Editing (Symmetric) Private Information Retrieval (section)

==Protocols==
<!-- List of different types of example protocol achieving the functionality-->

===Classical database===
In the quantum setting, protocols aiming at achieving (S)PIR for a ''classical'' database fall into two main categories:
====Single-database protocols====
As in the classical setting, in the case of the database being owned by a ''single'' server, the trivial solution (downloading the whole database) is the only way to achieve information-theoretically secure PIR – even in the case of a specious (may deviate from the protocol if its malicious operations are unknown to the user) server [[#References|[2]]]. <br>
As for (quantum or classical) SPIR, it is impossible to achieve information-theoretic security with a single-server; this result was proved in the quantum setting by Lo [[#References|[3]]]. Intuitively, this comes from the fact that the (unique) trivial solution of information-theoretically secure PIR is the worst in terms of data privacy. Therefore, to design efficient PIR protocols or to achieve SPIR, several assumptions have been considered; they include:
* Hardness assumptions: PIR protocols with computational security.
* Assumptions on the adversarial model:
** to achieve SPIR: cheat-sensitive protocols (also known as quantum private queries (QPQ) protocols) where it is assumed that the server will not cheat if there is a non-zero probability that he will be caught cheating. 
***[[Quantum Private Queries Protocol Based on Quantum Oblivious Key Distribution|QPQ protocols based on quantum oblivious key distribution]]
***[[Quantum Private Queries Protocol Based on Quantum Random Access Memory|QPQ protocols based on quantum random access memory]]
** to achieve efficient PIR: assuming an honest server.
***[[Single-Database Quantum Private Information Retrieval in the Honest Server Model|QPIR protocols in the honest server model]]
* Prior shared entanglement between server and user: in the honest server model, efficient PIR protocols exist, however for a specious or malicious server, the trivial solution is optimal for PIR[[#References|[4]]].
**[[Single-Database Quantum Private Information Retrieval with Prior Shared Entanglement in the Honest Server Model|QPIR protocols with prior shared entanglement in the honest server model]]
* Relativistic assumptions: quantum SPIR protocols whose security uses properties from special relativity.
**[[Relativistic Quantum Oblivious Transfer|Relativistic QOT protocols]]

====Multi-database protocols====
It is possible to achieve information-theoretic (S)PIR with reduced communication complexity (i.e., compared to this of the trivial solution) by considering several servers instead of one, each holding a copy of the database, and with the help of extra assumptions. Usually, to achieve (S)PIR, it is assumed that the servers cannot communicate with each other during and after the protocol ended (no-communication assumption), and that servers share randomness (in the symmetric case only). Examples of such protocols are:


* [[Multi-Database Quantum Symmetric Private Information Retrieval without Shared Randomness|Quantum multi-database SPIR protocols without shared randomness]] (replaced by prior shared entanglement between servers)
* [[Multi-Database Classical Symmetric Private Information Retrieval with Quantum Key Distribution|Classical multi-database SPIR protocols with QKD secured classical channels]]
* [[Multi-Database Quantum Symmetric Private Information Retrieval for Communicating and Colluding Servers|Multi-database quantum (S)PIR protocols for communicating and colluding servers]] – to do without the no-communication assumption
* [[Multi-Database Quantum Symmetric Private Information Retrieval for Coded Servers|Multi-database quantum (S)PIR protocols for coded servers]]

===Quantum database===
For the case of a ''quantum'' database, the trivial solution of downloading the whole database is proved to be optimal for one-round QPIR, and for multi-round QPIR in the blind setting (i.e., the servers do not have a classical description of the quantum states of the database) and for the honest server model (and any other attack model)[[#References|[1]]].<br>

Prior shared entanglement between the user and the server allows for efficient one-server QPIR protocols in the honest server model and in the blind setting. Multi-database QSPIR protocols for a quantum database with pure states, in the visible setting (servers know a classical description of the quantum database elements) exist as shown by Song and Hayashi [[#References|[1]]].

* [[Single-Database Quantum Private Information Retrieval for a Quantum Database|Single-database quantum PIR protocols in the honest server model and in the blind setting for a quantum database]]
* [[Multi-Database Quantum Symmetric Private Information Retrieval for a Quantum Database|Multi-database quantum SPIR protocols in the visible setting for a quantum database]]