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arXiv:2610.09022

Teleportation of a programmable gate

Nada Ali, Mark Hillery

quant-phSubmitted Oct 6, 2026• Announced Oct 8, 2026• 0 citations
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Abstract

Alice and Bob each have a qubit, and they would like to perform a two-qubit gate on them with the assistance of Charlie. The action of this gate depends on a parameter, which either Charlie knows, will receive later as classical information, or is encoded in a program state. We discuss both the case in which Alice and Bob send Charlie their qubits, which he entangles with his state, and the case where Alice and Bob use teleportation to entangle their states with Charlie's state. All of these procedures depend on the ability of Alice and Bob to apply local correction operations that depend on the results of measurements that Charlie makes, and we discuss under what conditions such operations are possible.

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The problem of discriminating between non-orthogonal states is one that has generated a lot of interest. This basic formalism is useful in many areas of quantum information. It serves as a fundamental basis for many quantum key distribution schemes, it functions as an integral part of other quantum algorithms, and it is useful in experimental settings where orthogonal states are not always possible to generate. Additionally, the discrimination problem reveals important fundamental properties, and is intrinsically related to entanglement. In this thesis, the focus is on exploring the problem of sequentially discriminating between non-orthogonal states. In the simplest version these schemes, Alice sends one of two known pure states to Bob who performs a non-optimal discrimination procedure such that the post measurement states resulting from his measurement can then be discriminated by a third participant, Charlie. In these schemes, the goal is to optimize the joint probability of both Bob and Charlie succeeding. In devising such a scheme, there are several different criteria that can be prioritized. The most basic scheme, referred to as Minimum Error (ME) discrimination, prioritizes Bob's and Charlie's abilities to successfully determine which state was sent by Alice. In this scheme, Bob and Charlie each set up two detectors and based on the result from the detector they make a guess as to which state was sent. For instance, if Bob registers a click in his first detector, he concludes that Alice sent the first state. As each detector has some probability to produce a result for either incoming result, Bob and Charlie optimize their joint probability of success by optimizing the probability that each detector will fire when the correlated state is sent by Alice. Another possible scheme, referred to as Unambiguous Discrimination (UD), prioritizes Bob's and Charlie's ability to correctly determine the state sent by Alice. In this scheme, Bob and Charlie each set up three detectors, where if a result is obtained from the first two detectors Bob or Charlie can determine with certainty which state was sent by Alice. One final setup, referred to as Discrimination with a Fixed Rate of Inconclusive Outcome, is a combination of the previous two schemes, where Bob and Charlie maximize their probability of successfully determining the state sent by Alice where they allow some fixed probability that they will not be able to determine which state Alice sent. This fixed inconclusive probability allows Bob and Charlie to control how much they prioritize correctly determining the state that was sent, as in the Unambiguous Discrimination, versus prioritizing successfully determining the state sent by Alice, as in Minimum Error discrimination. One final topic that will be discussed by this thesis is Quantum Retrodiction. Quantum Retrodiction applies an alternate perspective on the communication protocol between Alice and Bob. In the predictive model, Alice calculates the probability that Bob gets a specific measurement result given that she prepares her system in a specific state. In the retrodictive model, Bob calculates the probability that Alice prepared her system in a specific state given the result of his measurement. This alternate perspective on the communication procedure gives new a new understanding and new tools for approaching the problem of state discrimination, as exemplified by applying the retrodictive formalism to unambiguous discrimination.

•Jan 1, 2019•0 citations
Alice and Bob each have a qubit, and they would like to perform a two-qubit gate on them with the assistance of Charlie. The action of this gate depends on a parameter, which either Charlie knows, will receive later as classical information, or is encoded in a program state. We discuss both the case in which Alice and Bob send Charlie their qubits, which he entangles with his state, and the case where Alice and Bob use teleportation to entangle their states with Charlie's state. All of these procedures depend on the ability of Alice and Bob to apply local correction operations that depend on the results of measurements that Charlie makes, and we discuss under what conditions such operations are possible.
In a recently introduced coset guessing game, Alice plays against Bob and Charlie, aiming to meet a joint winning condition. Bob and Charlie can only communicate before the game starts to devise a joint strategy. The game we consider begins with Alice preparing a 2m-qubit quantum state based on a random selection of three parameters. She sends the first m qubits to Bob and the rest to Charlie, and then reveals to them her choice for one of the parameters. Bob is supposed to guess one of the hidden parameters, Charlie the other, and they win if both guesses are correct. From previous work, we know that the probability of Bob’s and Charlie’s guesses being simultaneously correct goes to zero exponentially as m increases. We derive a tight upper bound on this probability and show how Bob and Charlie can achieve it. While developing an optimal strategy, we devised an encoding circuit using only and Hadamard gates, which builds CSS codes from EPR pairs using only local operations. We found that the role of quantum information that Alice communicates to Bob and Charlie is to make their responses correlated rather than improve their individual (marginal) correct guessing rates.
Abstract This article proposes an asymmetric bidirectional hierarchical quantum teleportation protocol, which is based on a quantum channel composed of a maximum of eight-qubit entangled state. With this method, Alice can transmit an unknown single-qubit state to Bob, meanwhile, Bob can transmit an arbitrary unknown two-qubit quantum state to Alice. As a sender with high authority, Bob can send any unknown two-qubit quantum state to Alice only under the sole control of the controller Charlie; Alice, as a sender with low-level permissions, if Bob intends to receive the unknown single-qubit quantum state sent by Alice, he must get the permission and assistance of Charlie and David to complete the communication.
The problem of discriminating between non-orthogonal states is one that has generated a lot of interest. This basic formalism is useful in many areas of quantum information. It serves as a fundamental basis for many quantum key distribution schemes, it functions as an integral part of other quantum algorithms, and it is useful in experimental settings where orthogonal states are not always possible to generate. Additionally, the discrimination problem reveals important fundamental properties, and is intrinsically related to entanglement. In this thesis, the focus is on exploring the problem of sequentially discriminating between non-orthogonal states. In the simplest version these schemes, Alice sends one of two known pure states to Bob who performs a non-optimal discrimination procedure such that the post measurement states resulting from his measurement can then be discriminated by a third participant, Charlie. In these schemes, the goal is to optimize the joint probability of both Bob and Charlie succeeding. In devising such a scheme, there are several different criteria that can be prioritized. The most basic scheme, referred to as Minimum Error (ME) discrimination, prioritizes Bob's and Charlie's abilities to successfully determine which state was sent by Alice. In this scheme, Bob and Charlie each set up two detectors and based on the result from the detector they make a guess as to which state was sent. For instance, if Bob registers a click in his first detector, he concludes that Alice sent the first state. As each detector has some probability to produce a result for either incoming result, Bob and Charlie optimize their joint probability of success by optimizing the probability that each detector will fire when the correlated state is sent by Alice. Another possible scheme, referred to as Unambiguous Discrimination (UD), prioritizes Bob's and Charlie's ability to correctly determine the state sent by Alice. In this scheme, Bob and Charlie each set up three detectors, where if a result is obtained from the first two detectors Bob or Charlie can determine with certainty which state was sent by Alice. One final setup, referred to as Discrimination with a Fixed Rate of Inconclusive Outcome, is a combination of the previous two schemes, where Bob and Charlie maximize their probability of successfully determining the state sent by Alice where they allow some fixed probability that they will not be able to determine which state Alice sent. This fixed inconclusive probability allows Bob and Charlie to control how much they prioritize correctly determining the state that was sent, as in the Unambiguous Discrimination, versus prioritizing successfully determining the state sent by Alice, as in Minimum Error discrimination. One final topic that will be discussed by this thesis is Quantum Retrodiction. Quantum Retrodiction applies an alternate perspective on the communication protocol between Alice and Bob. In the predictive model, Alice calculates the probability that Bob gets a specific measurement result given that she prepares her system in a specific state. In the retrodictive model, Bob calculates the probability that Alice prepared her system in a specific state given the result of his measurement. This alternate perspective on the communication procedure gives new a new understanding and new tools for approaching the problem of state discrimination, as exemplified by applying the retrodictive formalism to unambiguous discrimination.