Our quantum mutual information result quantifies the leakage of the ramp quantum secret-sharing schemes. 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 continuous-variable quantum mutual information to obtain quantum mutual information in terms of squeezing. 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 continuous-variable quantum secret-sharing scheme. We devise pseudocodes in order to represent the sequence of steps taken to solve the certification problem. Here we introduce a technique for certifying continuous-variable ramp quantum secret-sharing schemes in the framework of quantum interactive-proof systems. The first step is to initialise a 3 qubit register. I am not an expert on 6 or 7, but doing a search on for those topics should throw up some interesting papers.AbstractOur aim is to formulate continuous-variable quantum secret-sharing as a continuous-variable ramp quantum secret-sharing protocol, provide a certification procedure for it and explain the criteria for the certification. Step 1: Initialise the quantum and classical registers. This will give you a good picture of the field up to about 1997.Īlso recommended is his introductory article. Of course, you probably only want to cover two or three of these topics.Ī good starting point is Dan Gottesman's Ph.D. We develop bottom-up approaches to the problem of noisy qubits and incorporate error correction techniques to realize this technology’s true potential. This goal requires scalable, error-corrected quantum systems. erasure channel and quantum error correction codes that satisfy the quantum Singleton bound, as these codes are closely related to ramp QSS schemes.
Secret sharing is a scheme to share a secret among multiple. We give necessary and sufficient conditions.
#Quantum error correction ramp code#
collective decoherence and encoding in decoherence free subspaces. IBM Quantum has a clear roadmap to practical quantum advantage in the coming years. Keywords: secret sharing quantum error-correcting code symplectic form. In this paper, we consider to use the quantum stabilizer codes as secret sharing schemes for classical secrets. Nonstandard methods of error correction, e.g. We give explicit examples of various verifiable hybrid schemes based on existing quantum error correcting codes. Experimental implementations of error correction codes (these have mainly been done in NMR).ħ. Fault tolerance - how error correction can be used to prove the threshold theorem for quantum computation.Ħ. Gottesman's stabilizer formalism for quantum error correcting codes and its connection to classical error correction codes.ĥ. Simple examples of error correction codes - quantum repetition code, Shor's nine-qubit code, CSS codes and the 5 qubit code.Ĥ. The ``standard model'' of quantum error correction and how it leads to the requirements and definitions of quantum error correction codes.Ģ. As I see it, the main topics you could choose to cover are:ġ.
I have also written a dissertation on quantum error correction, although that was in graduate school, so maybe mine was more technical than yours has to be.
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