Quantum Information

Is there a theory yet to be discovered that underlies quantum theory and explains its structure? If there is such a theory, one of the features it will have to explain is the central role of complex numbers as probability amplitudes. In this talk I explore the physical meaning of the statement “probability amplitudes are complex” by comparing ordinary complex-vector- space quantum theory with the real-vector-space theory having the same basic structure. Specifically, I discuss three questions that bring out qualitative differences between the two theories: (i) Is information about a preparation expressed optimally in the outcomes of a measurement? (ii) Are multipartite states locally accessible? (iii) Is entanglement “monogamous”?

A recent breakthrough in quantum computing has been the realization that quantum computation can proceed solely through single-qubit measurements on an appropriate quantum state. One exciting prospect is that the ground or low-temperature thermal state of an interacting quantum many-body system can serve as such a resource state for quantum computation. The system would simply need to be cooled sufficiently and then subjected to local measurements. It would be unfortunate, however, if the usefulness of a ground or low-temperature thermal state for quantum computation was critically dependent on the details of the system's Hamiltonian; if so, engineering such systems would be difficult or even impossible. A much more powerful result would be the existence of a robust ordered phase which is characterized by the ability to perform measurement-based quantum computation. I’ll discuss some recent results on the existence of such a computational phase of matter. I’ll first outline some positive results on a phase of a toy model that contains the cluster state. Then, in a realistic model of coupled spin-1 particles, I’ll demonstrate the existence of a computational phase. This result is obtained by using a local measurement sequence to “renormalize” the state to a computationally-universal fixed point. Together, these results reveal that the characterization of computational phases of matter has a rich, complex structure – one which is still poorly understood. Joint work with Gavin Brennen, Akimasa Miyake, and Joseph Renes.

The mysteries of quantum theory run deep. Despite 80 years of research, there is still no consensus on its interpretation. This talk will explore some of the important issues in the foundations of quantum theory, from the idea that we have only a limited knowledge of a deeper reality, like the prisoner in Plato’s cave who sees only the shadows of objects and never the objects themselves, to John Bell’s famous discovery of the difference between quantum correlations and Dr. Bertlmann’s socks, namely, that whereas the mismatched colours of the doctor’s socks can be attributed to a decision at the sock drawer that morning, certain quantum correlations cannot be explained by a common cause, at least not without doing violence to some cherished principles of physics, such as the fact that causes cannot travel faster than the speed of light.

This panel will explore some of the deepest questions facing those who would harness the power of quantum mechanics in new quantum technologies: What are the newest and most interesting discoveries researchers have made about quantum information? What progress has been made in recent years towards experimentally harnessing quantum devices for quantum computation? What are the main motivations for building quantum information processing technologies? Drs. Aharonov and Shor appear courtesy of Institute for Quantum Computing.

Quantum computers hold the promise to revolutionize the way we secure information, compute and understand the quantum world. Although general-purpose quantum computers appear to be a long way off, we do have good test-beds of small quantum processors. One of the most versatile quantum test-beds is nuclear magnetic resonance (NMR): a version of which is familiar to many in the guise of the medical imaging modality, MRI. In fact NMR has broad importance to society: it is used in drug discovery, in oil exploration and to monitor the processing of cheese and chocolate. We will introduce NMR, show how it helps us understand quantum computing and we will look at how concepts based on quantum computing can improve NMR applications.

Adiabatic quantum optimization has attracted a lot of attention because small scale simulations gave hope that it would allow to solve NP-complete problems efficiently. Later, negative results proved the existence of specifically designed hard instances where adiabatic optimization requires exponential time. In spite of this, there was still hope that this would not happen for random instances of NP-complete problems. This is an important issue since random instances are a good model for hard instances that can not be solved by current classical solvers, for which an efficient quantum algorithm would therefore be desirable. Here, we will show that because of a phenomenon similar to Anderson localization, an exponentially small eigenvalue gap appears in the spectrum of the adiabatic Hamiltonian for large random instances, very close to the end of the algorithm. This implies that unfortunately, adiabatic quantum optimization also fails for these instances by getting stuck in a local minimum, unless the computation is exponentially long. Joint work with Boris Altshuler and Hari Krovi

Applications of the quantum nature of our universe to potential new technologies like quantum cryptography and quantum computation. In particular, theoretical developments such as fault-tolerant quantum codes and protocols for quantum error correction.

Applications of quantum theory to cryptography and computation; understanding in more concrete, physical terms what quantum theory is telling us about the nature of reality. Applications of information theory to better understand the quantum “wave function”.

At NIST we are engaged in an experiment whose goal is to create superpositions of optical coherent states (such superpositions are sometimes called "Schroedinger cat" states). We use homodyne detection to measure the light, and we apply maximum likelihood quantum state tomography to the homodyne data to estimate the state that we have created. To assist in this analysis we have made a few improvements to quantum state tomography: we have devised a new iterative method (that has faster convergence than R*\rho*R iterations) to find the maximum likelihood state, we have formulated a stopping criterion that can upper-bound the actual maximum likelihood, and we have implemented a bias-corrected resampling strategy to estimate confidence intervals.

Information has always been valuable, never more so than in recent decades, and throughout history people have turned to cryptography in an attempt to keep important information secret. New technologies are now emerging based on the counterintuitive laws of quantum physics that govern the atomic scale. These technologies threaten cryptographic methods which are in widespread use today, but offer new quantum cryptographic protocols which could profoundly alter the world of cryptography.