## Program

#### SESSION 9c: Quantum information theory and algorithms (Alvarado FGH)

Chair: (Yigit Subasi)
3:45pm - 4:15pmMark Wilde, Louisiana State University
Exact entanglement cost of quantum states and channels under PPT-preserving operations
Abstract. This paper establishes single-letter formulas for the exact entanglement cost of generating bipartite quantum states and simulating quantum channels under free quantum operations that completely preserve positivity of the partial transpose (PPT). First, we establish that the exact entanglement cost of any bipartite quantum state under PPT-preserving operations is given by a single-letter formula, here called the κ-entanglement of a quantum state. This formula is calculable by a semidefinite program, thus allowing for an efficiently computable solution for general quantum states. Notably, this is the first time that an entanglement measure for general bipartite states has been proven not only to possess a direct operational meaning but also to be efficiently computable, thus solving a question that has remained open since the inception of entanglement theory over two decades ago. Next, we introduce and solve the exact entanglement cost for simulating quantum channels in both the parallel and sequential settings, along with the assistance of free PPT-preserving operations. The entanglement cost in both cases is given by the same single-letter formula and is equal to the largest κ-entanglement that can be shared by the sender and receiver of the channel. It is also efficiently computable by a semidefinite program.
4:15pm - 4:45pmFelix Leditzky, University of Colorado JILA
Dephrasure channel and superadditivity of coherent information
Abstract. The quantum capacity of a quantum channel captures its capability for noiseless quantum communication. It lies at the heart of quantum information theory. Unfortunately, our poor understanding of nonadditivity of coherent information makes it hard to understand the quantum capacity of all but very special channels. In this paper, we consider the dephrasure channel, which is the concatenation of a dephasing channel and an erasure channel. This very simple channel displays remarkably rich and exotic properties: we find nonadditivity of coherent information at the two-letter level, a big gap between single-letter coherent and private informations, and positive quantum capacity for all complementary channels. Its clean form simplifies the evaluation of coherent information substantially and, as such, we hope that the dephrasure channel will provide a much-needed laboratory for the testing of new ideas about nonadditivity.
4:45pm - 5:15pmAniruddha Bapat, University of Maryland Joint Quantum Institute
Bang-bang control as a design principle for classical and quantum optimization algorithms
Abstract. Physically motivated classical heuristic optimization algorithms such as simulated annealing (SA) treat the objective function as an energy landscape, and allow walkers to escape local minima. It has been speculated that quantum properties such as tunneling may give quantum algorithms the upper hand in finding ground states of vast, rugged cost landscapes. Indeed, the Quantum Adiabatic Algorithm (QAO) and the recent Quantum Approximate Optimization Algorithm (QAOA) have shown promising results on various problem instance that are considered classically hard. Here, we argue that the type of \emph{control} strategy used by the optimization algorithm may be crucial to its success, both classically and quantumly. Along with SA, QAO and QAOA, we define a new, bang-bang version of simulated annealing, BBSA, and study the performance of these algorithms on two well-studied problem instances from the literature. Rather than a quantum advantage, we find evidence for a design advantage. Both classically and quantumly, the successful control strategy is found to be bang-bang, exponentially outperforming the annealing analogues on the same instances. Lastly, we construct O(1) time QAOA protocols for a large class of symmetric cost functions, and provide an accompanying physical picture.
5:15pm - 5:45pmArjendu Pattanayak, Carleton College
Unusual entanglement dynamics in the quantum kicked top
Abstract. We study the quantum kicked top in the experimentally accessible regime of a few qubits $$N \in \{2, 8\}$$. We focus on the entanglement dynamics $$|\psi(t)>$$ of intial spin coherent states on the $$(J_x,J_y,J_z)$$ sphere. We demonstrate that the quantum behavior at a given location can correlate with, or anti-correlate with, or be decorrelated with the limiting $$N \to \infty$$ classical phase-space behavior. Globally, quantum spectra and eigenfunctions visualized via expansion coefficients in the Hilbert space of the $$J_z$$ operator are shown to be periodic in $$K$$ whence the quantum dynamics are (quasi-)periodic in time $$T$$ and nonlinear kick strength $$K$$, unlike the classical dynamics although decoherence distinguishes between different $$K$$ regimes. Further, there are patterns in the quantum dynamics that repeat as a function of $$N$$. We explore novel oscillations where |$$\psi>$$ moves between two maximally entangled (GHZ-like) configurations $$(|\chi_+>, |\chi_->)$$ which occur for $$N=4,8$$ in our system. We show that linear combinations of the $$\chi$$ states relax to different final entangled states for a decoherent Kraus map of weighted sum of Floquet operators. Thus quantum entanglement for a classically chaotic system can depend on initial conditions (but not as for the classical system) and can yield final high entanglement even for states 'thermalized' under decoherence. We connect to the classical phase-space dynamics via the Husimi projections of these $$\chi$$ states.
5:45pm - 6:15pmAlexander Meill, University of California San Diego
Entanglement properties of quantum random walks
Abstract. We examine the entanglement assumptions used to derive dynamics in highly symmetric quantum random walks.

SQuInT Chief Organizer
Akimasa Miyake, Associate Professor
amiyake@unm.edu

SQuInT Local Organizers
Rafael Alexander, Postdoctoral Fellow
Chris Jackson, Postdoctoral Fellow