Scientific Series

The theory of alphabits is a natural generalisation of approximate quantum error correction that proves fundamental to the study of asymptotic quantum resources. In particular, it leads to an asymptotically reversible variation on quantum teleportation, called zerobit teleportation, which decomposes qubits of communication into correlation and transmission components. They also naturally arise in the study of black holes with significant consequences for the nature of quantum error correction in AdS/CFT.

After reviewing the three things in the title I will argue that they represent the same physical phenomenon. In details, Jackiw–Teitelboim (JT) gravity coupled to an arbitrary quantum field theory results in a gravitational dressing of field theoretical scattering amplitudes. The exact expression for the dressed S-matrix was previously known as a solvable example of a novel UV asymptotic behavior, dubbed asymptotic fragility. This dressing is equivalent to the T\barT deformation of the initial quantum field theory compactified on a circle. The same dressed S-matrix is also obtained as a flat space limit of the near AdS2 holography based on (JT) gravity. In order to preserve the flat space unitarity, however, the conventional Schwarzian dressing of boundary correlators needs to be slightly extended. As an intermediate result I will present a new simple expression for flat space amplitudes of massive particles in terms of correlators of holographic CFT’s. 

Primordial black holes (PBHs) can appear from early Universe dynamics. We show that some or all of heavy element abundance from r-process nucleosynthesis can be produced in interactions of tiny primordial black holes with neutron stars (NSs), if PBHs make up a few percent or more of the dark matter. A PBH captured by a NS will eventually consume it. For a rapidly rotating pulsar, the resulting star spin-up will eject significant amount of cold neutron rich material. The ejection, decompression and decay of nuclear matter can produce electromagnetic transients, like kilonovae and fast radio bursts. Beta decay of ejected material yields positron emission consistent with the observed 511 keV-line from the Galactic Center. Lack of accompanying gravity wave (GW) signal and neutrino emission allows to distinguish these events from supernovae and compact object mergers. Finally, if the consumed star was part of a binary system, long after the event a distinct detectable GW signal from the binary merger with an atypically small solar mass BH will carry information about star's destruction.

We construct a hidden variable model for the EPR correlations using a Restricted Boltzmann Machine. The model reproduces the expected correlations and thus violates the Bell inequality, as required by Bell's theorem. Unlike most hidden-variable models, this model does not violate the locality assumption in Bell's argument. Rather, it violates measurement independence, albeit in a decidedly non-conspiratorial way.

In quantum theory, there can exist correlations between subsystems of a new kind that are absent in classical systems. These correlations are nowadays called "entanglement".

An entanglement measure is a functional on states quantifying the amount of entanglement across two subsystems (i.e. causally disjoint regions in the context of quantum field theory). A reasonable measure should satisfy certain general properties: for example, it should assign zero entanglement to separable states, and be monotonic under separable, completely positive maps ("LOCC-operations"). The v. Neumann entropy of the "reduced state" (to one of the subsystems) is one such measure if the state for the total system is pure. But for mixed states, it is not, and one has to consider other measures. In particular, one has to consider other measures if the subsystems have a finite non-zero distance.

In this talk I will present several good measures, and in particular analyze the « relative entanglement entropy", $E_R$, defined as the "distance" of the given state to the set of separable states, where "distance" is defined using Araki's relative entropy. I will show several features of this measure for instance: (i) charged states, where the relative entanglement entropy is related to the quantum dimension of the charge, (ii) vacuum states in 1+1 dimensional integrable models, (iii) general upper bounds for certain special regions in general CFTs in d dimensions, (iv) area law type bounds. I will also explain the relationship between $E_R$ and other entanglement measures, such as distillable entropy.

[Based on joint work with Jacobus Sanders.]

Universality classes of inflation as phases of condensed matter: slow-roll, solids, gaugids etc.
Abstract: Cosmology and condensed matter systems share the same basic symmetries: both are characterised by a (spontaneous) breaking of Lorentz boosts and by approximate translation and rotation invariances. It is therefore not completely surprising that the basic mechanisms for cosmic acceleration be in one to one correspondence with different condensed matter realisations. This point of view has recently unveiled inflationary models well beyond single-field inflation. The different inequivalent ways in which translation and rotation invariance can be recovered at low energy lead to different "universality classes” for cosmic acceleration. Among those, solid inflation and the recently proposed gaugid inflation have substantially different properties than those of single-field slow-roll scenarios.

A burst of gravitational radiation passing through an arrangement of freely falling test masses far from the source will cause a permanent displacement of the masses, called the ''gravitational memory''. It has recently been found that this memory is closely related to the change in the so called ''super-translation'' charge carried by the spacetime, where ''super-translations'' here refer to an unexpected enlargement of the asymptotic symmetries of general relativity beyond the expected asymptotic Poincare-transformations, known already since the work of Bondi et al. in the early 60s (no relation with ‘’supersymmetry''). I will describe these concepts from an intuitive perspective and point out that super-translations, as well as gravitational memory, are a phenomenon that is unique to relativity in 3+1, but not higher, dimensions. I close the talk by explaining the relation between these results and the notion of a ''charge super-selection sector'' in quantum field theories with massless particles such as QED.

[Based on joint work with A. Ishibashi and R. M. Wald]

Quantum complexity is conjectured to probe inside of black hole horizons (or wormhole) via gauge gravity correspondence. In order to have a better understanding of this correspondence, we study time evolutions of complexities for generic Abelian pure gauge theories. For this purpose, we discretize U(1) gauge group as Z_N and also continuum spacetime as lattice spacetime, and this enables us to define a universal gate set for these gauge theories, and evaluate time evolutions of the complexities explicitly. We find that to achieve a large complexity ∼exp(entropy), which is one of the conjectured criteria necessary to have a dual  black hole, the Abelian gauge theory needs to be maximally nonlocal. (Based on collaboration with Norihiro Iizuka and Sotaro Sugishita, https://arxiv.org/abs/1707.03840)

In models of inflation driven by an axion-like pseudoscalar field, the inflaton, a, may couple to the standard model hypercharge gauge field via a Chern-Simons-type interaction, L ⊃ a F F̃. This coupling results in the explosive production of hypermagnetic fields during inflation, which has two interesting consequences: (1) The primordial hypermagnetic field is maximally helical. It is therefore capable of sourcing the generation of nonzero baryon number around the electroweak phase transition (via the chiral anomaly in the standard model). (2) The gauge field production during inflation feeds back into the stochastic background of gravitational waves (GWs). In this talk, I am going to discuss the correlation between these two phenomena. To this end, I will (a) present an updated study of baryogenesis via hypermagnetic fields after pseudoscalar inflation and (b) describe the corresponding implications for GWs. As it turns out, successful baryogenesis is feasible---provided the axion coupling to the gauge fields is suppressed by a decay constant \Lambda ~ 3 x 10^17 GeV. Moreover, in the case of successful baryogenesis, one expects a characteristic peak in the GW spectrum at frequencies in the MHz range

Transversality is one of the most desirable features of fault-tolerant circuits because it automatically limits the propagation of errors. However, it was shown by Eastin & Knill that no universal set of quantum gates on any quantum code is transversal. In this talk, we strengthen this result for stabilizer codes to say that transversal gates must in fact be contained in the Clifford hierarchy. Moreover, we present new circuits on Bacon-Shor codes that saturate our bounds. In particular, we show how a k-qubit controlled-Z gate can be implemented by a transversal circuit on m-by-m^k Bacon-Shor codes and provide some estimates of its performance in terms of pseudo-thresholds and resource overhead.