The $N$-qubit Dicke states $|D^N_k\rangle$, of Hamming-weight $k$, are a class of entangled states which play an important role in quantum algorithm optimization. We present a general calculation of entanglement entropy in Dicke states, which we use to describe the $|D^N_k\rangle$ entropy cone. We demonstrate that all $|D^N_k\rangle$ entropy vectors emerge symmetrized, and use this to define a min-cut protocol on star graphs which realizes $|D^N_k\rangle$ entropy vectors. We identify the stabilizer group for all $|D^N_k\rangle$, under the action of the $N$-qubit Pauli group and two-qubit Clifford group, which we use to construct $|D^N_k\rangle$ reachability graphs. We use these reachability graphs to analyze and bound the evolution of $|D^N_k\rangle$ entropy vectors in Clifford circuits.

The quantum entropy cones (QEC) for $W_N$ states of qubits and $W_N^d$ states of qudits are computed. These cones emerge as symmetrized quantum entropy cones (SQEC) for arbitrary $N$ and $d$. Directed graph models are presented which describe the SQEC for $W_N$ states and $W_N^d$ states. Monogamous mutual information (MMI) is violated for all $N>3$.

This project covered research in theoretical high energy physics at Brandeis University by PI Albion Lawrence and Co-PIs Matthew Headrick and Howard Schnitzer. The work of Albion Lawrence covered quantum field theoretic models of cosmic inflation and of quintessence-type dark energy, consistent with constraints on quantum gravity; the dynamics of open quantum systems, with an eye towards applications to holography; and the application of quantum information theory – particularly measures of quantum entanglement – to quantum field theories and quantum gravity. The work of Matthew Headrick covered the intersection of quantum information theory and quantum gravity, with a focus on the holographic encoding of quantum information theoretic concepts such as entanglement and computational complexity in field theory. Headrick also achieved significant technical results in closed string field theory. The work of Howard Schnitzer covered the computation of quantum information theoretic quantities in quantum field theories.

Graph states and hypergraph states can be constructed from products of basic operations that appear in SU(N)1. The level-rank dual of a theorem of Salton, Swingle, and Walter implies that these operations can be prepared topologically in the n-torus Hilbert space of Chern-Simons theory for N neq 5 mod 4. For SU(N)1, N = 5 mod 4, only stabilizer states can be prepared on the n-torus Hilbert space, which restricts the construction to graph states.

The level-rank duality of SU(2)k Chern-Simons theory is discussed, and applied to graph, hypergraph, and magic states.

A number of results for the level-rank duality of $G(N)_K$ $\leftrightarrow$ $G(K)_N$ Chern-Simons theory are summarized, with emphasis on the applications to knot and link invariants. Explicit examples for $SU(2)_K$ $\leftrightarrow$ $SU(K)_2$ illustrate general results. A criterion to distinguish torus knots and links from hyperbolic knots and links, based on tables constructed by Kaul for one and two strand invariants, is presented. Possible symmetries of hyperbolic knot and link invariants are discussed. The level-rank duality of torus knot and link invariants of minimal models is examined

Entropy cones for SU(N)1 Chern-Simons theory are discussed. It is shown that stabilizer states can be constructed from topological operators in SU(N)1 for N odd prime, but not for SU(N)K; K >= 2. This implies that the topological entropy cone is properly contained in the stabilizer entropy cone for SU(N)K; K >= 2.

Crucial experiments have a long history of contributions to progress in physics. Similarly, we claim that in the period roughly from 1955 to 1985 crucial calculations played a significant role in setting the agenda for elementary particle physics. The highlights of the contributions of theoretical physics to the achievement of the standard model is emphasized

Farinholt gives a characterization of Clifford operators for qudits; d both odd and even. In this comment it is shown that the necessary gates for the construction of Clifford operators; N both odd and even, are obtained directly from operations that appear in SU(N)1. A witness for W3 states in SU(2)1 is discussed. See e.g. [1-4].

A tree tensor network is proposed for the entanglement distillation of large N SU(N)1 Chern-Simons theory and Riemann surfaces, adopting a proposal of Bao, et al. This is illustrated for the entanglement entropy S(A) of a bipartite many-body system A, where here S(A) = log N.

The construction of generators of the Clifford group and of stabilizer states from Chern-Simons theory is presented for the Kac-Moody algebras SU(2)1, U(N)N,N(K+N) with N = 2 and K = 1, and SU(N)1 extending results of Salton, et. al.

It is shown, using level-rank duality that a universal topological quantum computer based on Chern-Simons theory for SU(2)$_3$ also implies an analogous universal quantum computer based on SU(3)$_2$. Suggestions are made for the possible role of level-rank duality in entanglement from topology.

We compute the three-loop contribution to theN = 4 supersymmetric Yang-Mills planar four-gluon amplitude using the recently-proposed Higgs IR regulator of Alday, Henn, Plefka, and Schuster. In particular, we test the proposed exponential ansatz for the four-gluon amplitude that is the analog of the BDS ansatz in dimensional regularization. By evaluating our results at a number of kinematic points, and also in several kinematic limits, we establish the validity of this ansatz at the three-loop level. We also examine the Regge limit of the planar four-gluon amplitude using several different IR regulators: dimensional regularization, Higgs regularization, and a cutoff regularization. In the latter two schemes, it is shown that the leading logarithmic (LL) behavior of the amplitudes, and therefore the lowest-order approximation to the gluon Regge trajectory, can be correctly obtained from the ladder approximation of the sum of diagrams. In dimensional regularization, on the other hand, there is no single dominant set of diagrams in the LL approximation. We also compute the NLL and NNLL behavior of the L-loop ladder diagram using Higgs regularization. Research supported in part by the NSF under grant PHY-0756518 Research supported in part by the DOE under grant DE–FG02–92ER40706 Research supported in part by the DOE under grant DE–DE-FG02-91ER40688 henn@physik.hu-berlin.de, naculich@bowdoin.edu, schnitzr@brandeis.edu, spradlin@het.brown.edu

We compute the next-to-leading order term in the long-distance expansion of the mutual information for free scalars in three space-time dimensions. The geometry considered is two disjoint disks separated by a distance r between their centers. No evidence for non-analyticity in the Rényi parameter n for the continuation n → 1 in the next-to-leading order term is found.

Rényi and entanglement entropies are constructed for 2d q-deformed topological Yang-Mills theories with gauge group U(N), as well as the dual 3d Chern-Simons (CS) theory on Seifert manifolds. When q=exp[2π i/(N+K)], and K is odd, the topological Rényi entropy and Wilson line observables of the CS theory can be expressed in terms of the modular transformation matrices of the WZW theory, Û(N)_K,N(K+N). If both K and N are odd, there is a level-rank duality of the 2d qYM theory and of the associated CS theory, as well as that of the Rényi and entanglement entropies, and Wilson line observables.

The Rényi entropy for the SU(N)_1 WZW model as described by N free fermions coupled to a U(1) constraint field is computed on an n-sheeted branched torus. The boundary condition of the harmonic component of the gauge field on the homology cycles of the genus g Riemann surface is central to the final result. This calculation is complementary to that of arXiv:1510.05993, which presents the bose side of the bose-fermi equivalence.

The 1 WZW model is constructed on a n-sheeted branched torus, which allows the investigation of the Rényi entropy for a single interval at finite temperature. The small and large interval limits, as well as the low temperature expansion are presented for this theory.

We consider the left-right entanglement (LREE) entropy in 1+1 dimen- sions for WZW models on a circle, and for WZW models on untwisted and twisted D-branes. The consequences of level-rank duality for these applications is presented which provides a map of LREE from large to small central charge.

The holographic mutual information for the small separation of two circles and two strips in 2+1 dimensional space-time is considered based on the known exact minimal surfaces spanning the boundaries on AdS4. The results suggest a universality for the leading term in the short-distance expansion of holographic mutual information. A conjecture for a similar result for d > 2 is also presented, as well as comments about the analogous expansion in conformal field theory.

We examine the high energy (Regge) limit of gravitational scattering using a Wilson line approach previously used in the context of non-Abelian gauge theories. Our aim is to clarify the nature of the Reggeization of the graviton and the interplay between this Reggeization and the so-called eikonal phase which determines the spectrum of gravitational bound states. Furthermore, we discuss finite corrections to this picture. Our results are of relevance to various supergravity theories, and also help to clarify the relationship between gauge and gravity theories.