Related papers: Quantification and manipulation of magic states

Spontaneous symmetry breaking (SSB) is the cornerstone of our understanding of quantum phases of matter. Recent works have generalized this concept to the domain of mixed states in open quantum systems, where symmetries can be realized in…

In generalized resource theories, one aims to reformulate the problem of deciding whether a suitable transition (typically a transition that preserves the Gibbs state of the theory) between two given states $\rho$ and $\sigma$ exists or…

Quantum state exclusion is the task of identifying at least one state from a known set that was not used in the preparation of a quantum system. A set of quantum states is said to admit state exclusion if there exists a measurement whose…

We show that quantum states with "low stabilizer complexity" can be efficiently distinguished from Haar-random. Specifically, given an $n$-qubit pure state $|\psi\rangle$, we give an efficient algorithm that distinguishes whether…

Magic state distillation (MSD) is a quantum algorithm that enables performing logical non-Clifford gates with in principle arbitrarily low noise level. It is herein typically assumed that logical Clifford gates can be executed without…

In this paper, we study the exact dynamics of open quantum systems to the case with periodic driving field. It is shown that different from the static adjustment of the system on-site energy that can either generate or destroy the…

The distillation of magic states is an often-cited technique for enabling universal quantum computing once the error probability for a special subset of gates has been made negligible by other means. We present a routine for magic-state…

We studied pure state transformations using local operations assisted by finitely many rounds of classical communication ($LOCC_{\mathbb{N}}$) in C. Spee, J.I. de Vicente, D. Sauerwein, B. Kraus, arXiv:1606.04418 (2016). Here, we first of…

State convertibility is fundamental in the study of resource theory of quantum coherence. It is aimed at identifying when it is possible to convert a given coherent state to another using only incoherent operations. In this paper, we give a…

Alice and Bob are given an unknown initial state chosen from a set of pure quantum states. Their task is to transform the initial state to a corresponding final pure state using local operations only. We prove necessary and sufficient…

Conversion of entangled states under (Stochastic) Local Operations and Classical Communication admits the phenomenon of catalysis. Here we explore the possibility of a copy of the initial state itself to perform as a catalyst, which we call…

To run large-scale algorithms on a quantum computer, error-correcting codes must be able to perform a fundamental set of operations, called logic gates, while isolating the encoded information from…

Absolutely stabilizer states are those that remain convex mixtures of stabilizer states after conjugation by any unitary. Here we give a characterization of such states for multiple qudits of all prime dimensions by introducing a polytope…

For two symmetric quantum states one may be interested in maximizing the overlap under local operations applied to one of them. The question arises whether the maximal overlap can be obtained by applying the same local operation to each…

To implement any quantum operation (a.k.a. ``superoperator'' or ``CP map'') on a d-dimensional quantum system, it is enough to apply a suitable overall unitary transformation to the system and a d^2-dimensional environment which is…

We analyze the problem of reconstructing an unknown quantum state of a multipartite system from repeated measurements of local observables. In particular, via a system-theoretic observability analysis, we show that, even when the initial…

We present a theory of entanglement transformations of Gaussian pure states with local Gaussian operations and classical communication. This is the experimentally accessible set of operations that can be realized with optical elements such…

The optimal entanglement manipulation for a single copy of mixed states of two qubits is to transform it to a Bell diagonal state. In this paper we derive an explicit form of the local operation that can realize such a transformation. The…

We investigate probabilistic transformations of quantum states from a `source' set to a `target' set of states. Such transforms have many applications. They can be used for tasks which include state-dependent cloning or quantum state…

We prove that magic states from the Clifford hierarchy give optimal solutions for tasks involving nonlocality and entropic uncertainty with respect to Pauli measurements. For both the nonlocality and uncertainty tasks, stabilizer states are…