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In the standard model of quantum secret sharing, typically, one is interested in minimal authorized sets for the reconstruction of the secret. In such a setting, reconstruction requires the communication of all the shares of the…
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…
We define and show how to construct nonbinary quantum stabilizer codes. Our approach is based on nonbinary error bases. It generalizes the relationship between selforthogonal codes over $GF_{4}$ and binary quantum codes to one between…
This paper investigates a new information reconciliation method for quantum key distribution in the case where two parties exchange key in the presence of a malevolent eavesdropper. We have observed that reconciliation is a special case of…
Surface codes based on stabilizer circuits may pave the way for large scale fault-tolerant quantum computation. The surface code uses only single- and two-qubit gates and the error threshold falls close to 1% for a large range of errors.…
With the advantages of both classical and quantum secret sharing, many practical hybrid quantum secret sharing have been proposed. In this paper, we propose a hybrid quantum secret sharing scheme based on mutually unbiased bases and…
We present two experimental schemes to perform continuous variable (2,3) threshold quantum secret sharing on the quadratures amplitudes of bright light beams. Both schemes require a pair of entangled light beams. The first scheme utilizes…
To improve the efficiency of the encoding and the decoding is the important problem in the quantum error correction. In a preceding work, a general algorithm for decoding the stabilizer code is shown. This paper will show an decoding which…
Active quantum error correction using qubit stabilizer codes has emerged as a promising, but experimentally challenging, engineering program for building a universal quantum computer. In this review we consider the formalism of qubit…
Secret sharing is a procedure for splitting a message into several parts so that no subset of parts is sufficient to read the message, but the entire set is. We show how this procedure can be implemented using GHZ states. In the quantum…
Stabilizer codes are the most widely studied class of quantum error-correcting codes and form the basis of most proposals for a fault-tolerant quantum computer. A stabilizer code is defined by a set of parity-check operators, which are…
Understanding how a stabilizer circuit responds to different input is important to formulating an effective strategy for resource management. In this paper, we further investigate the many ways of using stabilizer operations to generate a…
A ($t$, $n$) threshold quantum secret sharing (QSS) is proposed based on a single $d$-level quantum system. It enables the ($t$, $n$) threshold structure based on Shamir's secret sharing and simply requires sequential communication in…
We study the implementation of quantum key distribution (QKD) systems over quantum repeater infrastructures. We particularly consider quantum repeaters with encoding and compare them with probabilistic quantum repeaters. To that end, we…
We show how to convert a quantum stabilizer code to a one-way or two-way entanglement distillation protocol. The proposed conversion method is a generalization of those of Shor-Preskill and Nielsen-Chuang. The recurrence protocol and the…
We investigate quantum secret sharing schemes constructed from $[[n,k,\delta]]_D$ non-binary stabilizer quantum error correcting codes with carrier qudits of prime dimension $D$. We provide a systematic way of determining the access…
The importance of quantum error correction in paving the way to build a practical quantum computer is no longer in doubt. This dissertation makes a threefold contribution to the mathematical theory of quantum error-correcting codes.…
Optimizing quantum circuits is critical: the number of quantum operations needs to be minimized for a successful evaluation of a circuit on a quantum processor. In this paper we unify two disparate ideas for optimizing quantum circuits,…
Quantum computing is an emerging technology that has the potential to achieve exponential speedups over their classical counterparts. To achieve quantum advantage, quantum principles are being applied to fields such as communications,…
Secret sharing is a method of dividing a secret among n par- ticipants and allows only qualified subset to reconstruct the secret and hence provides better reliability and availability of secret data.In the generalized secret sharing…