Optimal quantum networks and one-shot entropies

Abstract

We develop a semidefinite programming method for the optimization of quantum networks, including both causal networks and networks with indefinite causal structure. Our method applies to a broad class of performance measures, defined operationally in terms of interactive tests set up by a verifier. We show that the optimal performance is equal to a max relative entropy, which quantifies the informativeness of the test. Building on this result, we extend the notion of conditional min-entropy from quantum states to quantum causal networks. The optimization method is illustrated in a number of applications, including the inversion, charge conjugation, and controlization of an unknown unitary dynamics. In the non-causal setting, we show a proof-of-principle application to the maximization of the winning probability in a non-causal quantum game.

37 + 15 pages, 6 figures, accepted for publication in New Journal of Physics

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Cited by in corpus (52)

• Quantum stochastic processes and quantum non-Markovian phenomena
• Comparison of Quantum Channels by Superchannels
• Quantum Shannon theory with superpositions of trajectories
• Reversing Unknown Quantum Transformations: Universal Quantum Circuit for Inverting General Unitary Operations
• Certification and Quantification of Multilevel Quantum Coherence
• Strict hierarchy between parallel, sequential, and indefinite-causal-order strategies for channel discrimination
• Quantum metrology for non-Markovian processes
• Resource theory of asymmetric distinguishability for quantum channels
• Kolmogorov extension theorem for (quantum) causal modelling and general probabilistic theories
• Entanglement of a bipartite channel
• Optimal Strategies of Quantum Metrology with a Strict Hierarchy
• Probabilistic exact universal quantum circuits for transforming unitary operations
• Entropy of a quantum channel
• Quantum operations with indefinite time direction
• Deterministic transformations between unitary operations: Exponential advantage with adaptive quantum circuits and the power of indefinite causality
• Resetting uncontrolled quantum systems
• Reversing Unknown Qubit-Unitary Operation, Deterministically and Exactly
• Query-optimal estimation of unitary channels in diamond distance
• Complex conjugation supermap of unitary quantum maps and its universal implementation protocol
• Symmetries of quantum evolutions
• Success-or-Draw: A Strategy Allowing Repeat-Until-Success in Quantum Computation
• Characterising the Hierarchy of Multi-time Quantum Processes with Classical Memory
• Reassessing the advantage of indefinite causal orders for quantum metrology
• Fully-Optimized Quantum Metrology: Framework, Tools, and Applications
• Experimental superposition of time directions
• Experimental demonstration of input-output indefiniteness in a single quantum device
• Units of rotational information
• Universal control of quantum processes using sector-preserving channels
• Necessary and Sufficient Conditions on Measurements of Quantum Channels
• A general theory of comparison of quantum channels (and beyond)
• Communication Cost of Quantum Processes
• Optimal universal quantum circuits for unitary complex conjugation
• Reversing Unknown Quantum Processes via Virtual Combs for Channels with Limited Information
• Universal construction of decoders from encoding black boxes
• Evaluating the Advantage of Adaptive Strategies for Quantum Channel Distinguishability
• Composition rules for quantum processes: a no-go theorem
• Quasi-inversion of quantum and classical channels in finite dimensions
• Strategies for single-shot discrimination of process matrices
• Tsirelson bounds for quantum correlations with indefinite causal order
• Achieving the Multi-parameter Quantum Cramér-Rao Bound with Antiunitary Symmetry
• The Min-Entropy of Classical-Quantum Combs for Measurement-Based Applications
• Universal adjointation of isometry operations using conversion of quantum supermaps
• Experimentally undoing an unknown single-qubit unitary
• Parameterized quantum comb and simpler circuits for reversing unknown qubit-unitary operations
• Simulating the quantum switch with quantum circuits is computationally hard
• Representation matching for delegated quantum computing
• Characterising transformations between quantum objects, 'completeness' of quantum properties, and transformations without a fixed causal order
• Ordering states and channels based on positive Bayesian evidence
• Optimal Hamiltonian recognition of unknown quantum dynamics
• Time-reversal of rank-one quantum strategy functions
• Analytical Lower Bound on Query Complexity for Transformations of Unknown Unitary Operations
• The entropy of quantum causal networks