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Verifiable Hybrid Secret Sharing With Few Qubits
Quantum Physics · Submitted 21 Nov 2019
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We propose a protocol that achieves this task, while reducing the number of required qubits, as compared to the existing protocols.
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The abstract, sentence by sentence
We consider the task of sharing a secret quantum state in a quantum network in a verifiable way. We propose a protocol that achieves this task, while reducing the number of required qubits, as compared to the existing protocols. To achieve this, we combine classical encryption of the quantum secret with an existing verifiable quantum secret sharing scheme based on Calderbank-Shor-Steane quantum error correcting codes. In this way we obtain a verifiable hybrid secret sharing scheme for sharing qubits, which combines the benefits of quantum and classical schemes. Our scheme does not reveal any information to any group of less than half of the $n$ nodes participating in the protocol. Moreover, for sharing a one-qubit state each node needs a quantum memory to store $n$ single-qubit shares, and requires a workspace of at most $3n$ qubits in total to verify the quantum secret. Importantly, in our scheme an individual share is encoded in a single qubit, as opposed to previous schemes requiring $\Omega(\log n)$ qubits per share. Furthermore, we define a ramp verifiable hybrid scheme. We give explicit examples of various verifiable hybrid schemes based on existing quantum error correcting codes.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We consider the task of sharing a secret quantum state in a quantum network in a verifiable way. | background 0.99 | 0.22 | 0.06 | unclear 0.50 |
| s1 | We propose a protocol that achieves this task, while reducing the number of required qubits, as compared to the existing protocols. | contribution 0.99 | 0.92 | 0.50 | asserted 0.99 |
| s2 | To achieve this, we combine classical encryption of the quantum secret with an existing verifiable quantum secret sharing scheme based on Calderbank-Shor-Steane quantum error correcting codes. | method 0.98 | 0.80 | 0.08 | asserted 1.00 |
| s3 | In this way we obtain a verifiable hybrid secret sharing scheme for sharing qubits, which combines the benefits of quantum and classical schemes. | contribution 0.63 | 0.88 | 0.25 | asserted 1.00 |
| s4 | Our scheme does not reveal any information to any group of less than half of the $n$ nodes participating in the protocol. | result 0.96 | 0.87 | 0.16 | asserted 1.00 |
| s5 | Moreover, for sharing a one-qubit state each node needs a quantum memory to store $n$ single-qubit shares, and requires a workspace of at most $3n$ qubits in total to verify the quantum secret. | result 0.90 | 0.90 | 0.15 | asserted 1.00 |
| s6 | Importantly, in our scheme an individual share is encoded in a single qubit, as opposed to previous schemes requiring $\Omega(\log n)$ qubits per share. | result 0.54 | 0.85 | 0.23 | asserted 1.00 |
| s7 | Furthermore, we define a ramp verifiable hybrid scheme. | contribution 1.00 | 0.93 | 0.05 | asserted 0.99 |
| s8 | We give explicit examples of various verifiable hybrid schemes based on existing quantum error correcting codes. | contribution 0.99 | 0.91 | 0.07 | asserted 1.00 |
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The paper
Original abstract
We consider the task of sharing a secret quantum state in a quantum network in a verifiable way. We propose a protocol that achieves this task, while reducing the number of required qubits, as compared to the existing protocols. To achieve this, we combine classical encryption of the quantum secret with an existing verifiable quantum secret sharing scheme based on Calderbank-Shor-Steane quantum error correcting codes. In this way we obtain a verifiable hybrid secret sharing scheme for sharing qubits, which combines the benefits of quantum and classical schemes. Our scheme does not reveal any information to any group of less than half of the $n$ nodes participating in the protocol. Moreover, for sharing a one-qubit state each node needs a quantum memory to store $n$ single-qubit shares, and requires a workspace of at most $3n$ qubits in total to verify the quantum secret. Importantly, in our scheme an individual share is encoded in a single qubit, as opposed to previous schemes requiring $\Omega(\log n)$ qubits per share. Furthermore, we define a ramp verifiable hybrid scheme. We give explicit examples of various verifiable hybrid schemes based on existing quantum error correcting codes.
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How the literature uses it
1 arXiv paper cite this in 13 sentences
Papers citing it · 6 sentences without a confident label
Uses its method or tool 1 paper
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This way nodes create logical $Ψ_i$ encoded twice with $$, see Figure [ref]. * The nodes publicly create sets $B_i,ℓ$ containing all second-level errors from all $n$ executions of sequential VQSS (see [ref] for details).
Secure multi-party quantum computation with few qubits · Multi-party quantum computation · 0.93
What it cites · 8 sentences without a confident label
Builds on 1 paper
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In order to evaluate probability of aborting, we will follow the solution suggested in [ref] for the parallel execution of the and we will show how to use this result for the sequential setting.
Multi-party Quantum Computation · Security of the scheme CITEMARK77Z in the sequential setting · 0.91
Uses the method or tool of 3 papers
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We adapt the verification procedure from the work of [ref] to run in a sequential way.
Multi-party Quantum Computation · Verifiable Quantum Secret Sharing · 0.83
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For the construction we use higher-distance quantum error correcting codes, for example toric codes and color codes [ref] , and scheme of [ref] .
Fault-tolerant quantum computing with color codes · Resource reduction · 0.96
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For the construction we use higher-distance quantum error correcting codes, for example toric codes and color codes [ref] , and scheme of [ref] .
Quantum codes on a lattice with boundary · Resource reduction · 0.96
Compares with 1 paper
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In comparison, in [ref] all of the above steps are performed in parallel, and effectively, each node needs to control $Ω(r^2nlog(n))$ at once.
Multi-party Quantum Computation · Verifiable Quantum Secret Sharing · 1.00
Cites as background 3 papers
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This property is formally defined in [ref] and is dubbed .
Multi-party Quantum Computation · Verifiable Quantum Secret Sharing · 0.89
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Such codes are well-studied in the literature and therefore, numerous schemes with defined encoding and decoding exist [ref] .
Fault-tolerant quantum computing with color codes · Implications for resource reduction. · 0.94
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Such codes are well-studied in the literature and therefore, numerous schemes with defined encoding and decoding exist [ref] .
Quantum codes on a lattice with boundary · Implications for resource reduction. · 0.94
Discussion
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