Bounds on continuous entanglement gain
Entanglement is a physical resource that is important in quantum teleportation, quantum dense coding and quantum cryptography. In this thesis, we investigate entanglement distribution between particles A and B (possibly located in different laboratories) via continuous interaction with an ancilla, C...
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Final Year Project (FYP) |
| Language: | English |
| Published: |
2018
|
| Subjects: | |
| Online Access: | http://hdl.handle.net/10356/75304 |
| _version_ | 1811677736386691072 |
|---|---|
| author | Koo, Edmund Sui Ho |
| author2 | Tomasz Paterek |
| author_facet | Tomasz Paterek Koo, Edmund Sui Ho |
| author_sort | Koo, Edmund Sui Ho |
| collection | NTU |
| description | Entanglement is a physical resource that is important in quantum teleportation, quantum dense coding and quantum cryptography. In this thesis, we investigate entanglement distribution between particles A and B (possibly located in different laboratories) via continuous interaction with an ancilla, C. We assume that A and B do not interact directly with each other, but only via C, and therefore the total Hamiltonian is of the form HAC + HBC. Our first result is the simplification of the expressions for HAC and HBC for a class of commuting Hamiltonians, i.e. [HAC, HBC] = 0 in which HAC is neither a free Hamiltonian on A nor a free Hamiltonian on C (which implies that A and C interact), and likewise HBC is neither a free Hamiltonian on B nor a free Hamiltonian on C. Using these simplifications, we looked at the time evolution of pure product states |αβγi and bi-product states |χiAB |γiC . We were able to analytically prove for pure product states that entanglement A : BC (or B : AC) is bounded by entanglement AB : C, that is the amount of entanglement in C. For bi-product states, we found a promising bound stating that entanglement gain, i.e. entanglement at time t minus initial entanglement is bounded by the entanglement in C. This is confirmed by extensive numerical simulations. We also considered the case where HAC realizes the swap operator SA−C at a particular time and swaps the state of A with C while HBC is just the identity operator. This scenario falls outside the class considered above. For this case, we managed to prove analytically (for bi-product states |χiAB |γiC ) the same bound that we conjectured above |
| first_indexed | 2024-10-01T02:42:06Z |
| format | Final Year Project (FYP) |
| id | ntu-10356/75304 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T02:42:06Z |
| publishDate | 2018 |
| record_format | dspace |
| spelling | ntu-10356/753042023-02-28T23:11:23Z Bounds on continuous entanglement gain Koo, Edmund Sui Ho Tomasz Paterek School of Physical and Mathematical Sciences DRNTU::Science::Physics::Atomic physics::Quantum theory Entanglement is a physical resource that is important in quantum teleportation, quantum dense coding and quantum cryptography. In this thesis, we investigate entanglement distribution between particles A and B (possibly located in different laboratories) via continuous interaction with an ancilla, C. We assume that A and B do not interact directly with each other, but only via C, and therefore the total Hamiltonian is of the form HAC + HBC. Our first result is the simplification of the expressions for HAC and HBC for a class of commuting Hamiltonians, i.e. [HAC, HBC] = 0 in which HAC is neither a free Hamiltonian on A nor a free Hamiltonian on C (which implies that A and C interact), and likewise HBC is neither a free Hamiltonian on B nor a free Hamiltonian on C. Using these simplifications, we looked at the time evolution of pure product states |αβγi and bi-product states |χiAB |γiC . We were able to analytically prove for pure product states that entanglement A : BC (or B : AC) is bounded by entanglement AB : C, that is the amount of entanglement in C. For bi-product states, we found a promising bound stating that entanglement gain, i.e. entanglement at time t minus initial entanglement is bounded by the entanglement in C. This is confirmed by extensive numerical simulations. We also considered the case where HAC realizes the swap operator SA−C at a particular time and swaps the state of A with C while HBC is just the identity operator. This scenario falls outside the class considered above. For this case, we managed to prove analytically (for bi-product states |χiAB |γiC ) the same bound that we conjectured above Bachelor of Science in Physics 2018-05-30T08:24:38Z 2018-05-30T08:24:38Z 2018 Final Year Project (FYP) http://hdl.handle.net/10356/75304 en 62 p. application/pdf |
| spellingShingle | DRNTU::Science::Physics::Atomic physics::Quantum theory Koo, Edmund Sui Ho Bounds on continuous entanglement gain |
| title | Bounds on continuous entanglement gain |
| title_full | Bounds on continuous entanglement gain |
| title_fullStr | Bounds on continuous entanglement gain |
| title_full_unstemmed | Bounds on continuous entanglement gain |
| title_short | Bounds on continuous entanglement gain |
| title_sort | bounds on continuous entanglement gain |
| topic | DRNTU::Science::Physics::Atomic physics::Quantum theory |
| url | http://hdl.handle.net/10356/75304 |
| work_keys_str_mv | AT kooedmundsuiho boundsoncontinuousentanglementgain |