Port-Based State Preparation and Applications
Abstract: We introduce Port-Based State Preparation (PBSP), a teleportation task where Alice holds a complete classical description of the target state and Bob's correction operations are restricted to only tracing out registers. We show a protocol that implements PBSP with error decreasing exponentially in the number of ports, in contrast to the polynomial trade-off for the related task of Port-Based Teleportation, and we prove that this is optimal when a maximally entangled resource state is used. As an application, we introduce approximate Universal Programmable Hybrid Processors (UPHP). Here the goal is to encode a unitary as a quantum state, and the UPHP can apply this unitary to a quantum state when knowing its classical description. We give a construction that needs strictly less memory in terms of dimension than the optimal approximate Universal Programmable Quantum Processor achieving the same error. Additionally, we provide lower bounds for the optimal trade-off between memory and error of UPHPs.
- “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels” In Physical review letters 70.13, 1993, pp. 1895–1899 DOI: 10.1103/PhysRevLett.70.1895
- M.A. Nielsen and Isaac L. Chuang “Programmable Quantum Gate Arrays” In Physical review letters 79.2, 1997, pp. 321–324 DOI: 10.1103/PhysRevLett.79.321
- “Dense quantum coding and a lower bound for 1-way quantum automata” In Proceedings of the thirty-first annual ACM symposium on Theory of Computing Atlanta Georgia USA: ACM, 1999, pp. 376–383 DOI: 10.1145/301250.301347
- Ashwin Nayak “Optimal lower bounds for quantum automata and random access codes” IEEE, 1999, pp. 369–376 DOI: 10.1109/SFFCS.1999.814608
- “Remote state preparation” In Physical review letters 87.7, 2001, pp. 077902 DOI: 10.1103/PhysRevLett.87.077902
- “Remote preparation of quantum states” In IEEE Transactions on Information Theory 51.1, 2005, pp. 56–74 DOI: 10.1109/TIT.2004.839476
- Mark Hillery, Mário Ziman and Vladimír Bužek “Approximate programmable quantum processors” In Physical Review A 73.2, 2006, pp. 022345 DOI: 10.1103/PhysRevA.73.022345
- David Pérez-García “Optimality of programmable quantum measurements” In Physical Review A 73.5, 2006, pp. 052315 DOI: 10.1103/PhysRevA.73.052315
- “Asymptotic teleportation scheme as a universal programmable quantum processor” In Physical review letters 101.24, 2008, pp. 240501 DOI: 10.1103/PhysRevLett.101.240501
- “Simplified instantaneous non-local quantum computation with applications to position-based cryptography” In New Journal of Physics 13.9, 2011, pp. 093036 DOI: 10.1088/1367-2630/13/9/093036
- Damián Pitalúa-García “Deduction of an upper bound on the success probability of port-based teleportation from the no-cloning theorem and the no-signaling principle” In Physical Review A 87.4, 2013, pp. 040303 DOI: 10.1103/PhysRevA.87.040303
- Satoshi Ishizaka “Some remarks on port-based teleportation” In arXiv preprint, 2015 arXiv:1506.01555
- “Quantum communication complexity advantage implies violation of a Bell inequality” In Proceedings of the National Academy of Sciences 113.12, 2016, pp. 3191–3196 DOI: 10.1073/pnas.1507647113
- “Port-based teleportation in arbitrary dimension” In Scientific Reports 7.1, 2017, pp. 10871 DOI: 10.1038/s41598-017-10051-4
- Christian Majenz “Entropy in Quantum Information Theory – Communication and Cryptography” In Ph.D. thesis, Faculty of Science, University of Copenhagen, 2018 arXiv:1810.10436
- “Optimal port-based teleportation” In New Journal of Physics 20.5, 2018, pp. 053006 DOI: 10.1088/1367-2630/aab8e7
- Aleksander M Kubicki, Carlos Palazuelos and David Pérez-García “Resource quantification for the no-programing theorem” In Physical review letters 122.8, 2019, pp. 080505 DOI: 10.1103/PhysRevLett.122.080505
- “Fundamental limits to quantum channel discrimination” In npj Quantum Information 5.1, 2019 DOI: 10.1038/s41534-019-0162-y
- “Probabilistic exact universal quantum circuits for transforming unitary operations” In Physical Review A 100.6, 2019 DOI: 10.1103/physreva.100.062339
- “Reversing Unknown Quantum Transformations: Universal Quantum Circuit for Inverting General Unitary Operations” In Physical review letters 123.21, 2019 DOI: 10.1103/physrevlett.123.210502
- Michal Sedlák, Alessandro Bisio and Mário Ziman “Optimal Probabilistic Storage and Retrieval of Unitary Channels” In Physical Review Letters 122.17, 2019 DOI: 10.1103/physrevlett.122.170502
- Yuxiang Yang, Renato Renner and Giulio Chiribella “Optimal Universal Programming of Unitary Gates” In Physical review letters 125.21, 2020, pp. 210501 DOI: 10.1103/PhysRevLett.125.210501
- “Asymptotic Performance of Port-Based Teleportation” In Communications in Mathematical Physics 381.1, 2021, pp. 379–451 DOI: 10.1007/s00220-020-03884-0
- Felix Leditzky “Optimality of the pretty good measurement for port-based teleportation” In Letters in Mathematical Physics 112.5, 2022, pp. 98 DOI: 10.1007/s11005-022-01592-5
- Jiani Fei, Sydney Timmerman and Patrick Hayden “Efficient Quantum Algorithm for Port-based Teleportation” In arXiv preprint, 2023 arXiv:2310.01637
- Dmitry Grinko, Adam Burchardt and Maris Ozols “Efficient quantum circuits for port-based teleportation” In arXiv preprint, 2023 arXiv:2312.03188
- Quynh T. Nguyen “The mixed Schur transform: efficient quantum circuit and applications” In arXiv preprint, 2023 arXiv:2310.01613
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