Continuous-monitoring measured signals bounded by past and future conditions in enlarged quantum systems. (English) Zbl 1508.81042
Summary: In a quantum system that is bounded by past and future conditions, weak continuous-monitoring forward-evolving and backward-evolving quantum states are usually carried out separately. Therefore, measured signals at a given time \(t\) cannot be monitored continuously. Here, we propose an enlarged quantum system method to combine these two processes together. Therein, we introduce an enlarged quantum state that contains both the forward- and backward-evolving quantum states. The enlarged state is governed by an enlarged master equation and propagates one-way forward in time. As a result, the measured signals at time \(t\) can be monitored continuously and can provide advantages in the signals amplification and signal processing techniques. Our proposal can be implemented on various physical systems, such as superconducting circuits, NMR systems, ion traps, quantum photonics, and among others.
MSC:
| 81P15 | Quantum measurement theory, state operations, state preparations |
| 81P45 | Quantum information, communication, networks (quantum-theoretic aspects) |
References:
| [1] | Campagne-Ibarcq, P., Bretheau, L., Flurin, E., Auffeves, A., Mallet, F., Huard, B.: Observing interferences between past and future quantum states in resonance fluorescence. Phys. Rev. Lett. 112, 180402 (2014) · doi:10.1103/PhysRevLett.112.180402 |
| [2] | Foroozani, N., Naghiloo, M., Tan, D., Mølmer, K., Murch, K.W.: Correlations of the time dependent signal and the state of a continuously monitored quantum system. Phys. Rev. Lett. 116, 110401 (2016) · doi:10.1103/PhysRevLett.116.110401 |
| [3] | Tan, D., Weber, S.J., Siddiqi, I., Mølmer, K., Murch, K.W.: Prediction and retrodiction for a continuously monitored superconducting qubit. Phys. Rev. Lett. 114, 090403 (2015) · doi:10.1103/PhysRevLett.114.090403 |
| [4] | Dressel, J., Chantasri, A., Jordan, A.N., Korotkov, A.N.: Arrow of time for continuous quantum measurement. Phys. Rev. Lett. 119, 220507 (2017) · doi:10.1103/PhysRevLett.119.220507 |
| [5] | Aharonov, Y., Albert, D.Z., Vaidman, L.: How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100. Phys. Rev. Lett. 60, 1351 (1988) · doi:10.1103/PhysRevLett.60.1351 |
| [6] | Aharonov, Y., Popescu, S., Tollaksen, J.: A time-symmetric formulation of quantum mechanics. Phys. Today 63, 27 (2010) · doi:10.1063/1.3518209 |
| [7] | Wu, S., Li, Y.: Weak measurements beyond the Aharonov-Albert-Vaidman formalism. Phys. Rev. A 83, 052106 (2011) · doi:10.1103/PhysRevA.83.052106 |
| [8] | Nakamura, K., Nishizawa, A., Fujimoto, M.K.: Evaluation of weak measurements to all orders. Phys. Rev. A 85, 012113 (2012) · doi:10.1103/PhysRevA.85.012113 |
| [9] | Tan, D., Foroozani, N., Naghiloo, M., Kiilerich, A.H., Mølmer, K., Murch, K.W.: Homodyne monitoring of postselected decay. Phys. Rev. A 96, 022104 (2017) · doi:10.1103/PhysRevA.96.022104 |
| [10] | Garcia-Pintos, L.P., Dressel, J.: Past observable dynamics of a continuously monitored qubit. Phys. Rev. A 96, 062110 (2017) · doi:10.1103/PhysRevA.96.062110 |
| [11] | Murch, K.W., Weber, S.J., Macklin, C., Siddiqi, I.: Observing single quantum trajectories of a superconducting quantum bit. Nature 502, 211 (2013) · doi:10.1038/nature12539 |
| [12] | Ho, L.B., Imoto, N.: Quantum weak and modular values in enlarged Hilbert spaces. Phys. Rev. A 97, 012112 (2018) · doi:10.1103/PhysRevA.97.012112 |
| [13] | Silberfarb, A., Jessen, P.S., Deutsch, I.H.: Quantum state reconstruction via continuous measurement. Phys. Rev. Lett. 95, 030402 (2005) · Zbl 1255.81038 · doi:10.1103/PhysRevLett.95.030402 |
| [14] | Casanova, J., Sabin, C., Leon, J., Egusquiza, I.L., Gerritsma, R., Roos, C.F., Garcia-Ripoll, J.J., Solano, E.: Quantum simulation of the Majorana equation and unphysical operations. Phys. Rev. X 1, 021018 (2011) |
| [15] | Noh, C., Rodriguez-Lara, B.M., Angelakis, D.G.: Proposal for realization of the Majorana equation in a tabletop experiment. Phys. Rev. A 87, 040102(R) (2013) · doi:10.1103/PhysRevA.87.040102 |
| [16] | Rodriguez-Lara, B.M., Moya-Cessa, H.M.: Optical simulation of Majorana physics. Phys. Rev. A 89, 015803 (2014) · doi:10.1103/PhysRevA.89.015803 |
| [17] | Zhang, X., Shen, Y., Zhang, J., Casanova, J., Lamata, L., Solano, E., Yung, M.H., Zhang, J.N., Kim, K.: Time reversal and charge conjugation in an embedding quantum simulator. Nat. Commu 6, 7917 (2015) · doi:10.1038/ncomms8917 |
| [18] | DiCandia, R., Mejia, B., Castillo, H., Pedernales, J.S., Casanova, J., Solano, E.: Embedding quantum simulators for quantum computation of entanglement. Phys. Rev. Lett. 111, 240502 (2013) · doi:10.1103/PhysRevLett.111.240502 |
| [19] | Pedernales, J.S., DiCandia, R., Schindler, P., Monz, T., Hennrich, M., Casanova, J., Solano, E.: Entanglement measures in ion-trap quantum simulators without full tomography. Phys. Rev. A 90, 012327 (2014) · doi:10.1103/PhysRevA.90.012327 |
| [20] | Loredo, J.C., Almeida, M.P., Di Candia, R., Pedernales, J.S., Casanova, J., Solano, E., White, A.G.: Measuring entanglement in a photonic embedding quantum simulator. Phys. Rev. Lett. 116, 070503 (2016) · doi:10.1103/PhysRevLett.116.070503 |
| [21] | Chen, M.C., Wu, D., Su, Z.E., Cai, X.D., Wang, X.L., Yang, T., Li, L., Liu, N.L., Lu, C.Y., Pan, J.W.: Efficient measurement of multiparticle entanglement with embedding quantum simulator. Phys. Rev. Lett. 116, 070502 (2016) · doi:10.1103/PhysRevLett.116.070502 |
| [22] | Alvarez-Rodriguez, U., Casanova, J., Lamata, L., Solano, E.: Quantum simulation of noncausal kinematic transformations. Phys. Rev. Lett. 111, 090503 (2013) · doi:10.1103/PhysRevLett.111.090503 |
| [23] | Ho, L.B.: Improving direct state measurements by using rebits in real enlarged Hilbert spaces. Phys. Lett. A 383, 289 (2019) · Zbl 1472.81016 · doi:10.1016/j.physleta.2018.10.047 |
| [24] | Wiseman, H.M., Milburn, G.J.: Quantum Measurement and Control. Cambridge University Press, New York (2010) · Zbl 1350.81004 |
| [25] | Jacobs, K., Steck, D.A.: A straightforward introduction to continuous quantum measurement. Contemp. Phys. 47, 279 (2006) · doi:10.1080/00107510601101934 |
| [26] | Gammelmark, S., Julsgaard, B., Mølmer, K.: Past quantum states of a monitored system. Phys. Rev. Lett. 111, 160401 (2013) · doi:10.1103/PhysRevLett.111.160401 |
| [27] | Reznik, B., Aharonov, Y.: Time-symmetric formulation of quantum mechanics. Phys. Rev. A 52, 2538 (1995) · doi:10.1103/PhysRevA.52.2538 |
| [28] | Shikano, Y., Hosoya, A.: Weak values with decoherence. J. Phys. A Math. Theor. 43, 025304 (2010) · Zbl 1181.81011 · doi:10.1088/1751-8113/43/2/025304 |
| [29] | Oreshkov, O., Giarmatzi, C.: Causal and causally separable processes. New J. Phys. 18, 093020 (2016) · Zbl 1456.81017 · doi:10.1088/1367-2630/18/9/093020 |
| [30] | Silva, R., Guryanova, Y., Short, A.J., Skrzypczyk, P., Brunner, N., Popescu, S.: Connecting processes with indefinite causal order and multitime quantum states. New J. Phys. 19, 103022 (2017) · Zbl 1516.81007 · doi:10.1088/1367-2630/aa84fe |
| [31] | Vaidman, L., Ben-Israel, A., Dziewior, J., Knips, L., Weißl, M., Meinecke, J., Schwemmer, C., Ber, R., Weinfurter, H.: Weak value beyond conditional expectation value of the pointer readings. Phys. Rev. A 96, 032114 (2017) · doi:10.1103/PhysRevA.96.032114 |
| [32] | Aharonov, Y., Botero, A.: Quantum averages of weak values. Phys. Rev. A 72, 052111 (2005) · doi:10.1103/PhysRevA.72.052111 |
| [33] | Aharonov, Y., Popescu, S., Tollaksen, J., Vaidman, L.: Multiple-time states and multiple-time measurements in quantum mechanics. Phys. Rev. A 79, 052110 (2009) · doi:10.1103/PhysRevA.79.052110 |
| [34] | Koch, J., Yu, T.M., Gambetta, J., Houck, A.A., Schuster, D.I., Majer, J., Blais, A., Devoret, M.H., Girvin, S.M., Schoelkopf, R.J.: Charge-insensitive qubit design derived from the Cooper pair box. Phys. Rev. A 76, 042319 (2007) · doi:10.1103/PhysRevA.76.042319 |
| [35] | Paik, H., Schuster, D.I., Bishop, L.S., Kirchmair, G., Catelani, G., Sears, A.P., Johnson, B.R., Reagor, M.J., Frunzio, L., Glazman, L.I., Girvin, S.M., Devoret, M.H., Schoelkopf, R.J.: Observation of high coherence in josephson junction qubits measured in a three-dimensional circuit QED architecture. Phys. Rev. Lett. 107, 240501 (2011) · doi:10.1103/PhysRevLett.107.240501 |
| [36] | Vijay, R., Macklin, C., Slichter, D.H., Weber, S.J., Murch, K.W., Naik, R., Korotkov, A.N., Siddiqi, I.: Stabilizing Rabi oscillations in a superconducting qubit using quantum feedback. Nature 490, 77 (2012) · doi:10.1038/nature11505 |
| [37] | Weber, S.J., Chantasri, A., Dressel, J., Jordan, A.N., Murch, K.W., Siddiqi, I.: Mapping the optimal route between two quantum states. Nature 511, 570 (2014) · doi:10.1038/nature13559 |
| [38] | Abe, M., Ban, M.: Decoherence of weak values in a pure dephasing process. Quantum Stud. Math. Found. 2, 23 (2015) · Zbl 1317.81012 · doi:10.1007/s40509-015-0028-8 |
| [39] | Peterer, M.J., Bader, S.J., Jin, X., Yan, F., Kamal, A., Gudmundsen, T.J., Leek, P.J., Orlando, T.P., Oliver, W.D., Gustavsson, S.: Coherence and decay of higher energy levels of a superconducting transmon qubit. Phys. Rev. Lett. 114, 010501 (2015) · doi:10.1103/PhysRevLett.114.010501 |
| [40] | Casanova, J., Mezzacapo, A., Lamata, L., Solano, E.: Quantum simulation of interacting fermion lattice models in trapped ions. Phys. Rev. Lett. 108, 190502 (2012) · doi:10.1103/PhysRevLett.108.190502 |
| [41] | Majer, J., Chow, J.M., Gambetta, J.M., Koch, J., Johnson, B.R., Schreier, J.A., Frunzio, L., Schuster, D.I., Houck, A.A., Wallraff, A., Blais, A., Devoret, M.H., Girvin, S.M., Schoelkopf, R.J.: Coupling superconducting qubits via a cavity bus. Nature 449, 443 (2007) · doi:10.1038/nature06184 |
| [42] | Leibfried, D., Blatt, R., Monroe, C., Wineland, D.: Quantum dynamics of single trapped ions. Rev. Mod. Phys. 75, 281 (2003) · doi:10.1103/RevModPhys.75.281 |
| [43] | Batt, R., Roos, C.F.: Quantum simulations with trapped ions. Nat. Phys. 8, 277 (2012) · doi:10.1038/nphys2252 |
| [44] | Lamata, L., Mezzacapo, A., Casanova, J., Solano, E.: Efficient quantum simulation of fermionic and bosonic models in trapped ions. EPJ Quantum Technol. 1, 9 (2014) · doi:10.1140/epjqt9 |
| [45] | Paraoanu, G.S.: Recent progress in quantum simulation using superconducting circuits. J. Low. Temp. Phys. 175, 633 (2014) · doi:10.1007/s10909-014-1175-8 |
| [46] | Feynman, R.P.: Simulating physics with computers. Int. J. Theor. Phys. 21, 467 (1982) · doi:10.1007/BF02650179 |
| [47] | Georgescu, I.M., Ashhab, S., Nori, F.: Quantum simulation. Rev. Mod. Phys. 86, 153 (2014) · doi:10.1103/RevModPhys.86.153 |
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