On the Theory of Quantum Secret Sharing

Abstract

I present a variety of results on the theory of quantum secret sharing. I show that any mixed state quantum secret sharing scheme can be derived by discarding a share from a pure state scheme, and that the size of each share in a quantum secret sharing scheme must be at least as large as the size of the secret. I show that the only constraints on the existence of quantum secret sharing schemes with general access structures are monotonicity (if a set is authorized, so are larger sets) and the no-cloning theorem. I also discuss some aspects of sharing classical secrets using quantum states. In this situation, the size of each share can sometimes be half the size of the classical secret.

9 pages, REVTeX

References in corpus (1)

• Quantum Teleportation is a Universal Computational Primitive

Cited by in corpus (181)

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• Quantum secret sharing without entanglement
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• Quantum secret sharing between multi-party and multi-party without entanglement
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• Unconditional security of entanglement-based continuous-variable quantum secret sharing
• Bidirectional quantum secret sharing and secret splitting with polarized single photons
• Entanglement properties of multipartite entangled states under the influence of decoherence
• Semi-quantum secret sharing using entangled states
• Quantum state sharing of an arbitrary two-qubit state with two-photon entanglements and Bell-state measurements
• Hiding classical data in multi-partite quantum states
• Quantum protocols for anonymous voting and surveying
• Multiparty quantum secret sharing of secure direct communication
• Quantum secret sharing with qudit graph states
• Circular quantum secret sharing
• Quantum secret sharing based on local distinguishability
• Quantum network communication -- the butterfly and beyond
• How to share a continuous-variable quantum secret by optical interferometry
• An efficient quantum secret sharing scheme with Einstein-Podolsky-Rosen Pairs
• Many-agent controlled teleportation of multi-qubit quantum information
• Hierarchical quantum information splitting
• Entanglement-Based Quantum Information Technology
• Quantum teleportation and state sharing using a genuinely entangled six qubit state
• A resource theory of entanglement with a unique multipartite maximally entangled state
• Quantum secret sharing with continuous-variable cluster states
• Quantum secret sharing with polarization-entangled photon pairs
• Three-party qutrit-state sharing
• Multiparty quantum secret splitting and quantum state sharing
• Quantum homomorphic encryption from quantum codes
• N-qubit Quantum Teleportation, Information Splitting and Superdense Coding through the composite GHZ-Bell Channel
• Unified criterion for security of secret sharing in terms of violation of Bell inequality
• Secret sharing of quantum information via entanglement swapping in cavity QED
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• Entanglement manipulation of multipartite pure states with finite rounds of classical communication
• Multiparty data hiding of quantum information
• Quantum Secret Sharing Schemes and Reversibility of Quantum Operations
• Experimentally Feasible Security Check for n-qubit Quantum Secret Sharing
• Minimal classical communication and measurement complexity for quantum information splitting
• Quantum secret sharing protocol between multiparty and multiparty with single photons and unitary transformations
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• When do Local Operations and Classical Communication Suffice for Two-Qubit State Discrimination?
• Efficient and economic five-party quantum state sharing of an arbitrary m-qubit state
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• Multiparty hierarchical quantum-information splitting
• Multi-party quantum private comparison of size relation with d-level single-particle states
• Absolutely Maximally Entangled Qudit Graph States
• Reducing the quantum communication cost of quantum secret sharing
• Absolutely Maximally Entangled States: Existence and Applications
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• Framework for classifying logical operators in stabilizer codes
• Matroids and Quantum Secret Sharing Schemes
• Generalized Semi-Quantum Secret Sharing Schemes
• Circular multi-party quantum private comparison with n-level single-particle states
• Resource theories of multi-time processes: A window into quantum non-Markovianity
• Transmitting qubits through relativistic fields
• On the equivalence between sharing quantum and classical secrets, and error correction
• Masking Quantum Information on Hyperdisks
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• Quantum secret sharing for general access structures
• Implementation of quantum secret sharing and quantum binary voting protocol in the IBM quantum computer
• Verifiable Hybrid Secret Sharing With Few Qubits
• Communication Efficient Quantum Secret Sharing
• Accessing quantum secrets via local operations and classical communication
• Tripartite entanglement measure under local operations and classical communication
• A Generalized Information Theoretical Model for Quantum Secret Sharing
• Detection and characterization of multipartite entanglement in optical lattices
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• Controlled Quantum Secret Sharing
• Two Efficient Measurement Device Independent Quantum Dialogue Protocols
• Computing on quantum shared secrets
• Subtraction better than addition: Entanglement in multimode squeezed vacuum post-interface with photons
• Approximate reconstructability of quantum states and noisy quantum secret sharing schemes
• Unitary Reconstruction of Secret for Stabilizer Based Quantum Secret Sharing
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• Local Indistinguishability and Possibility of Hiding cbits in Activable Bound Entangled States
• Asymptotic survival of genuine multipartite entanglement in noisy quantum networks depends on the topology
• Multi-party Quantum Computation
• Symmetries and entanglement of stabilizer states
• Multipartite correlations in mutually unbiased bases
• A Quantum Information Theoretical Model for Quantum Secret Sharing Schemes
• New Protocols and Lower Bound for Quantum Secret Sharing with Graph States
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• On Weak Odd Domination and Graph-based Quantum Secret Sharing
• Unveiling the Importance of Nonshortest Paths in Quantum Networks
• Secure multi-party quantum computation with few qubits
• The Min-entropy as a Resource for One-Shot Private State Transfer, Quantum Masking and State Transition
• Cryptography in a Quantum World
• Quantum Strongly Secure Ramp Secret Sharing
• Quantum memory for individual polarization photon
• Eavesdropping on the improved three-party quantum secret sharing protocol
• A symmetric extensible protocol for quantum secret sharing
• Enhancing robustness of multiparty quantum correlations using weak measurement
• Unified Approach to Secret Sharing and Symmetric Private Information Retrieval with Colluding Servers in Quantum Systems
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• Improving entanglement purification through coherent superposition of roles
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• Encrypted Qubits can be Cloned
• Entanglement Sharing Protocol via Quantum Error Correcting Codes
• Coding Theoretic Construction of Quantum Ramp Secret Sharing
• Polymatroids and polyquantoids
• Classical Access Structures of Ramp Secret Sharing Based on Quantum Stabilizer Codes
• Classification and Quantification of Entanglement Through Wedge Product and Geometry
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• Distributed Encoding and Decoding of Quantum Information over Networks
• Secure and authenticated quantum secret sharing
• Fundamental limits on quantum cloning from the no-signalling principle
• Classical versus Quantum Graph-based Secret Sharing
• Efficient Code for Relativistic Quantum Summoning
• Designing locally maximally entangled quantum states with arbitrary local symmetries
• Bounds on the Information Rate of Quantum Secret Sharing Schemes
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• Quantum Stabilizer Codes Can Realize Access Structures Impossible by Classical Secret Sharing
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• Advance sharing of quantum shares for quantum secrets
• Tip of the Quantum Entropy Cone
• Secure Multi-Party Quantum Conference and Xor Computation
• Entropic Inequalities for a Class of Quantum Secret Sharing States
• Quantum Optimal Multiple Assignment Scheme for Realizing General Access Structure of Secret Sharing
• A distributed and parallel $(k,n)$ QSS scheme with verification capability
• Message Randomization and Strong Security in Quantum Stabilizer-Based Secret Sharing for Classical Secrets
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• Comment on "Quantum key agreement protocol"
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• Performance comparison of the two reconstruction methods for stabilizer-based quantum secret sharing
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• Small sets of locally indistinguishable orthogonal maximally entangled states
• Advance Sharing Procedures for the Ramp Quantum Secret Sharing Schemes With the Highest Coding Rate
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• Evolution of Entanglement Witness of Dicke State under Noise and Error Mitigation
• Correlational Resource Theory of Catalytic Quantum Randomness under Conservation Law
• How to hide a secret direction
• Single-Shot Secure Quantum Network Coding for General Multiple Unicast Network with Free One-Way Public Communication
• Study on Entanglement and its Utility in Information Processing
• Revocation and Reconstruction of Shared Quantum States
• Structure Theorem for Quantum Replacer Codes
• Undetermined states: how to find them and their applications
• Sharing a quantum secret without a trusted party
• Entanglement - A Queer In The World Of Quantum : Some Perspectives
• Distillation of multipartite entangled states for arbitrary subsets of parties in noisy quantum networks of increasing size
• Efficient decoding of stabilizer code by single-qubit local operations and classical communication
• Sharing classical secrets with continuous-variable entanglement: Composable security and network coding advantage
• Revocation and Reconstruction of Shared Quantum States
• Quantum Access Structure and Secret Sharing