Peter W. Shor
While stabilizer tableaus have proven useful as a descriptive tool for additive quantum codes, they otherwise offer little guidance for concrete constructions or algorithm analysis. We introduce a representation of stabilizer codes as…
We present a quantum compilation algorithm that maps Clifford encoders, encoding maps for stabilizer quantum codes, to a unique graphical representation in the ZX calculus. Specifically, we develop a canonical form in the ZX calculus and…
We introduce a new class of algorithms for finding a short vector in lattices defined by codes of co-dimension $k$ over $\mathbb{Z}_P^d$, where $P$ is prime. The co-dimension $1$ case is solved by exploiting the packing properties of the…
We introduce various measures of forward classical communication for bipartite quantum channels. Since a point-to-point channel is a special case of a bipartite channel, the measures reduce to measures of classical communication for…
I recount some of my memories of the early development of quantum computation, including the discovery of the factoring algorithm, of error correcting codes, and of fault tolerance.
Publicly verifiable quantum money is a protocol for the preparation of quantum states that can be efficiently verified by any party for authenticity but is computationally infeasible to counterfeit. We develop a cryptographic scheme for…
The out-of-time-ordered correlation (OTOC) and entanglement are two physically motivated and widely used probes of the "scrambling" of quantum information, a phenomenon that has drawn great interest recently in quantum gravity and many-body…
We prove that the classical capacity of an arbitrary quantum channel assisted by a free classical feedback channel is bounded from above by the maximum average output entropy of the quantum channel. As a consequence of this bound, we…
Associated to every finite group, Kitaev has defined the quantum double model for every orientable surface without boundary. In this paper, we define boundaries for this model and characterize condensations; that is, we find all…
Recently, physicists have started applying quantum information theory to black holes. This led to the conjecture that black holes are the fastest scramblers of information, and that they scramble it in time order M log M, where M is the…
Non-Gaussian states and operations are crucial for various continuous-variable quantum information processing tasks. To quantitatively understand non-Gaussianity beyond states, we establish a resource theory for non-Gaussian operations. In…
In this article, we investigate the additivity phenomenon in the dynamic capacity of a quantum channel for trading classical communication, quantum communication and entanglement. Understanding such additivity property is important if we…
Finding the optimal encoding strategies can be challenging for communication using quantum channels, as classical and quantum capacities may be superadditive. Entanglement assistance can often simplify this task, as the…
We give a capacity formula for the classical information transmission over a noisy quantum channel, with separable encoding by the sender and limited resources provided by the receiver's pre-shared ancilla. Instead of a pure state, we…
A digital computer is generally believed to be an efficient universal computing device; that is, it is believed able to simulate any physical computing device with an increase in computation time of at most a polynomial factor. This may not…
The sub-volume scaling of the entanglement entropy with the system's size, $n$, has been a subject of vigorous study in the last decade [1]. The area law provably holds for gapped one dimensional systems [2] and it was believed to be…
The Systematic Normal Form (SysNF) is a canonical form of lattices introduced in [Eldar,Shor '16], in which the basis entries satisfy a certain co-primality condition. Using a "smooth" analysis of lattices by SysNF lattices we design a…
O. H. Keller conjectured in 1930 that in any tiling of $\Bbb R^n$ by unit $n$-cubes there exist two of them having a complete facet in common. O. Perron proved this conjecture for $n\le 6$. We show that for all $n\ge 10$ there exists a…
We introduce a new canonical form of lattices called the systematic normal form (SNF). We show that for every lattice there is an efficiently computable "nearby" SNF lattice, such that for any lattice one can solve lattice problems on its…
We show that for the tensor product of an entanglement-breaking quantum channel with an arbitrary quantum channel, both the minimum entropy of an output of the channel and the Holevo-Schumacher-Westmoreland capacity are additive. In…