Quantum Threshold Scheme , no cloning theorem

In summary, a (k,n) quantum threshold scheme (QTS) is a way to divide an unknown secret quantum state |S> into n pieces (shares), with the condition that k must be greater than n/2. This restriction is necessary to avoid violating the quantum no-cloning theorem, as it would allow two separate groups to reconstruct the secret information. For more information, you can refer to the Generalized Quantum Secret Sharing paper or the PI institute's intro page on quantum secret sharing.
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Shivam Saluja
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A (k,n) quantum threshold scheme (QTS) as a method to split up an unknown secret quantum state | S > into n pieces (shares) with the restriction that k > n / 2 (for if this inequality were violated, two disjoint sets of players can reconstruct the secret, in violation of the quantum no-cloning theorem).
what is the reason behind the above restriction?
 
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You should link to the paper you're confused about ( Generalized Quantum Secret Sharing ) instead of just quoting it (also you should actually indicate that you're quoting; otherwise it looks like you know that material already or that you're plagiarising).

I'm not sure exactly what you're asking. The reason ##k## has to be greater than ##\frac{n}{2}## is stated in the quote you included: otherwise you could violate the no-cloning theorem by decoding the secret quantum information two independent times.

Maybe the PI institute's intro page on quantum secret sharing will help?
 
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1. What is a Quantum Threshold Scheme?

A Quantum Threshold Scheme is a type of quantum cryptography that allows for secure sharing of information among multiple parties. It uses quantum properties to distribute secret information and allows for the detection of any attempt at eavesdropping.

2. How does a Quantum Threshold Scheme work?

In a Quantum Threshold Scheme, secret information is divided into shares and distributed among participants. A certain number of shares, known as the threshold, are required to retrieve the original secret information. Any attempt at accessing the information without the required number of shares will result in the information being destroyed.

3. What is the no cloning theorem in relation to Quantum Threshold Scheme?

The no cloning theorem states that it is impossible to create an exact copy of an unknown quantum state. This plays a crucial role in quantum cryptography, as it prevents potential eavesdroppers from copying the shared secret information without being detected.

4. How is Quantum Threshold Scheme different from traditional cryptography?

Traditional cryptography relies on mathematical algorithms and large prime numbers to secure information. Quantum Threshold Scheme, on the other hand, uses quantum properties such as superposition and entanglement to distribute and protect secret information, making it more secure against potential attacks.

5. What are the potential applications of Quantum Threshold Scheme?

Quantum Threshold Scheme has potential applications in secure communication, data sharing, and even in quantum computing. It can be used in industries such as finance, healthcare, and government to protect sensitive information from being intercepted or accessed by unauthorized parties.

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