April 23, 2014

Workshop on Mathematical Methods of
Quantum Tomography

February 19-22, 2013

Fields Institute, 222 College St.,Toronto

Robin Blume-Kohout (Los Alamos National Lab) - Thursday 9:35am
Adaptive Gate-Set Tomography

Quantum information hardware needs to be characterized and calibrated. This is the job of quantum state and process tomography, but standard tomographic methods have an Achilles heel: to characterize an unknown process, they rely on a set of absolutely calibrated measurements. Many technologies (e.g., solid-state qubits) admit only a single native measurement basis, and other bases are measured using unitary control. So tomography becomes circular -- tomographic protocols are using gates to calibrate themselves! Gate-set tomography confronts this problem head-on and resolves it by treating gates relationally. We abandon all assumptions about what a given gate operation does, and characterize entire universal gate sets from the ground up using only the observed statistics of an [unknown] 2-outcome measurement after various strings of [unknown] gate operations. The accuracy and reliability of the resulting estimates depend critically on which gate strings are used, and benefits greatly from adaptivity. We demonstrate gate-set tomography and quantify the accuracy with which the individual gates can be estimated.

Agata Branczyk (University of Toronto) - Tuesday 2:00pm
Holistic Tomography

Quantum state tomography is the characterization of a quantum state by repeated state preparation and measurement. It relies on the ability to prepare well-characterized unitary operations to change the measurement basis. Conversely, quantum process tomography is the characterization of a quantum process, relying on the preparation of well-characterized quantum states. While parallels between state and process tomography are well-known, the two have largely been treated independently. In the last year, however, we saw the development of a number of more holistic approaches, where unknown parameters in both the state and process are treated on an equal footing [1-5]. I will discuss advances made in these approaches, focusing on our results for unitary processes, and look to the future with a discussion of open problems and possible future directions.

[1] A M Branczyk, D H. Mahler, L A. Rozema, A Darabi, A M. Steinberg, and D F V James. "Self-calibrating quantum state tomography", New Journal of Physics 14, no. 8 (2012): 085003.
[2] D Mogilevtsev, J. Rehácek, and Z. Hradil. "Self-calibration for self-consistent tomography", New Journal of Physics 14, no. 9 (2012): 095001.
[3] S T Merkel, J M Gambetta, J A Smolin, S Poletto, A D Córcoles, B R Johnson, Colm A. Ryan, and M Steffen. "Self-Consistent Quantum Process Tomography", arXiv:1211.0322 [quant-ph] (2012).
[4] N Quesada, A M Branczyk, and D F V James. "Self-calibrating tomography of multi-dimensional systems.",arXiv:1212.0556 [quant-ph] (2012)
[5] Stanislav Straupe, Denis Ivanov, Alexander Kalinkin, Ivan Bobrov, Sergey P Kulik, D Mogilevtsev, "Self-calibrating Tomography for Angular Schmidt Modes in Spontaneous Parametric Down-Conversion", arXiv:1112.3806 [quant-ph](2013)

Maria Chekhova (Max-Planck Institute for the Science of Light) - Wednesday 11:am
Polarization quantum tomography of macroscopic Bell states

We study the polarization properties of macroscopic Bell states, which are multi-photon analogues of two-photon polarization-entangled Bell states. The states are produced using two orthogonally polarized non-degenerate optical parametric amplifiers coherently pumped by strong picosecond pulses. For one of macroscopic Bell states, the singlet one, all three Stokes observables S1,2,3 have noise suppressed below the shot-noise level. For each of the other three states, the triplet ones, only one Stokes observable has noise suppressed. These and other polarization properties are revealed by reconstructing the quasiprobability W(S1,S2,S3), which is the polarization analog of the Wigner function. The reconstruction procedure is similar to the classical 3D inverse Radon transformation. It is performed on the histograms obtained by measuring the probability distributions of various Stokes observables. For comparison, we also reconstruct the polarization quasiprobability of a pseudo-coherent state and study the robustness of the reconstruction against the state displacement in the Stokes space

Matthias Christandl (ETH Zurich) - Tuesday 9:35am
Reliable quantum state tomography

Quantum state tomography is the task of inferring the state of a quantum system by appropriate measurements. Since the frequency distributions of the outcomes of any finite number of measurements will generally deviate from their asymptotic limits, the estimates computed by standard methods do not in general coincide with the true state, and therefore have no operational significance unless their accuracy is defined in terms of error bounds. Here we show that quantum state tomography, together with an appropriate data analysis procedure, yields reliable and tight error bounds, specified in terms of confidence regions - a concept originating from classical statistics. Confidence regions are subsets of the state space in which the true state lies with high probability, independently of any prior assumption on the distribution of the possible states. Our method for computing confidence regions can be applied to arbitrary measurements including fully coherent ones; it is practical and particularly well suited for tomography on systems consisting of a small number of qubits, which are currently in the focus of interest in experimental quantum information science.

Rafal Demkowicz-Dobrzanski (University of Warsaw) - Thursday 11:00am
All you need is squeezing! Optimal schemes for realistic quantum metrology.

The presence of decoherence makes the quantum precision enhancement offered by quantum metrology less spectacular than in idealized scenarios. Nevertheless, the quantum gain may still be important from a practical point in e.g. atomic clocks or gravitational wave detectors. Interestingly, while decoherence certainly should be regarded as a nuisance, it has a positive aspect namely, that when decoherence is taken into account, simple quantum metrological protocols based on squeezed states efficiently reach the fundamental theoretical limits on precision. Therefore no more sophisticated quantum states nor measurements are necessary for practical quantum metrology.

Jens Eisert (Freie Universität Berlin) - Wednesday 9:00am
Progress on quantum compressed sensing

Intuitively, if a density operator has small rank, then it should be easier to estimate from experimental data, since in this case only a few eigenvectors need to be learned. Quantum compressed sensing provides a rigorous formalism confirming this intuition. This talk will report recent progress in tomography based on compressed sensing. In particular, it is shown that a low-rank density matrix can be estimated using fewer copies of the state, i.e., the sample complexity of tomography decreases with the rank. Second, we show that unknown low-rank states can be reconstructed from an incomplete set of measurements, using techniques from compressed sensing and matrix completion. We will further elaborate on continuous-variable instances of this idea, and sketch how similar ideas can be used for feasible tomography in quantum optical systems, e.g., in systems of ultracold atoms in optical lattices.

Berge Englert (Centre for Quantum Technologies, Singapore) - Tuesday 9:00am
Maximum-likelihood regions and smallest credible regions

Rather than point estimators, states of a quantum system that represent one's best guess for the given data, we consider optimal regions of estimators. As the natural counterpart of the popular maximum-likelihood point estimator, we introduce the maximum-likelihood region -- the region of largest likelihood among all regions of the same size.
Here, the size of a region is its prior probability. Another concept is the smallest credible region -- the smallest region with pre-chosen posterior probability. For both optimization problems, the optimal region has constant likelihood on its boundary. We discuss criteria for assigning prior probabilities to regions, and illustrate the concepts and methods with several examples.
Collaborators Jiangwei Shang, Hui Khoon Ng, Arun Sehrawat, Xikun Li

Alessandro Ferraro (University College London) - Friday 2:00pm
Reconstructing the quantum state of oscillator networks with a single qubit

A minimal scheme to reconstruct arbitrary states of networks composed of quantum oscillators is introduced. The scheme uses minimal resources in the sense that it i) requires only the interaction between one-qubit probe and one constituent of the network; ii) provides the reconstructed state directly from the data, avoiding any tomographic transformation; iii) involves the tuning of only one coupling parameter. In addition, a number of quantum properties can be extracted without full reconstruction of the state. The scheme can be used for probing quantum simulations of anharmonic many-body systems and quantum computations with continuous variables. Experimental implementation with trapped ions is also discussed and shown to be within reach of current technology.
Ref.: T. Tufarelli, A. Ferraro, M. S. Kim, S. Bose, Phys. Rev. A 85, 032334 (2012)

Steve Flammia (University of Sydney) - Wednesday 9:35am
The Sample Complexity of Tomography and New Estimators for Compressed Sensing

We will present a new theoretical analysis of quantum tomography, focusing on efficient use of measurements, statistical sampling, and classical computation. Our results are several fold. Using Liu's restricted isometry property (RIP) for low-rank matrices via Pauli measurements, we obtain near-optimal error bounds, for the realistic situation where the data contains noise due to finite statistics, and the density matrix is full-rank with decaying eigenvalues. We also obtain upper-bounds on the sample complexity of compressed tomography, and almost-matching lower bounds on the sample complexity of any procedure using adaptive sequences of Pauli measurements.
We will additionally show numerical simulations that compare the performance of two compressed sensing estimators with standard maximum-likelihood estimation (MLE). We find that the compressed sensing estimators consistently produce higher-fidelity state reconstructions than MLE given comparable experimental resources. In addition, the use of an incomplete set of measurements leads to faster classical processing with no loss of accuracy.
Finally, we show how to certify the accuracy of a low rank estimate using direct fidelity estimation and we describe a method for compressed quantum process tomography that works for processes with small Kraus rank, and requires only Pauli eigenstate preparations and Pauli measurements.
Joint work with David Gross, Yi-Kai Liu, and Jens Eisert, New J. Phys. 14, 095022 (2012).

Marco Genovese (INRIM) - Thursday 2:00pm
Quantum Tomography of the POVM of PNR detectors: different methods.

The rapid development of quantum systems has enabled a wide range of novel and innovative technologies, from quantum information processing to quantum metrology and imaging, mainly based on optical systems.
Precise characterization techniques of quantum resources, i.e. states, operations and detectors play a critical role in development of such technologies. In this talk we will present recent experiments addressed to reconstruct the POVM of photon number resolving (PNR) detectors and their application. In the first case [1] we will discuss the reconstruction of a TES POVM based on the use of a quorum of coherent states. In the second case [2] we present the first experimental characterization of quantum properties of an unknown PNR detector, a detector tree, that takes advantage of a quantum resource, i.e. an ancillary state . This quantum-assisted reconstruction method requires no prior information about the detector under test, and its convergence is more stable and faster to reach a final result. This is achieved by exploiting strong quantum correlations of twin beams generated in a parametric down conversion process: one beam is characterized by a quantum tomographer, while the other is used to calibrate the unknown detector.Finally, we will discuss the experimental realisation a self consistent quantum tomography of a PNR detector POVM and its application [3].
[1] G.Brida, L.Ciavarella, I.Degiovanni, M. Genovese, L.Lolli, M.Mingolla, F. Piacentini, M. Rajteri, E. Taralli, M.Paris, New J. Phys. 14 (2012) 085001
[2] G. Brida, L. Ciavarella, I. P. Degiovanni, M. Genovese, A. Migdall,
M. G. Mingolla, M. G. A. Paris, F. Piacentini, S. V. Polyakov, Phys. Rev. Lett. 108, 253601 (2012)
[3] G.Brida et al., work to be submitted.

Lane P. Hughston (University College London) - Wednesday 2:35pm
Universal Tomographic Measurements

The purpose of this paper is to introduce certain rather general classes of operations in quantum mechanics that one can regard as \universal quantum measurements" (UQMs) in the sense that they are applicable to all quantum systems and involve the specification of only a minimal amount of structure on the system. The first class of UQM that we consider involves the Hilbert space of the system together with the specification of the stateof the system- no further structure is brought into play. We call operations of this type "universal tomographic measurements", since given the statistics of the outcomes of such measurements it is possible to reconstruct the state of the system. The second class of UQM that we consider is also universal in the sense that the only additional structure involved is the specification of the Hamiltonian. Apart from the usual projective measurements of the energy, one is also led to a number of other less familiar measurement operations, which we discuss. Among these, for example, is a direct measurement of the "expected" energy of the system. Finally, we consider the large class of UQMs that can be constructed when the universal tomographic measurements on one or more quantum systems are lifted, through appropriate embeddings, to induce certain associated operations on the embedding space.
As an example, one can make a measurement of the direction in space along which the spin of a spin-s particle is oriented (s =1/2,1, ….) In this case the additional structure involves the embedding of CP1 as a rational curve of degree 2s in CP2s. As another example, we show how one can construct a universal disentangling measurement, the outcome of which, when applied to a mixed state of an entangled compose system, is a disentangled product of pure constituent states.
Joint work with Dorje C. Brody

Andrei Klimov (Universidad de Guadalajara) - Friday 11:00am
Distribution of quantum fluctuations in the macroscopic limit of N qubit systems

We analyze the structure of quasidistribution functions of N qubit systems projected into the space of symmetric measurements in the asymptotic limit of large number of qubits. We discuss the possibility of reconstruction of the Q-function in this 3-dimensional space of symmetric measurements from higher order moments. Analytical expressions for the projected Q - function are found for different classes of both factorized and entangled multi-qubit states. Macroscopic features of discrete quasidistribution functions are also discussed.

Alex Lvovsky (University of Calgary) - Friday 9:00am
Three ways to skin a cat: numerical approaches in coherent-state quantum process tomography

Coherent-state quantum process tomography (csQPT) is a method for completely characterizing a quantum-optical 'black box' by probing it with coherent states and carrying out homodyne measurements on the output. While conceptually simple, practical implementation of csQPT faces a few challenges associated with the highly singular nature of the Glauber-Sudarshan function as well as the infinite nature of the set of coherent states required for probing. To date, three different approaches have been developed to address these challenges. The presentation will describe these approaches and their relative advantages and disadvantages.

Paolo Mataloni (Università degli Studi di Roma "La Sapienza") - Thursday 2:35pm
Tomographic reconstruction of integrated waveguide optical devices

Integrated photonics is a fundamental instrument for the realization of linear optical quantum circuits. Integrated waveguide optical devices of increasing complexity, eventually reconfigurable, play a fundamental role for the realization of a number of experiments implementing quantum logic gates, enabling quantum simulations, and coding photon states for quantum communication.
An integrated photonic device is usually based on an interferometric network, given by an array of suitably chosen directional couplers and is described by a unitary matrix that allows to map the distribution of amplitudes and phases of the quantum optical field traveling therein. To efficiently reconstruct the transfer matrix of a complex optical network is essential in many cases, for instance when one wants to perform different unitary transformations in a controlled way. This task becomes more and more difficult as the complexity grows and may be highly non trivial when the unavoidable optical losses of the device need to be considered.
I will present the results obtained in our laboratory in characterizing the operation of novel integrated optical devices built by the 3-dimensional capability of the femtosecond laser writing technique and in realizing their tomographic reconstruction.

Dimitry Mogilevtsev (Universidade Federal do ABC) - Tuesday 2:35pm
Self-calibrating tomography

A possibility of simultaneous tomography of a signal state and measurement set-up will be discussed and illustrated with a number of practical examples.

Tobias Moroder (University of Siegen) - Wednesday 2:00pm
Detection of systematic errors in quantum tomography experiments

When systematic errors are ignored in an experiment, the subsequent analysis of its results becomes questionable. We develop tests to identify systematic errors in experiments where only a finite amount of data is recorded and apply these tests to tomographic data taken in an ion-trap experiment. We put particular emphasis on quantum state tomography and present two detection methods: the first employs linear inequalities while the second is based on the generalized likelihood ratio.

joint work with: Matthias Kleinmann, Philipp Schindler, Thomas Monz, Otfried Gühne, Rainer Blatt
reference: arXiv:1204.3644

Joshua Nunn (University of Oxford) - Thursday 11:35am
Optimal experiment design for quantum state tomography: Fair, precise, and minimal tomography

Given an experimental setup and a fixed number of measurements, how should one take data to optimally reconstruct the state of a quantum system? The problem of optimal experiment design (OED) for quantum state tomography was first broached by Kosut et al. [R. Kosut, I. Walmsley, and H. Rabitz, e-print arXiv:quant- ph/0411093 (2004)]. Here we provide efficient numerical algorithms for finding the optimal design, and analytic results for the case of 'minimal tomography'. We also introduce the average OED, which is independent of the state to be reconstructed, and the optimal design for tomography (ODT), which minimizes tomographic bias. Monte Carlo simulations confirm the utility of our results for qubits. Finally, we adapt our approach to deal with constrained techniques such as maximum-likelihood estimation. We find that these are less amenable to optimization than cruder reconstruction methods, such as linear inversion.

Jaroslav Rehácek (Palacky University) - Tuesday 4:05pm
A little bit different quantum state tomography

Any quantum tomography scheme combines prior information about the measured system and apparatus with the results of the measurement. Here we show how to play around with these issues. While the standard tomography requires perfect knowledge about the measurement apparatus and a choice of a finite reconstruction subspace, the proposed data pattern tomography allows us to release some of these conditions.

Guided by optical analogies, tomography can be done even without precise knowledge of the measurement, in a way resembling the classical image processing, when recorded response to a sufficiently rich family of reference states provides quantum mechanical analog of the optical response function. This will be suggested as a toolbox for time multiplexed detection devices. Besides this, quantum homodyne tomography will be revisited from the point of view of informational completeness and all this will provide an interesting link between the tomography of discrete and continuous variable systems.

Barry C Sanders (University of Calgary) - Thursday 9:00am
Artificial-Intelligence Reinforcement Learning for Quantum Metrology with Adaptive Measurements

Quantum metrology aims for measurements of quantum channel (or process) parameters that are more precise than allowed by classical partition noise (shot noise) given a fixed number of input particles. Specifically the imprecision of the process-parameter estimate scales inversely with the square root of the number of particles in the classical domain and up to inverse-linear in the number of particles in the quantum domain by exploiting entanglement between particles. Quantum adaptive-measurement schemes employ entangled-particle inputs and sequential measurements of output particles with feedback control on the channel in order to maximize the knowledge gain from the subsequent particles being sequentially processed. Quantum-adaptive approaches have the advantage that input states are expected to be easier to make experimentally than for non-adaptive schemes.

We are interested in devising input states and adaptive feedback control on the processes to beat the standard quantum-measurement limit in real-world scenarios with noise, decoherence and particle losses. As such procedures are difficult to find even in ideal cases, the usual method of clever guessing is inadequate for this purpose. Instead we employ artificial-intelligence machine learning to find adaptive-measurement procedures that beat the standard quantum limit. I will discuss our approaches using reinforcement learning and evolutionary computation to finding procedures for adaptive interferometric phase estimation and show that machine learning has enabled us to find procedures in the ideal case that outperform previously known best cases in the ideal noiseless, decoherence-free, lossless scenario as well as easily devising robust procedures for noisy, decoherent, lossy scenario.

Marcus Silva (Raytheon BBN Technologies) - Friday 9:35am
Process tomography without preparation and measurement errors

Randomized benchmarking (RB) can be used to estimate the fidelity to Clifford group operations in a manner that is robust against preparation and measurement errors --- thus allowing for a more accurate quantification of the error compared to standard quantum process tomography protocols. In this talk we will show how to combine multiple RB experiments to reconstruct the unital part of any trace preserving quantum process, while maintaining robustness against preparation and measurement errors. This enables, in particular, the reconstruction of any unitary or random unitary (e.g. dephasing) error, and the quantification of the fidelity to any unitary operation.
Authors: Marcus P. da Silva (1), Shelby Kimmel (2), Colm A. Ryan (1), Blake Johnson (1), Thomas Ohki (1)
(1) Quantum Information Processing Group, Raytheon BBN Technologies, Cambridge, MA, USA
(2) Center for Theoretical Physics, MIT, Cambridge, MA

Denis Sych (Max-Planck Institute for the Science of Light) - Friday 11:35am
Informational completeness of continuous-variable measurements

Measurement lies at the very heart of quantum information. A set of measurements whose outcome probabilities are sufficient to determine an arbitrary quantum state is called informationally complete, while the process of reconstructing the state itself is broadly called quantum tomography. In our work, we consider continuous-variable measurements and prove that homodyne tomography turns out to be informationally complete when the number of independent quadrature measurements is equal to dimensionality of a density matrix in the Fock representation. Using this as our thread, we examine the completeness of other schemes, when the continuous-variable observations are truncated to discrete finite-dimensional subspaces.
Joint work with J. Rehácek, Z. Hradil, G. Leuchs, and L. L. Sánchez-Soto

Geza Toth (University of the Basque Country UPV/EHU) - Friday 2:35pm
Permutationally Invariant Quantum Tomography and State Reconstruction

We present a scalable method for the tomography of large multiqubit quantum registers. It acquires information about the permutationally invariant part of the density operator, which is a good approximation to the true state in many, relevant cases. Our method gives the best measurement strategy to minimize the experimental effort as well as the uncertainties of the reconstructed density matrix. We apply our method to the experimental tomography of a photonic four-qubit symmetric Dicke state. We also discuss how to obtain a physical density matrix in a scalable way based on maximum likelihood and least mean square fitting.

Peter S Turner (University of Tokyo) - Monday 11:00am
t-designs in quantum optics

This talk is meant to be a brief review of the concept of t-designs, with applications in quantum information theory, particularly in the realm of quantum optics. I will discuss both vector ("state") and matrix ("unitary") t-designs, and try to give some feeling for why they are interesting both mathematically and physically. I will then summarize some recent research regarding the surprising non-existence of Gaussian vector 2-designs, with implications for continuous variable tomography, as well as outline current work aimed at implementing matrix designs in photonic circuits in collaboration with experimentalists.

Guoyong Xiang (University of Science and Technology of China) - Wednesday 11:35am
Experimental verification of an entangled state with finite data

Entanglement is the irreplaceable resource to the quantum information science and because of the superposition property, quantum states are highly complex and difficult to identify. How to verify the entanglement of a quantum state has always been attracted significant attention. several methods have been developed for verifying entanglement. Recently, more and more particles entangled states have been prepared on a wide variety of physical systems, but, most of time, we have only finite copies of the state we want to know. And the above methods can only give a probabilistic conclusions with the finite copies. People have tried to reduce the measurements and improve the precision. But the problem still has not been solved fundamentally. So we need to consider how good we can verify the entanglement of a quantum state with finite copies.
Blume-Kohout and coauthors recently proposed a method to give the confidence of verifying entanglement with finite data[1]. They propose a reliable method to quantify the weight of evidence for (or against) entanglement, based on a likelihood ratio test. In this work, we inplement a experiment to demonstrate that the entangled states can be distinguished easier with concurrence increased and the states on the boundary between entangled sates and seperated states are hard to be distinguished. Then we use the likelihood ratio to give the quantity of the entanglement of a quantum state and the confidence are increased as data increased as shown in experiment.

[1] R. Blume-Kohout, J. O. S. Yin, and S. J. van Enk, Phys. Rev. Lett. 105, 170501 (2010)

Karol Zyczkowski (Jagiellonian University) - Wednesday 4:05pm
Measurements on random states and numerical shadow

Reconstructing quantum states from data measured one usually assumes that the measurement procedure is optimized. Here we analyze the complementary problem of interpretation of data obtained from 'measurements on random samples'. We assume that the observable A is given, while the input states of dimension N are distributed uniformly with respect to the natural, unitary invariant, Fubini--Study measure. We show a link of the possible outcome of a measurement of A in k copies of the same random pure state with the mathematical notion of the numerical range of A. Repeating such a measurement for several samples of random states leads to the probability distribution P(x), which coincides with the numerical shadow of the observable A. We show in particular, that for any observable A acting on a single qubit, N=2, the distribution P(x) is constant in a certain interval. For higher dimensions the distributions obtained can be interpreted as projections of the set of pure quantum states on a line. In the case of coincidence measurement of any two observables, A_1 and A_2, one arrives at distributions equivalent to the shadow of the set of quantum states projected onto a plane.
A joint work with Piotr Gawron, Jaroslaw Miszczak and Zbigniew Puchala (Gliwice, Poland)

Poster Abstracts

Full Name University Name Poster Abstract
Gittsovich, Oleg
Institute for Quantum Computing
University of Waterloo,
Reliable Entanglement Verification
Any experiment attempting to verify the presence of entanglement in a physical system can only generate a finite amount of data. The statement that entanglement was present in the system can thus never be issued with certainty, requiring instead a statistical analysis of the data. Because entanglement plays a central role in the performance of quantum devices, it is crucial to make statistical claims in entanglement verification experiments that are reliable and have a clear interpretation. In this work, we apply recent results by M. Christandl and R. Renner to construct a reliable entanglement verification procedure based on the concept of confidence regions. The statements made do not require the specification of a prior distribution, the assumption of independent measurements nor the assumption of an independent and identically distributed (i.i.d.) source of states. Moreover, we develop numerical tools that are necessary to employ this approach in practice, rendering the procedure ready to be applied to current experiments. We demonstrate this technique by analyzing the data of a photonic experiment generating two-photon states whose entanglement is verified with the use of an accessible nonlinear witness.
Godoy, Sergio Pontificia Universidad Catolica de Chile Local sampling of phase space by unbalanced optical homodyning
Authors: S. Godoy, S. Wallentowitz, B. Seifert
Goyeneche, Dardo Center for Optics and Photonics Efficient tomography for pure quantum states
Hou, Zhibo Key Laboratory of Quantum Information
Quantum State Reconstruction via Linear Model Theory
Johnston, Nathaniel University of Waterloo Uniqueness of Quantum States Compatible with Given Measurement Results

Kimmel, Shelby &
da Silva, Marcus P.

Massachusetts Institute of Technology Robust Randomized Benchmarking Beyond Cliffords

Kueng, R. &
Gross, D.

University of Freiburg Qubit Stobilizer States are Complex Projective 3-design
Magesan, Easwar Massacusetts Institute of Technology Efficient Measurement of Gate Error by Interleaved Randomized Benchmarking
Mahler, Dylan University of Toronto Experimental Demonstration of Adaptive Tomography
Quesada, Nicolás University of Toronto

Simultaneous State and Process Tomography of Qudits
by N. Quesada, A. M. Branczyk and D. F. V. James

Rapcan, Peter Institute of Physics, Slovak Academy of Sciences Direct Estimation of Decoherence Rates
(joint work/poster with Dr. Mario Ziman)
Salazar, Roberto University of Concepción Quantum Bayesianism for an infinite countable set of dimensions
Quantum Bayesianism is a novel mathematical formulation of quantum mechanics whose origin lies in optimal
tomographic schemes. Usually this formulation is implemented by changing Born´s rule by Bayesian modified
rule. Until now this have been done by the use of a special kind of POVM known as SIC-POVM. The main problem
of this formulation is that SIC-POVM´s existence in every finite dimension is still unknown but conjectured.
Here we show that a different set of POVM allows the replacement of Born rule by a Bayesian modified rule.
In particular we have shown that such POVM exist for a infinite countable set of finite dimensions.
Schwemmer, Christian Max-Planck-Institut für Quantenoptik Permutationally Invariant Tomography of Symmetric Dicke States
Sedlak, Michal Palacky University Discrimination of quantum measurements
Sugiyama, Takanori University of Tokyo Error analysis of maximum likelihood estimator in one-qubit state tomography with finite data
Tanaka, Fuyuhiko University of Tokyo Minimax estimation of density operators for general parametric models
Ziman, Mario Institute of Physics SAS Direct estimations of decoherence parameters


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