Waterloo professor Michele Mosca shares best practices for using quantum to safeguard important data.
A multivariate polynomial is said to be positive if it takes only non-negative values over reals. Hilbert's 17th problem concerns whether every positive polynomial can be expressed as a sum of squares of other polynomials. In general, we say a noncommutative polynomial is positive (resp. matrix positive) if plugging operators (resp. matrices) always yields a positive operator. Many problems in math and computer science are closely connected to deciding whether a given polynomial is positive and finding certificates (e.g., sum-of-squares) of positivity.
In the study of nonlocal games in quantum information, we are interested in tensor product of free algebras. Such an algebra models a physical system with two spatially separated subsystems, where in each subsystem we can make different quantum measurements. The recent and remarkable MIP*=RE result shows that it is undecidable to determine whether a polynomial in a tensor product of free algebras is matrix positive. In this talk, I'll present joint work with Arthur Mehta and William Slofstra, in which we show that it is undecidable to determine positivity in tensor product of free algebras. As a consequence, there is no sum-of-square certificate for positivity in such algebras.
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Abstract: Quantum dot-based entangled photon sources are promising candidates for quantum key distribution (QKD), as they can in principle emit deterministically, with high brightness and low multiphoton contribution. However, quantum dots (QD) often inherently possess a fine structure splitting (FSS). Since the entangled photonic state in the presence of non-zero FSS is oscillating, one must settle for a lower efficiency source through temporal post-selection or a lower measured entanglement fidelity. In both cases, the overall key rate is reduced. Our QKD analysis shows that this trade-off can be overcome by constructing a time-resolved QKD protocol where all photon pairs emitted by a QD with non-zero FSS can be used in secret key generation. This protocol works only when the detection system's temporal resolution is much smaller than the FSS period. By implementing our protocol, higher key rates can be achieved as compared to previous QKD experiments with QD entangled photon pair sources.
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Machine learning is a powerful tool, yet we often do not know how well a learning algorithm might perform on any given task. One standard approach to bound the accuracy of a learning algorithm is to reduce the learning task to hypothesis testing. Fano's inequality then states that a large amount of mutual information between the learner's observations and the set of unknown parameters is a necessary condition for success.
In this talk, I will describe how such a condition is also sufficient for succeeding at some learning task, thereby providing a purely information-theoretic guarantee for learning. Noting that this guarantee has an immediate extension to quantum information theory, I will then introduce the task of "testing quantum hypotheses", in which the unknown parameters of the learning task are prepared in a quantum register in superposition (rather than being sampled stochastically) and the learner's success at this task is measured by their ability to establish quantum correlations with that register. I will discuss ongoing attempts to characterize this scenario.
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While universal quantum computers are still years away from being used for simulating complicated quantum systems, analog quantum simulators have become an increasingly attractive approach to studying classically intractable quantum systems in condensed matter physics, chemistry, and high-energy physics.
I will discuss our recent work on finding lower bounds to solve three problems in Quantum Learning Theory: Quantum PAC learning, Quantum Agnostic Learning and Quantum Coupon Collector. Our main goal was to use tools from Quantum Information Theory, specifically the data processing inequality, to obtain these results, instead of going for more exotic ones. We succeed in doing so for the first two problems, and we show concretely that it doesn't work for the last problem, due to an inherent loss of information that is possible even for valid learning algorithms, for which we give a bound using an alternate method that utilizes the analysis we went through previously. We hope that these tools are broadly applicable to other quantum learning problems.
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Classical drives on a qudit have been extensively used to create, control and read out quantum states. We consider a qudit-oscillator system where the qudit is continuously driven. We show that strong driving allows for qudit-conditional operations on the oscillator such as displacement, squeezing and higher order effects. We discuss the case of a driven qubit with linear or quadratic coupling to the oscillator, and we generalize the scheme to multi-qubit and qudit (d>2) systems. We discuss the use of driven qudit-oscillator systems for encoding and performing operations on bosonic codes.
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Today, we’re celebrating some of the female-identifying engineers in our community by showcasing their remarkable achievements, experiences, and valuable guidance for those aspiring to help build a brighter future.
This talk will investigate the possibility of a Markovian quantum master equation (QME) that consistently describes a finite-dimensional system, a part of which is weakly coupled to a thermal bath. For physical consistency, we will demand that the QME should preserve local conservation laws and be able to show thermalization. After providing some background on QMEs, I will present our three main results:
Taken together, our results indicate that the possibility of a Markovian QME with the desired properties must be taken on a case-by-case basis, since there are setups where such a QME is impossible.
This talk is based on https://arxiv.org/abs/2301.02146.
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Ultra-cold atoms have been used to simulate phenomena in condensed matter physics as well as in cosmology such as black holes. In this talk, we will give an overview of the field of ultra-cold atoms by discussing the physics behind the cooling and the manipulation of these atoms. Aimed to show the beautiful physics behind this process, this talk will be easy and general, requiring just an undergraduate level of physics understanding.
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