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Unconstrained Summoning

Adrian Kent

Published Jun 5, 2018• 0 citations
OpenAlex

Abstract

We define a summoning task to require propagating an unknown quantum state to a point in space-time belonging to a set determined by classical inputs at points in space-time. We consider the classical analogue, in which a known classical state must be returned at precisely one allowed point. We show that, when the inputs are unconstrained, any summoning task that is possible in the classical case is also possible in the quantum case.

Related papers

Unconstrained summoning for relativistic quantum information processing

Adrian Kent

We define a summoning task to require propagating an unknown quantum state to a point in space-time belonging to a set determined by classical inputs at points in space-time. We consider the classical analog, in which a known classical state must be returned at precisely one allowed point. We show that, when the inputs are unconstrained, any summoning task that is possible in the classical case is also possible in the quantum case.

arXiv:1806.01736•Physical Review A•Dec 26, 2018•7 citations

Quantum paradox of choice: More freedom makes summoning a quantum state harder

Emily Adlam, Adrian Kent

The properties of quantum information in space-time can be investigated by studying operational tasks, such as ``summoning,'' in which an unknown quantum state is supplied at one point and a call is made at another for it to be returned at a third. Hayden and May [arXiv:1210.0913] recently proved necessary and sufficient conditions for guaranteeing successful return of a summoned state for finite sets of call and return points when there is a guarantee of at most one summons. We prove necessary and sufficient conditions when there may be several possible summonses and complying with any one constitutes success, and we demonstrate the existence of an apparent paradox: The extra freedom makes it strictly harder to complete the summoning task. This result has practical applications for distributed quantum computing and cryptography and implications for our understanding of relativistic quantum information and its localization in space-time.

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Entanglement summoning from entanglement sharing

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In an entanglement summoning task, a set of distributed, co-operating parties attempt to fulfill requests to prepare entanglement between distant locations. The parties share limited communication resources: timing constraints may require the entangled state be prepared before some pairs of distant parties can communicate, and a restricted set of links in a quantum network may further constrain communication. Building on earlier work, we continue the characterization of entanglement summoning. We give an if and only if condition on entanglement summoning tasks with only bidirected causal connections, and provide a set of sufficient conditions addressing the most general case containing both oriented and bidirected causal connections. Our results rely on the recent development of entanglement sharing schemes.

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Summoning, No-Signalling and Relativistic Bit Commitments

Adrian Kent

Summoning is a task between two parties, Alice and Bob, with distributed networks of agents in space-time. Bob gives Alice a random quantum state, known to him but not her, at some point. She is required to return the state at some later point, belonging to a subset defined by communications received from Bob at other points. Many results about summoning, including the impossibility of unrestricted summoning tasks and the necessary conditions for specific types of summoning tasks to be possible, follow directly from the quantum no-cloning theorem and the relativistic no-superluminal-signalling principle. The impossibility of cloning devices can be derived from the impossibility of superluminal signalling and the projection postulate, together with assumptions about the devices' location-independent functioning. In this qualified sense, known summoning results follow from the causal structure of space-time and the properties of quantum measurements. Bounds on the fidelity of approximate cloning can be similarly derived. Bit commitment protocols and other cryptographic protocols based on the no-summoning theorem can thus be proven secure against some classes of post-quantum but non-signalling adversaries.

arXiv:1804.05246•Entropy•May 25, 2019•1 citation

A Quantum Paradox of Choice and Purported Classical Analogues

Emily Adlam, Adrian Kent

We recently considered the task of summoning an unknown quantum state and proved necessary and sufficient conditions for Alice to be able to guarantee to complete the task when there may be several possible calls, of which she need only respond to one. We showed that these are strictly stronger conditions than those previously established by Hayden and May for the case where Alice knows there will only be one call. We introduced the concept of a {\it quantum paradox of choice} to summarize the implications of these results: Alice is given more options to complete our version of the task, yet one can easily construct examples where our version is impossible and the apparently simpler version considered by Hayden-May is possible. Finkelstein has argued that one can identify analogous classical paradoxes of choice in a relativistic setting. We examine Finkelstein's proposed classical tasks and explain why they seem to us disanalogous.

arXiv:1509.08094•Sep 27, 2015•1 citation

Summoning information in spacetime, or where and when can a qubit be?

Patrick M. Hayden, Alex May

Abstract One of the most important properties of quantum information, and the one ultimately responsible for its cryptographic applications, is that it can not be copied. That statement, however, is not completely accurate. While the no-cloning theorem of quantum mechanics prevents quantum information from being copied in space, the reversibility of microscopic physics actually requires that the information be copied in time. In spacetime as a whole, therefore, quantum information is widely replicated but in a restricted fashion. We fully characterize which regions of spacetime can all hold the same quantum information. Because quantum information can be delocalized through quantum error correction and teleportation, it need not follow well-defined trajectories. Instead, replication of the information in any configuration of spacetime regions not leading to violations of causality or the no-cloning principle is allowed. To demonstrate this, we answer the operational question of exactly when the information can be summoned to a set of spacetime points, showing how to do so efficiently using a combination of teleportation and codeword-stabilized quantum codes. This provides a simple and complete description of where and when a qubit can be located in spacetime, revealing a remarkable variety of possibilities.

arXiv:1210.0913•Journal of Physics A Mathematical and Theoretical•Mar 22, 2016•32 citations
We define a summoning task to require propagating an unknown quantum state to a point in space-time belonging to a set determined by classical inputs at points in space-time. We consider the classical analogue, in which a known classical state must be returned at precisely one allowed point. We show that, when the inputs are unconstrained, any summoning task that is possible in the classical case is also possible in the quantum case.
The properties of quantum information in space-time can be investigated by studying operational tasks, such as ``summoning,'' in which an unknown quantum state is supplied at one point and a call is made at another for it to be returned at a third. Hayden and May [arXiv:1210.0913] recently proved necessary and sufficient conditions for guaranteeing successful return of a summoned state for finite sets of call and return points when there is a guarantee of at most one summons. We prove necessary and sufficient conditions when there may be several possible summonses and complying with any one constitutes success, and we demonstrate the existence of an apparent paradox: The extra freedom makes it strictly harder to complete the summoning task. This result has practical applications for distributed quantum computing and cryptography and implications for our understanding of relativistic quantum information and its localization in space-time.
In an entanglement summoning task, a set of distributed, co-operating parties attempt to fulfill requests to prepare entanglement between distant locations. The parties share limited communication resources: timing constraints may require the entangled state be prepared before some pairs of distant parties can communicate, and a restricted set of links in a quantum network may further constrain communication. Building on earlier work, we continue the characterization of entanglement summoning. We give an if and only if condition on entanglement summoning tasks with only bidirected causal connections, and provide a set of sufficient conditions addressing the most general case containing both oriented and bidirected causal connections. Our results rely on the recent development of entanglement sharing schemes.
Summoning is a task between two parties, Alice and Bob, with distributed networks of agents in space-time. Bob gives Alice a random quantum state, known to him but not her, at some point. She is required to return the state at some later point, belonging to a subset defined by communications received from Bob at other points. Many results about summoning, including the impossibility of unrestricted summoning tasks and the necessary conditions for specific types of summoning tasks to be possible, follow directly from the quantum no-cloning theorem and the relativistic no-superluminal-signalling principle. The impossibility of cloning devices can be derived from the impossibility of superluminal signalling and the projection postulate, together with assumptions about the devices' location-independent functioning. In this qualified sense, known summoning results follow from the causal structure of space-time and the properties of quantum measurements. Bounds on the fidelity of approximate cloning can be similarly derived. Bit commitment protocols and other cryptographic protocols based on the no-summoning theorem can thus be proven secure against some classes of post-quantum but non-signalling adversaries.
We recently considered the task of summoning an unknown quantum state and proved necessary and sufficient conditions for Alice to be able to guarantee to complete the task when there may be several possible calls, of which she need only respond to one. We showed that these are strictly stronger conditions than those previously established by Hayden and May for the case where Alice knows there will only be one call. We introduced the concept of a {\it quantum paradox of choice} to summarize the implications of these results: Alice is given more options to complete our version of the task, yet one can easily construct examples where our version is impossible and the apparently simpler version considered by Hayden-May is possible. Finkelstein has argued that one can identify analogous classical paradoxes of choice in a relativistic setting. We examine Finkelstein's proposed classical tasks and explain why they seem to us disanalogous.
Abstract One of the most important properties of quantum information, and the one ultimately responsible for its cryptographic applications, is that it can not be copied. That statement, however, is not completely accurate. While the no-cloning theorem of quantum mechanics prevents quantum information from being copied in space, the reversibility of microscopic physics actually requires that the information be copied in time. In spacetime as a whole, therefore, quantum information is widely replicated but in a restricted fashion. We fully characterize which regions of spacetime can all hold the same quantum information. Because quantum information can be delocalized through quantum error correction and teleportation, it need not follow well-defined trajectories. Instead, replication of the information in any configuration of spacetime regions not leading to violations of causality or the no-cloning principle is allowed. To demonstrate this, we answer the operational question of exactly when the information can be summoned to a set of spacetime points, showing how to do so efficiently using a combination of teleportation and codeword-stabilized quantum codes. This provides a simple and complete description of where and when a qubit can be located in spacetime, revealing a remarkable variety of possibilities.