telescope to help debug and calibrate its components, with particular emphasis on cross-talk between channels and I/Q imbalance. Finally, I present a scalable design for a computer network that can solve the corner-turning problem.by Andrew Lutomirski.Ph.D

Breaking and making quantum money: toward a new quantum cryptographic protocol

Public-key quantum money is a cryptographic protocol in which a bank can create quantum states which anyone can verify but no one except possibly the bank can clone or forge. There are no secure public-key quantum money schemes in the literature; as we show in this paper, the only previously published scheme [1] is insecure. We introduce a category of quantum money protocols which we call collision-free. For these protocols, even the bank cannot prepare multiple identical-looking pieces of quantum money. We present a blueprint for how such a protocol might work as well as a concrete example which we believe may be insecure.Comment: 14 page

Quantum state restoration and single-copy tomography

Given a single copy of an n qubit quantum state |psi>, the no-cloning theorem greatly limits the amount of information which can be extracted from it. Moreover, given only a procedure which verifies the state, for example a procedure which measures the operator |psi> in time polynomial in n . In this paper, we consider the scenario in which we are given both a single copy of |psi> and the ability to verify it. We show that in this setting, we can do several novel things efficiently. We present a new algorithm that we call quantum state restoration which allows us to extend a large subsystem of |psi> to the full state, and in turn this allows us to copy small subsystems of |psi>. In addition, we present algorithms that can perform tomography on small subsystems of |psi>, and we show how to use these algorithms to estimate the statistics of any efficiently implementable POVM acting on |psi> in time polynomial in the number of outcomes of the POVM.Comment: edited for clarity; 13 pages, 1 figur

Solving the Corner-Turning Problem for Large Interferometers

The so-called corner turning problem is a major bottleneck for radio telescopes with large numbers of antennas. The problem is essentially that of rapidly transposing a matrix that is too large to store on one single device; in radio interferometry, it occurs because data from each antenna needs to be routed to an array of processors that will each handle a limited portion of the data (a frequency range, say) but requires input from each antenna. We present a low-cost solution allowing the correlator to transpose its data in real time, without contending for bandwidth, via a butterfly network requiring neither additional RAM memory nor expensive general-purpose switching hardware. We discuss possible implementations of this using FPGA, CMOS, analog logic and optical technology, and conclude that the corner turner cost can be small even for upcoming massive radio arrays.Comment: Revised to match accepted MNRAS version. 7 pages, 4 fig

Mapping our Universe in 3D with MITEoR

Mapping our universe in 3D by imaging the redshifted 21 cm line from neutral hydrogen has the potential to overtake the cosmic microwave background as our most powerful cosmological probe, because it can map a much larger volume of our Universe, shedding new light on the epoch of reionization, inflation, dark matter, dark energy, and neutrino masses. We report on MITEoR, a pathfinder low-frequency radio interferometer whose goal is to test technologies that greatly reduce the cost of such 3D mapping for a given sensitivity. MITEoR accomplishes this by using massive baseline redundancy both to enable automated precision calibration and to cut the correlator cost scaling from N^2 to NlogN, where N is the number of antennas. The success of MITEoR with its 64 dual-polarization elements bodes well for the more ambitious HERA project, which would incorporate many identical or similar technologies using an order of magnitude more antennas, each with dramatically larger collecting area.Comment: To be published in proceedings of 2013 IEEE International Symposium on Phased Array Systems & Technolog