Enumerating all bilocal Clifford distillation protocols through symmetry reduction

Abstract

Entanglement distillation is an essential building block in quantum communication protocols. Here, we study the class of near-term implementable distillation protocols that use bilocal Clifford operations followed by a single round of communication. We introduce tools to enumerate and optimise over all protocols for up to $n=5$ (not necessarily equal) Bell-diagonal states using a commodity desktop computer. Furthermore, by exploiting the symmetries of the input states, we find all protocols for up to $n=8$ copies of a Werner state. For the latter case, we present circuits that achieve the highest fidelity with perfect operations and no decoherence. These circuits have modest depth and number of two-qubit gates. Our results are based on a correspondence between distillation protocols and double cosets of the symplectic group, and improve on previously known protocols.

arXiv commentFixed a typo in Table 6, n = 8; 16 pages main text, 7 pages appendices, 10 figures

References in corpus (45)

• Mixed State Entanglement and Quantum Error Correction
• Quantum cryptography: Public key distribution and coin tossing
• Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels
• Quantifying Entanglement
• Entanglement Measures and Purification Procedures
• Quantum privacy amplification and the security of quantum cryptography over noisy channels
• The Role of Relative Entropy in Quantum Information Theory
• A Theory of Fault-Tolerant Quantum Computation
• Distillation of secret key and entanglement from quantum states
• Quantum repeaters based on entanglement purification
• Distributed Quantum Computation over Noisy Channels
• Entanglement Distillation between Solid-State Quantum Network Nodes
• Quantum Clock Synchronization Based on Shared Prior Entanglement
• Entanglement purification and quantum error correction
• Topological quantum computing with a very noisy network and local error rates approaching one percent
• Local filtering operations on two qubits
• The Clifford group, stabilizer states, and linear and quadratic operations over GF(2)
• Optimizing practical entanglement distillation
• Entanglement purification for Quantum Computation
• Hadamard-free circuits expose the structure of the Clifford group
• Optimized Entanglement Purification
• Fully device independent Conference Key Agreement
• Experimental Single-Copy Entanglement Distillation
• Local permutations of products of Bell states and entanglement distillation
• Distilling entanglement from arbitrary resources
• Entanglement-assisted entanglement purification
• Interpolation of recurrence and hashing entanglement distillation protocols
• Entanglement Purification with Double Selection
• Shorter stabilizer circuits via Bruhat decomposition and quantum circuit transformations
• Quantum link bootstrapping using a RuleSet-based communication protocol
• Bound entanglement provides convertibility of pure entangled states
• Non-asymptotic entanglement distillation
• Useful states and entanglement distillation
• Quantum Telecomputation
• Adaptive recurrence quantum entanglement distillation for two-Kraus-operator channels
• Practical distributed quantum information processing with LOCCNet
• Entanglement Distillation Protocols and Number Theory
• One-shot entanglement distillation beyond local operations and classical communication
• Entanglement purification by counting and locating errors with entangling measurements
• Quantum nonlocality obtained from local states by entanglement purification
• General theory of environment-assisted entanglement distillation
• On bound entanglement assisted distillation
• Single-Step Distillation Protocol with Generalized Beam Splitters
• Conference Key Agreement and Quantum Sharing of Classical Secrets with Noisy GHZ States
• Purification and Entanglement Routing on Quantum Networks

Cited by in corpus (15)

• Thresholds for the distributed surface code in the presence of memory decoherence
• Near-term $n$ to $k$ distillation protocols using graph codes
• No-Go Theorems for Universal Entanglement Purification
• Stabilizer Entanglement Distillation and Efficient Fault-Tolerant Encoders
• Entanglement buffering with two quantum memories
• Comparing One- and Two-way Quantum Repeater Architectures
• Counting stabiliser codes for arbitrary dimension
• Disti-Mator: an entanglement distillation-based state estimator
• Fidelity-Aware Multipath Routing for Multipartite State Distribution in Quantum Networks
• Constant Overhead Entanglement Distillation via Scrambling
• Boosting end-to-end entanglement fidelity in quantum repeater networks via hybridized strategies
• Dynamic LOCC Circuits for Automated Entanglement Manipulation
• Fault-tolerant and secure long-distance quantum communication via uncorrectable-error-injection
• Basic entanglement distillation with realistic noise
• Enhancing Quantum Key Distribution with Entanglement Distillation and Classical Advantage Distillation