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

Abstract

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.

Random coding for sharing bosonic quantum secrets

“…This is not strictly true in any realistic realization of our scheme, as for any finite value of squeezing, all subsets can get some information about the secret. This is inherent to any CV protocol, as was recently discussed in detail in [56] for a family of singlemode CV-QSS schemes corresponding to a special case of our scheme. As it turns out, in the multi-mode case the access structure is further complicated by the fact that some subsets of less than m + n 2 players can access some of the secret quadratures even in the infinite-squeezing limit, while groups smaller than a threshold value k * are prevented from accessing the secret.…”

“…In the general case, the size of the sets that obtain no information about the secret (for infinite squeezing) depends on the size of the latter: any set of k or more players can reconstruct the full secret and sets of k * = k − m or less players are denied all information about it. Such schemes are known in the DV literature as ramp schemes [57] (note that the same term is used with a different meaning in [56], where only single-mode secrets are considered and the focus is on the information leakage due to finite squeezing). The amount of information leaked to the adversaries is also constrained by the fidelity of the state reconstructed by the access party with the secret, since the fidelity of the states reconstructed by disjoint sets of players is lim-ited by optimal cloning.…”

Quantitative security analysis of three-level unitary operations in quantum secret sharing without entanglement

“…Quantum secret sharing (QSS) is an important branch of quantum cryptography, whose security is based on the fundamental principle of quantum mechanics. It can share both the classical message [1][2][3][4][5][6][7][8][9][10][11] and quantum information [12][13][14][15][16][17][18][19][20][21][22]. Taking QSS protocols for classical message sharing into account, it is observed that it is a more efficient and lower cost way to use single particles instead of entangled particles.…”

Sender-controlled measurement-device-independent multiparty quantum communication

“…In 2004, Xiao et al [36] proposed a high-efficient QSS protocol, increasing its efficiency to asymptotically 100% by properly choosing measurement bases [37,38]. Subsequently, some interesting QSS protocols were proposed [39][40][41][42][43][44][45][46].…”