Editing Quantum Bit Commitment
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This [https://arxiv.org/abs/1108.2879 example protocol] achieves the task of [[ | This [https://arxiv.org/abs/1108.2879 example protocol] achieves the task of [[Bit Commitment]] securely by using a relativistic scheme. | ||
In bit commitment, the | In bit commitment, the commiter "commits" to a particular bit value. | ||
The receiver knows nothing about the committed bit value until the | The receiver knows nothing about the committed bit value until the commiter chooses to do so (''hiding property''). | ||
The receiver has a guarantee that once committed, the | The receiver has a guarantee that once committed, the commiter cannot change the committed bit value (''binding property''). | ||
Bit commitment cannot be done with non-relativistic schemes as proved by Mayers in his [https://arxiv.org/abs/quant-ph/9605044 paper]. | |||
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* Quantum theory is correct. | * Quantum theory is correct. | ||
* The background space-time is approximately Minkowski. | * The background space-time is approximately Minkowski. | ||
* The | * The commiter can signal at precisely light speed. | ||
* All information processing is instantaneous. | * All information processing is instantaneous. | ||
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==Outline== | ==Outline== | ||
The receiver securely pre-prepares a set of qubits randomly from the BB84 states and sends them to the commiter. | |||
To commit to the bit 0, the commiter measures the received qubits in the standard basis and in Hadamard basis to commit to 1. | |||
The commiter then sends the outcomes to their agents over secure classical channels. | |||
To unveil the committed bit, the commiter's agents reveal the outcomes to the receiver's agents. | |||
The receiver's agents then check if the outcomes they have received are the same and consistent with the states sent to the commiter. | |||
If the check passes, the receiver accepts the commitment. | |||
==Notation== | ==Notation== | ||
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* <math>N</math>: Number of random qubits used in the commitment. | * <math>N</math>: Number of random qubits used in the commitment. | ||
* <math>|\psi_i\rangle</math>: Random BB84 qubit with index <math>i</math>. | * <math>|\psi_i\rangle</math>: Random BB84 qubit with index <math>i</math>. | ||
* <math>P</math>: Space-time origin point for the Minkowski space | * <math>P</math>: Space-time origin point for the Minkowski space. | ||
* <math>Q_0</math>: Commiter's first agent. | * <math>Q_0</math>: Commiter's first agent. | ||
* <math>Q_1</math>: Commiter's second agent. | * <math>Q_1</math>: Commiter's second agent. | ||
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* Secure classical channels between the parties and their agents. | * Secure classical channels between the parties and their agents. | ||
* Basic state preparation abilities for the receiver. | * Basic state preparation abilities for the receiver. | ||
* Instantaneous measurement capabilities for the | * Instantaneous measurement capabilities for the commiter. | ||
<br/> | |||
[[File:Quantum Bit Commitment.png|center|Quantum Bit Commitment]] | |||
==Properties== | ==Properties== | ||
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== | ==Pseudocode== | ||
The | The commiter and the receiver agree on the space-time origin point P and two light-like separated points where the two agents of each party will be stationed. | ||
===Commitment Phase=== | ===Commitment Phase=== |