Quantum Physics

When a particle is accelerated, as in a scattering event, it will radiate gravitons and, if electrically charged, photons. The infrared tail of the spectrum of this radiation has a divergence: an arbitrarily small amount of total energy is divided into an arbitrarily large number of radiated bosons. Each of these in turn carries a momentum and a helicity degree of freedom, and thus this radiation carries significant amounts of quantum information. I will demonstrate that the infrared bosonic radiation causes nearly complete decoherence of the final state of the hard particles into the momentum basis. When applied to radiation coming from the incoming state, it appears that the entire dynamical history of the process will be distinguishable by the radiation, thus causing a loss of any interference effects between branches of an incoming momentum superposition, such as in a wavepacket. I will explain how infrared dressed states, in the framework of Fadeev and Kulish, evade this issue. Finally, I'll conclude with some remarks on the potential relevance of these issues to black hole information loss

[joint work with: Victor Albert, John Preskill (Caltech), Sepehr Nezami, Grant Salton, Patrick Hayden (Stanford University), and Fernando Pastawski (Freie Universität Berlin)]

Quantum error correction and symmetries are concepts that are relevant in many physical systems, such as in condensed matter physics and in holographic quantum gravity, and play a central role in error correction of reference frames [Hayden et al., arXiv:1709.04471]. I will show that codes that are covariant with respect to a continuous local symmetry necessarily have a limit to their ability to serve as approximate error-correcting codes against erasures at known locations. This is because the environment necessarily gets information about the global logical charge of the encoded state due to the covariance of the code. Our bound vanishes either in the limit of large individual subsystems, or in the limit of a large number of subsystems; in either case there exist codes which approximately achieve the scaling of our bound and become good covariant error-correcting codes. Our results can be interpreted as an approximate version of the Eastin-Knill theorem, quantifying to which extent it is not possible to carry out universal computation approximately on encoded states. In the context of holographic AdS/CFT, our approach provides some insight on time evolution in the bulk versus time evolution on the boundary. We expect further implications for symmetries in holography and in condensed matter physics.

Suppose the eigenvalue distributions of two matrices $M_1$ and $M_2$ are known. What is the eigenvalue distribution of the sum $M_1+M_2$? This problem has a rich pure mathematics history dating back to H. Weyl (1912) with many applications in various fields. Free probability theory (FPT) answers this question under certain conditions, which often involves some degree of randomness (disorder). We will describe FPT and show examples of its powers for the qualitative understanding (often approximations) of physical quantities such as density of states, and gapped vs. gapless phases of some Floquet systems. These physical quantities are often hard to compute exactly. Nevertheless, using FPT and other ideas from random matrix theory excellent approximations can be obtained. Besides the applications presented, we believe the techniques will find new applications in new contexts.

There has been a dissatisfaction with the postulates of quantum mechanics essentially since the moment that those postulates were first written down. Over the years since there have therefore been many attempts (some successful and some less so) to reconstruct quantum theory from various sets of postulates. The aim being to gain a deeper understanding of the theory by providing a conceptually clear underpinning from which the standard formalism can be derived. In this talk I present recent work with Carlo Maria Scandolo and Bob Coecke (arXiv:1802.00367) in which we reconstruct quantum theory from purely diagrammatic postulates within the process theory framework, showing that the conceptual bare-bones of quantum theory concerns the manner in which systems and processes compose.

When a system interacts with an environment with which it is initially uncorrelated, its evolution is described by a completely positive map.  The common wisdom in the field of quantum information theory, however, is that when the system is initially correlated with the environment, the map describing its evolution may fail to be completely positive. This has motivated many researchers to try and characterize this putatively more general sort of dynamics, and even the textbook of Nielsen and Chuang suggests that "It is an interesting problem for further research to study quantum information processing beyond the quantum operations formalism."  This talk will demonstrate that this common wisdom is mistaken.  The error can be traced to the standard argument for how the evolution map ought to be defined in such circumstances.  One can show that anomolous dynamics would arise even in completely classical examples if one were to follow the prescription of the standard argument.  The framework of classical causal models specifies how dynamics ought to be defined in such circumstances, and

the quantum analogue of this framework provides the correct definition of the quantum evolution map, which is found to be always completely positive.

Joint work with David Schmid

In order to think about the foundations of physics it is important to understand the logical relationships among the physical principles that sustain the building. As part of these axioms of physics there is the core hypothesis that, how the Universe is partitioned into systems and subsystems is a subjective choice of the observer that should not affect the predictions of physics. Other foundational principles are the Postulates of Quantum Mechanics. However, we prove that these are not independent from the “independence of subsystem partitioning” hypothesis described above. In particular, we prove that the mathematical structure of quantum measurements and the formula for assigning outcome probabilities are implied by the mentioned hypothesis and the rest of quantum postulates. 

Port-based teleportation (PBT) is a variant of the well-known task of quantum teleportation in which Alice and Bob share multiple entangled states called "ports". While in the standard teleportation protocol using a single entangled state the receiver Bob has to apply a non-trivial correction unitary, in PBT he merely has to pick up the right quantum system at a port specified by the classical message he received from Alice. PBT has applications in instantaneous non-local computation and can be used to attack position-based quantum cryptography. Since perfect PBT protocols are impossible, there is a trade-off between error and entanglement consumption (or the number of ports), which can be analyzed using representation theory of the symmetric and unitary groups. In particular, without loss of generality the resource state can be assumed to have a “purified" Schur-Weyl duality symmetry. I will give an introduction to the task of PBT and its symmetries, and show how the asymptotics of existing formulas for the optimal performance for a given number of ports can be derived using a connection between representation theory and the Gaussian unitary ensemble.

Joint work with M. Christandl, C. Majenz, G. Smith, F. Speelman & M. Walter

Several equivalent formulations of quantum error correction condition will be introduced. Subtleties arise

when the error correction conditions hold only approximately. We will discuss an equivalent formulation that is 

robust to the approximation error. One can leverage this tool to derive the existence of approximate quantum

error correcting code at low energy subspace of CFT that reproduces aspects of the holographic quantum error

correcting code. Using the same tool, we observe that two operators with greatly differing complexity approximately

commute in an appropriate code subspace. This leads to a notion of bulk locality in the entanglement shadow,

but the precise definition of complexity seems to play an important role in determining how well these operators commute

in the subspace.

Randomness is an essential tool in many disciplines of modern sciences, such as cryptography, black hole physics, random matrix theory, and Monte Carlo sampling. In quantum systems, random operations can be obtained via random circuits thanks to so-called q-designs and play a central role in condensed-matter physics and in the fast scrambling conjecture for black holes. Here, we consider a more physically motivated way of generating random evolutions by exploiting the many-body dynamics of a quantum system driven with stochastic external pulses. We combine techniques from quantum control, open quantum systems, and exactly solvable models (via the Bethe ansatz) to generate Haar-uniform random operations in driven many-body systems. We show that any fully controllable system converges to a unitary q-design in the long-time limit. Moreover, we study the convergence time of a driven spin chain by mapping its random evolution into a semigroup with an integrable Liouvillian and finding its gap. Remarkably, we find via Bethe-ansatz techniques that the gap is independent of q. We use mean-field techniques to argue that this property may be typical for other controllable systems, although we explicitly construct counterexamples via symmetry-breaking arguments to show that this is not always the case. Our findings open up new physical methods to transform classical randomness into quantum randomness, via a combination of quantum many-body dynamics and random driving.

Reference: L. Banchi, D. Burgarth, M. J. Kastoryano, Phys. Rev. X 7, 041015 (2017)

In quantum Shannon theory, the way information is encoded and decoded takes advantage of the laws of quantum mechanics, while the way communication channels are interlinked is assumed to be classical. In this talk, I will relax the assumption that quantum channels are combined classically, and I will show that, in certain situations, combining quantum channels in an indefinite causal order allows us to achieve tasks that are impossible in conventional quantum Shannon theory. Specifically, I will show a phenomenon of causal activation, whereby two identical copies of a completely depolarizing channel become able to transmit information when they are combined in a quantum superposition of two alternative orders. This finding runs counter to the intuition that if two communication channels are identical, using them in different orders should not make any difference.

In this talk, I will discuss two important cryptographic tasks in a post-quantum world. I will discuss the impossibility of bit-commitment and the possibility of physically unforgeable money in the framework of Generalized Probabilistic Theories. Our proofs rely crucially on cone programming, a natural generalization of semidefinite programming. This is based on work with John Selby, arXiv:1803.10279 and arXiv:1711.02662.