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Register a new userSequential quantum secret sharing in noisy environments
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Sequential Quantum Secret Sharing schemes (QSS) do not use entangled states for secret sharing, rather they rely on sequential operations of the players on a single state which is circulated between the players. In order to check the viability of these schemes under imperfect operations and noise in the channels, we consider one such scheme in detail and show that under moderate conditions it is still possible to extract viable secure shared keys in this scheme. Although we specifically consider only one type of sequential scheme and three different noise models, our method is fairly general to be applied to other QSS schemes and noise models as well.
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In this work we give a $(n,n)$-threshold protocol for sequential secret sharing of quantum information for the first time. By sequential secret sharing we refer to a situation where the dealer is not having all the secrets at the same time, at the beginning of the protocol; however if the dealer wishes to share secrets at subsequent phases she/he can realize it with the help of our protocol. First of all we present our protocol for three parties and later we generalize it for the situation where we have $(n>3)$ parties. Further in a much more realistic situation, we consider the sharing of qubits through two kinds of noisy channels, namely the phase damping channel (PDC) and the amplitude damping channel (ADC). When we carry out the sequential secret sharing in the presence of noise we observe that the fidelity of secret sharing at the $k^{th}$ iteration is independent of the effect of noise at the $(k-1)^{th}$ iteration. In case of ADC we have seen that the average fidelity of secret sharing drops down to $frac{1}{2}$ which is equivalent to a random guess of the quantum secret. Interestingly, we find that by applying weak measurements one can enhance the average fidelity. This increase of the average fidelity can be achieved with certain trade off with the success probability of the weak measurements.
In this paper we define a kind of decomposition for a quantum access structure. We propose a conception of minimal maximal quantum access structure and obtain a sufficient and necessary condition for minimal maximal quantum access structure, which shows the relationship between the number of minimal authorized sets and that of the players. Moreover, we investigate the construction of efficient quantum secret schemes by using these techniques, a decomposition and minimal maximal quantum access structure. A major advantage of these techniques is that it allows us to construct a method to realize a general quantum access structure. For these quantum access structures, we present two quantum secret schemes via the idea of concatenation or a decomposition of a quantum access structure. As a consequence, the application of these techniques allow us to save more quantum shares and reduce more cost than the existing scheme.
We develop a connection between tripartite information $I_3$, secret sharing protocols and multi-unitaries. This leads to explicit ((2,3)) threshold schemes in arbitrary dimension minimizing tripartite information $I_3$. As an application we show that Page scrambling unitaries simultaneously work for all secrets shared by Alice. Using the $I_3$-Ansatz for imperfect sharing schemes we discover examples of VIP sharing schemes.
In this work, we investigate what kinds of quantum states are feasible to perform perfectly secure secret sharing, and present its necessary and sufficient conditions. We also show that the states are bipartite distillable for all bipartite splits, and hence the states could be distillable into the Greenberger-Horne-Zeilinger state. We finally exhibit a class of secret-sharing states, which have an arbitrarily small amount of bipartite distillable entanglement for a certain split.
In single-qubit quantum secret sharing, a secret is shared between N parties via manipulation and measurement of one qubit at a time. Each qubit is sent to all N parties in sequence; the secret is encoded in the first participants preparation of the qubit state and the subsequent participants choices of state rotation or measurement basis. We present a protocol for single-qubit quantum secret sharing using polarization entanglement of photon pairs produced in type-I spontaneous parametric downconversion. We investigate the protocols security against eavesdropping attack under common experimental conditions: a lossy channel for photon transmission, and imperfect preparation of the initial qubit state. A protocol which exploits entanglement between photons, rather than simply polarization correlation, is more robustly secure. We implement the entanglement-based secret-sharing protocol with 87% secret-sharing fidelity, limited by the purity of the entangled state produced by our present apparatus. We demonstrate a photon-number splitting eavesdropping attack, which achieves no success against the entanglement-based protocol while showing the predicted rate of success against a correlation-based protocol.
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