Deterministic Twirling with Low Resources
arXiv:1912.06014 · doi:10.1016/j.physleta.2019.126179
Abstract
Twirling operations, which average a quantum state with respect to a unitary subgroup, have become a frequently-employed tool in quantum information processing. We investigate the efficient implementation of twirling operations with minimal resources, without necessitating the ability to perform all possible unitary operations on the quantum system of interest. We present a general algebraic method allowing us to choose a set of - typically very few - unitary operators which, when applied randomly and repeatedly, produce the given twirling operation exponentially quickly. The method is applied to twirling operations for bipartite quantum systems with respect to the unitary group , an essential ingredient in entanglement distillation protocols. In particular, we provide a complete classification of sets of unitary operators capable of performing twirling on two qubits. Moreover, we construct a generic set containing at most three unitary operators achieving the twirling operation for a general two-qudit system.
References in corpus (19)
- Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels
- Entanglement Measures under Symmetry
- Quantum Data Hiding
- Characterization of addressability by simultaneous randomized benchmarking
- Quantum speed limits, coherence and asymmetry
- The Entanglement of Formation for Isotropic States
- I-concurrence and tangle for isotropic states
- The theory of manipulations of pure state asymmetry: basic tools and equivalence classes of states under symmetric operations
- Convex-roof extended negativity as an entanglement measure for bipartite quantum systems
- Tradeoff between extractable mechanical work, accessible entanglement, and ability to act as a reference system, under arbitrary superselection rules
- Standard forms of noisy quantum operations via depolarization
- Entanglement of multiparty stabilizer, symmetric, and antisymmetric states
- Entanglement Distillation Protocols and Number Theory
- Alignment of reference frames and an operational interpretation for the G-asymmetry
- Efficient algorithm for multi-qudit twirling for ensemble quantum computation
- Asymptotic Evolution of Random Unitary Operations
- Generalized Semi-Quantum Secret Sharing Schemes
- Entanglement and decoherence: fragile and robust entanglement
- Construction of Random Unitary Operations for Asymptotic Preparation of Werner States