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Zero knowledge convincing protocol on quantum bit is impossible

Horodecki, P, Horodecki, M, Horodecki, R

Published Oct 12, 2000• 2 citations
OpenAlex

Abstract

Consider two parties: Alice and Bob and suppose that Bob is given a qubit system in a quantum state $\\phi$, unknown to him. Alice knows $\\phi$ and she is supposed to convince Bob that she knows $\\phi$ sending some test message. Is it possible for her to convince Bob providing him "zero knowledge" i. e. no information about $\\phi$ he has? We prove that there is no "zero knowledge" protocol of that kind. In fact it turns out that basing on Alice message, Bob (or third party - Eve - who can intercept the message) can synthetize a copy of the unknown qubit state $\\phi$ with nonzero probability. This "no-go" result puts general constrains on information processing where information {\\it about} quantum state is involved.

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Consider two parties: Alice and Bob and suppose that Bob is given a qubit system in a quantum state phi\\phiphi, unknown to him. Alice knows phi\\phiphi and she is supposed to convince Bob that she knows phi\\phiphi sending some test message. Is it possible for her to convince Bob providing him "zero knowledge" i. e. no information about phi\\phiphi he has? We prove that there is no "zero knowledge" protocol of that kind. In fact it turns out that basing on Alice message, Bob (or third party - Eve - who can intercept the message) can synthetize a copy of the unknown qubit state phi\\phiphi with nonzero probability. This "no-go" result puts general constrains on information processing where information {\it about} quantum state is involved.
Consider two parties: Alice and Bob and suppose that Bob is given a qubit system in a quantum state ϕ , unknown to him. Alice knows ϕ and she is supposed to convince Bob that she knows ϕ sending some test message. Is it possible for her to convince Bob providing him "zero knowledge" i. e. no information about ϕ he has? We prove that there is no "zero knowledge" protocol of that kind. In fact it turns out that basing on Alice message, Bob (or third party - Eve - who can intercept the message) can synthetize a copy of the unknown qubit state ϕ with nonzero probability. This "no-go" result puts general constrains on information processing where information about quantum state is involved.
We define a keyless communication as a message sent from one party (Alice) to another (Bob), such that the message is totally secure. This means that if a third party (Eve) is trying to eavesdrop, she will receive only random bits. She cannot understand the content of the message, even if she is able to intercept it in such away that Alice and Bob do not know it has been intercepted. For such a totally secure message, Alice and Bob do not need to set up any key beforehand, as it can add no further security. Starting with a system that we felt sure met such criteria, we were shocked to find out that it could be broken in at least two ways, by a semi-classical method and by a quantum method, such that Eve could read a message and Alice and Bob would not know it. Alice and Bob can counter such eavesdropping, but only by sending out test messages. This will enable them to ascertain that Eve is on the line, but then she can still occasionally pick up snippets of their conversation. In that case, in order to be totally secure, it is better to establish an unbreakable key beforehand. We postulate and give plausibility arguments that in general it is impossible to establish keyless communication between two parties.
Bob has a black box that emits a single pure state qudit which is, from his perspective, uniformly distributed. Alice wishes to give Bob evidence that she has knowledge about the emitted state while giving him little or no information about it. We show that zero-knowledge evidencing of such knowledge is impossible in quantum relativistic protocols, extending a previous result of Horodecki, Horodecki, and Horodecki. We also show that no such protocol can be both sound and complete. We present a new quantum relativistic protocol which we conjecture to be close to optimal in security against Alice and which reveals little knowledge to Bob, for large dimension d. We analyze its security against general attacks by Bob and restricted attacks by Alice.
A theoretical scheme for zero-knowledge proof quantum identity authentication is proposed by the absolutely impartial third party CA， which has been realized based on remote state preparation and assisted cloning controlled means. In the process of identification， only CA knows the information of quantum identity card and the first party Alice and the second party Bob can accomplish the quantum identity authentication without knowing it. We discuss the probability of accomplishing this job. The security of this scheme is unconditional and it is guaranteed by quantum mechanism.
In this paper, we propose a method of enciphering quantum states of two-state systems (qubits) for sending them in secrecy without entangled qubits shared by two legitimate users (Alice and Bob). This method has the following two properties. First, even if an eavesdropper (Eve) steals qubits, she can extract information from them with only a certain probability at most. Second, Alice and Bob can confirm that the qubits are transmitted between them correctly by measuring a signature. If Eve measures m qubits one by one from n enciphered qubits and sends alternative ones (the intercept/resend attack), the probability that Alice and Bob do not notice Eve's action is equal to (3/4) m or less. Passwords for decryption and the signature are given by classical binary strings and they are disclosed through a public channel. Enciphering classical information by this method is equivalent to the one-time pad method with distributing a classical key (random binary string) by the BB84 protocol. If Eve takes away qubits, Alice and Bob lose the original quantum information. If we apply our method to a state in iteration, Eve's success probability decreases exponentially. We cannot examine security against the case that Eve makes an attack using entanglement. This remains to be solved in the future.
A scheme is proposed for quantum information splitting of a two-qubit Bell state by using a four-qubit entangled state as a quantum channel. In the scenario, it is supposed that there are three legitimate parties, say Alice, Bob and Charlie. Alice is the sender of quantum information. Bob and Charlie are two agents. Alice first performs GHZ state measurement and tells Bob and Charlie the measurement results via a classical channel. It is impossible for Bob to reconstruct the original state with local operations unless help is obtained from Charlie. If Charlie allows Bob to reconstruct the original state information, he needs to perform a single-qubit measurement and tell Bob the measurement result. Using the measurement results from Alice and Charlie, Bob can reconstruct the original state. We also consider the problem of security attacks. This protocol is considered to be secure.