Symmetric M-ary phase discrimination using quantum-optical probe states
We present a theoretical study of minimum error probability discrimination, using quantum-optical probe states, of M optical phase shifts situated symmetrically on the unit circle. We assume ideal lossless conditions and full freedom for implementing quantum measurements and for probe-state selectio...
| Main Authors: | , , , , |
|---|---|
| Other Authors: | |
| Format: | Article |
| Language: | en_US |
| Published: |
American Physical Society
2012
|
| Online Access: | http://hdl.handle.net/1721.1/73840 https://orcid.org/0000-0002-6094-5861 |
| _version_ | 1826208096554319872 |
|---|---|
| author | Shapiro, Jeffrey H. Nair, Ranjith Yen, Brent J. Guha, Saikat Pirandola, Stefano |
| author2 | Massachusetts Institute of Technology. Research Laboratory of Electronics |
| author_facet | Massachusetts Institute of Technology. Research Laboratory of Electronics Shapiro, Jeffrey H. Nair, Ranjith Yen, Brent J. Guha, Saikat Pirandola, Stefano |
| author_sort | Shapiro, Jeffrey H. |
| collection | MIT |
| description | We present a theoretical study of minimum error probability discrimination, using quantum-optical probe states, of M optical phase shifts situated symmetrically on the unit circle. We assume ideal lossless conditions and full freedom for implementing quantum measurements and for probe-state selection, subject only to a constraint on the average energy, i.e., photon number. In particular, the probe state is allowed to have any number of signal and ancillary modes and to be pure or mixed. Our results are based on a simple criterion that partitions the set of pure probe states into equivalence classes with the same error probability performance. Under an energy constraint, we find the explicit form of the state that minimizes the error probability. This state is an unentangled but nonclassical single-mode state. The error performance of the optimal state is compared with several standard states in quantum optics. We also show that discrimination with zero error is possible only beyond a threshold energy of (M−1)/2. For the M=2 case, we show that the optimum performance is readily demonstrable with current technology. While transmission loss and detector inefficiencies lead to a nonzero erasure probability, the error rate conditional on no erasure is shown to remain the same as the optimal lossless error rate. |
| first_indexed | 2024-09-23T14:00:28Z |
| format | Article |
| id | mit-1721.1/73840 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T14:00:28Z |
| publishDate | 2012 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/738402022-09-28T17:39:12Z Symmetric M-ary phase discrimination using quantum-optical probe states Shapiro, Jeffrey H. Nair, Ranjith Yen, Brent J. Guha, Saikat Pirandola, Stefano Massachusetts Institute of Technology. Research Laboratory of Electronics Shapiro, Jeffrey H. Yen, Brent J. We present a theoretical study of minimum error probability discrimination, using quantum-optical probe states, of M optical phase shifts situated symmetrically on the unit circle. We assume ideal lossless conditions and full freedom for implementing quantum measurements and for probe-state selection, subject only to a constraint on the average energy, i.e., photon number. In particular, the probe state is allowed to have any number of signal and ancillary modes and to be pure or mixed. Our results are based on a simple criterion that partitions the set of pure probe states into equivalence classes with the same error probability performance. Under an energy constraint, we find the explicit form of the state that minimizes the error probability. This state is an unentangled but nonclassical single-mode state. The error performance of the optimal state is compared with several standard states in quantum optics. We also show that discrimination with zero error is possible only beyond a threshold energy of (M−1)/2. For the M=2 case, we show that the optimum performance is readily demonstrable with current technology. While transmission loss and detector inefficiencies lead to a nonzero erasure probability, the error rate conditional on no erasure is shown to remain the same as the optimal lossless error rate. United States. Defense Advanced Research Projects Agency. Quantum Sensors Program United States. Office of Naval Research. Basic Research Challenge Program Singapore. National Research Foundation (Grant NRF-NRFF2011- 07) 2012-10-10T16:28:46Z 2012-10-10T16:28:46Z 2012-08 2012-06 Article http://purl.org/eprint/type/JournalArticle 1050-2947 1094-1622 http://hdl.handle.net/1721.1/73840 Nair, Ranjith et al. “Symmetric M-ary Phase Discrimination Using Quantum-optical Probe States.” Physical Review A 86.2 (2012). ©2012 American Physical Society https://orcid.org/0000-0002-6094-5861 en_US http://dx.doi.org/10.1103/PhysRevA.86.022306 Physical Review A Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf American Physical Society APS |
| spellingShingle | Shapiro, Jeffrey H. Nair, Ranjith Yen, Brent J. Guha, Saikat Pirandola, Stefano Symmetric M-ary phase discrimination using quantum-optical probe states |
| title | Symmetric M-ary phase discrimination using quantum-optical probe states |
| title_full | Symmetric M-ary phase discrimination using quantum-optical probe states |
| title_fullStr | Symmetric M-ary phase discrimination using quantum-optical probe states |
| title_full_unstemmed | Symmetric M-ary phase discrimination using quantum-optical probe states |
| title_short | Symmetric M-ary phase discrimination using quantum-optical probe states |
| title_sort | symmetric m ary phase discrimination using quantum optical probe states |
| url | http://hdl.handle.net/1721.1/73840 https://orcid.org/0000-0002-6094-5861 |
| work_keys_str_mv | AT shapirojeffreyh symmetricmaryphasediscriminationusingquantumopticalprobestates AT nairranjith symmetricmaryphasediscriminationusingquantumopticalprobestates AT yenbrentj symmetricmaryphasediscriminationusingquantumopticalprobestates AT guhasaikat symmetricmaryphasediscriminationusingquantumopticalprobestates AT pirandolastefano symmetricmaryphasediscriminationusingquantumopticalprobestates |