Quantum secret sharing schemes and reversibility of quantum operations

Ogawa, Tetsuhiro; Sasaki, Akira; Iwamoto, Mitsugu; Yamamoto, Hirosuke

doi:10.1103/physreva.72.032318

Cited by 55 publications

(133 citation statements)

References 49 publications

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“…Thus, the overall scheme is a perfect (6,7) QSS scheme, but requiring only three quantum shares. schemes) and satisfies (6). For an initial boundary scheme, then, the optimal underlying QSS scheme will simply have a ( , ) structure.…”

Section: Hybrid Secret Sharingmentioning

confidence: 99%

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Reducing the Quantum Communication Cost of Quantum Secret Sharing

Fortescue

Gour

2012

IEEE Trans. Inform. Theory

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We demonstrate a new construction for perfect quantum secret sharing (QSS) schemes based on imperfect "ramp" secret sharing combined with classical encryption, in which the individual parties' shares are split into quantum and classical components, allowing the former to be of lower dimension than the secret itself. We show that such schemes can be performed with smaller quantum components and lower overall quantum communication than required for existing methods. We further demonstrate that one may combine both imperfect quantum and imperfect classical secret sharing to produce an overall perfect QSS scheme, and that examples of such schemes (which we construct) can have the smallest quantum and classical share components possible for their access structures, something provably not achievable using perfect underlying schemes. Our construction has significant potential for being adapted to other QSS schemes based on stabilizer codes.Index Terms-Quantum communication, quantum cryptography, quantum error correction, quantum secret sharing, secret sharing, stabilizer code.

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Section: Hybrid Secret Sharingmentioning

confidence: 99%

“…Proof: An optimal RQSS protocol has share size qubits, (we can always, though not exclusively, construct such protocols [6] for shares of ). For given , we wish to minimize (11) subject to (9) and (8).…”

Section: Hybrid Rqss Schemesmentioning

confidence: 99%

Reducing the Quantum Communication Cost of Quantum Secret Sharing

Fortescue

Gour

2012

IEEE Trans. Inform. Theory

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“…Various different QSS schemes have been developed [41], [42], [43], [44], [45], [46]. Among them, a (k, L, n)-threshold ramp QSS scheme is defined as a QSS scheme with n shares having the following property [43]: The original state can be reconstructed from any k shares, and any k − L shares has no information. Hence, partial information of the original state can be drived from t shares with k > t > k − L. The network codes given in the above subsections B and C are strongly related to (k, L, n)-threshold ramp QSS scheme with k = n. Here, the condition k = n means that all the n shares are required to reconstruct the original state.…”

Section: Quantum Threshold Ramp Secret Sharingmentioning

confidence: 99%

“…6. The network that can be derived from the third example by contracting the edge e(4n + 1) and merging vertices vi with 1 ≤ i ≤ n in graph theoretical sense sending n-quantum messages from the input node v 1 to the output node v n+2 , this network coding is nothing but (2n, 2n − 1, 2n) quantum threshold ramp secret sharing scheme [43].…”

Section: Quantum Threshold Ramp Secret Sharingmentioning

confidence: 99%

Single-Shot Secure Quantum Network Coding for General Multiple Unicast Network with Free Public Communication

Kato

Owari

Hayashi

2017

Lecture Notes in Computer Science

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It is natural in a quantum network system that multiple users intend to send their quantum message to their respective receivers, which is called a multiple unicast quantum network. We propose a canonical method to derive a secure quantum network code over a multiple unicast quantum network from a secure classical network code. Our code correctly transmits quantum states when there is no attack. It also guarantees the secrecy of the transmitted quantum state even with the existence of an attack when the attack satisfies a certain natural condition. In our security proof, the eavesdropper is allowed to modify wiretapped information dependently on the previously wiretapped messages. Our protocol guarantees the secrecy by utilizing one-way classical information transmission (public communication) in the same direction as the quantum network although the verification of quantum information transmission requires two-way classical communication. Our secure network code can be applied to several networks including the butterfly network.Index Terms secrecy, quantum state, network coding, multiple unicast, general network, one-way public communication secrecy, quantum state, network coding, multiple unicast, general network, one-way public communication I. INTRODUCTIONIn order to realize quantum information processing protocols to overwhelm the conventional information technologies among multiple users, it is needed to build up a quantum network system among multiple users. For example, various quantum protocols, e.g., quantum blind computation [2], [3], quantum public key cryptography [1], and quantum money [4] require the transmission of quantum states. To meet the demand, the paper [5] initiated the study of quantum network coding with the butterfly network as a typical example. Under this example, the paper [6] clarified the importance of prior entanglement in a quantum network code by proposing a network code, which was experimentally implemented recently [7]. Kobayashi et al. [8] discussed a method for generating GHZ-type states via quantum network coding. Leung et al. [9] investigated several types of networks when classical communication is allowed. Based on these studies, Kobayashi et al. [10] made a code to transmit quantum states based on a linear classical network code. Then, Kobayashi et al. [11] generalized the result to the case with non-linear network codes. These studies [8], [9], [10], [11], [12] clarified that quantum network coding is needed among multiple users for efficient transmission of the quantum states over a quantum network. However, these existing studies did not discuss the security for quantum network codes when an adversary attacks the quantum network.Since the improvement of the security is one of the most essential requirements for developing quantum networks, the security analysis is strongly required for quantum network codes. Indeed, it is possible to check the security in these existing methods by verifying the non-existence of the eavesdropper. However, the verification requires us...

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“…Secret sharing (SS) is an information theoretically secure cryptographic protocol that is applicable to online auctions, electronic voting, shared electronic banking and cooperative activation in the classical domain [1], and distributed quantum computing in the quantum regime [2]. Ramp classical [3,4] and quantum [5,6] SS schemes were proposed to reduce the communication complexity by the sacrifice of security conditions. Continuousvariable quantum secret sharing (CV QSS) [7][8][9] has been formulated in the framework of discrete-variable quantum SS schemes [10], which does not accommodate the quantum-information leakage inherent in continuous representations of quantum information.…”

Section: Introductionmentioning

confidence: 99%

Continuous-variable ramp quantum secret sharing with Gaussian states and operations

Habibidavijani

Sanders

2019

New J. Phys.

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We aim to quantify and mitigate quantum-information leakage in continuous-variable quantum secret sharing (CV QSS). Here we introduce a technique for certifying CV ramp quantum secretsharing (RQSS) schemes in the framework of quantum interactive-proof systems. We devise pseudocodes in order to represent the sequence of steps taken to solve the certification problem. Furthermore, we derive the expression for quantum mutual information between the quantum secret extracted by any multi-player structure and the share held by the referee corresponding to the Tyc-Rowe-Sanders CV QSS scheme. We solve by converting the Tyc-Rowe-Sanders position representation for the state into a Wigner function from which the covariance matrix can be found, then insert the covariance matrix into the standard formula for CR quantum mutual information to obtain quantum mutual information in terms of squeezing. Our quantum mutual information result quantifies the leakage of the RQSS schemes.

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Quantum secret sharing schemes and reversibility of quantum operations

Cited by 55 publications

References 49 publications

Reducing the Quantum Communication Cost of Quantum Secret Sharing

Reducing the Quantum Communication Cost of Quantum Secret Sharing

Single-Shot Secure Quantum Network Coding for General Multiple Unicast Network with Free Public Communication

Continuous-variable ramp quantum secret sharing with Gaussian states and operations

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