Device-independent lower bounds on the conditional von Neumann entropy
arXiv:2106.13692 · doi:10.22331/q-2024-08-27-1445
Abstract
The rates of several device-independent (DI) protocols, including quantum key-distribution (QKD) and randomness expansion (RE), can be computed via an optimization of the conditional von Neumann entropy over a particular class of quantum states. In this work we introduce a numerical method to compute lower bounds on such rates. We derive a sequence of optimization problems that converge to the conditional von Neumann entropy of systems defined on general separable Hilbert spaces. Using the Navascués-Pironio-Acín hierarchy we can then relax these problems to semidefinite programs, giving a computationally tractable method to compute lower bounds on the rates of DI protocols. Applying our method to compute the rates of DI-RE and DI-QKD protocols we find substantial improvements over all previous numerical techniques, demonstrating significantly higher rates for both DI-RE and DI-QKD. In particular, for DI-QKD we show a minimal detection efficiency threshold which is within the realm of current capabilities. Moreover, we demonstrate that our method is capable of converging rapidly by recovering all known tight analytical bounds up to several decimal places. Finally, we note that our method is compatible with the entropy accumulation theorem and can thus be used to compute rates of finite round protocols and subsequently prove their security.
21 (+11) pages, 4 (+2) figures. V2: improved numerics and restructured article. V3: Accepted in Quantum, minor changes
References in corpus (33)
- Quantum cryptography: Public key distribution and coin tossing
- Hacking commercial quantum cryptography systems by tailored bright illumination
- Distillation of secret key and entanglement from quantum states
- The operational meaning of min- and max-entropy
- Non-locality and Communication Complexity
- Device-independent quantum key distribution secure against collective attacks
- Bounding the set of quantum correlations
- General properties of Nonsignaling Theories
- Self-testing of quantum systems: a review
- Experimental device-independent quantum key distribution between distant users
- Testing the Hilbert space dimension
- Quantum Conference Key Agreement: A Review
- Simple and tight device-independent security proofs
- A Matrix Convexity Approach to Some Celebrated Quantum Inequalities
- Device-independent randomness expansion against quantum side information
- More Randomness from the Same Data
- Convergent relaxations of polynomial optimization problems with non-commuting variables
- Entropy accumulation
- Photonic verification of device-independent quantum key distribution against collective attacks
- Using complete measurement statistics for optimal device-independent randomness evaluation
- Device-independent Randomness Expansion with Entangled Photons
- Semidefinite approximations of the matrix logarithm
- Algorithm 950: Ncpol2sdpa---Sparse Semidefinite Programming Relaxations for Polynomial Optimization Problems of Noncommuting Variables
- Entropy accumulation with improved second-order term
- Noisy pre-processing facilitating a photonic realisation of device-independent quantum key distribution
- Device-independent quantum key distribution with asymmetric CHSH inequalities
- Computing secure key rates for quantum key distribution with untrusted devices
- Computing conditional entropies for quantum correlations
- A framework for quantum-secure device-independent randomness expansion
- A Genuine Multipartite Bell Inequality for Device-independent Conference Key Agreement
- Entropy bounds for multiparty device-independent cryptography
- Boosting device-independent cryptography with tripartite nonlocality
- Improved device-independent randomness expansion rates using two sided randomness
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- The future of secure communications: device independence in quantum key distribution
- Device independent security of quantum key distribution from monogamy-of-entanglement games
- Prepare-and-measure scenarios with photon-number constraints
- Entropy bounds for device-independent quantum key distribution with local Bell test
- Harnessing high-dimensional temporal entanglement using limited interferometric setups
- Optimising the relative entropy under semidefinite constraints
- Improving semi-device-independent randomness certification by entropy accumulation
- Quantum bounds and device-independent security with rank-one qubit measurements
- Quantum Chernoff divergence in advantage distillation for quantum key distribution and device-independent quantum key distribution
- Genuine multipartite entanglement is not necessary for standard device-independent conference key agreement
- Long-distance device-independent quantum key distribution with standard optics tools
- Device Independent Quantum Key Activation
- Composable framework for device-independent state certification
- Jahn-Teller Effect for Controlling Quantum Correlations in Hexanuclear Fe Magnets
- Quantum Key Distribution with Imperfections: Recent Advances in Security Proofs
- Maximal device-independent randomness in every dimension
- Device-independent secure correlations in sequential quantum scenarios
- Long-Distance Device-Independent Conference Key Agreement
- Sequential Semi-Device-Independent Quantum Randomness Certification