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Physical Review A

High-speed tomography of time-bin-entangled photons using a single-measurement setting

S. X. Wang, C. Chan, Paul M. Moraw, Daniel R. Reilly, Joseph B. Altepeter, Gregory S. Kanter

Published Oct 25, 2012• 11 citations
Publisher

Abstract

We generate time-bin entangled photons and measure the resulting quantum state with a tomography system that uses asymmetric interferometers having $3\ifmmode\times\else\texttimes\fi{}3$ output couplers. This configuration allows for measurements to be made simultaneously in all bases that are required for tomographic reconstruction. By eliminating the burden of tuning interferometer phases and by measuring all the spatial and temporal modes, substantial improvements in measurement speed are observed. Raw fidelities of 84$%$ with respect to an ideal entangled state are measured in about 2 s using a 12-MHz entangled state generator, with corresponding accidental count subtracted fidelities exceeding 90$%$.

DOI
10.1103/physreva.86.042122

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We generate time-bin entangled photons and measure the resulting quantum state with a tomography system that uses asymmetric interferometers having 3\ifmmode×\else\texttimes\fi33\ifmmode\times\else\texttimes\fi{}33\ifmmode×\else\texttimes\fi3 output couplers. This configuration allows for measurements to be made simultaneously in all bases that are required for tomographic reconstruction. By eliminating the burden of tuning interferometer phases and by measuring all the spatial and temporal modes, substantial improvements in measurement speed are observed. Raw fidelities of 84% with respect to an ideal entangled state are measured in about 2 s using a 12-MHz entangled state generator, with corresponding accidental count subtracted fidelities exceeding 90%.
We describe an experimental implementation to generate and measure high-dimensional time-bin-entangled qudits. Two-photon time-bin entanglement is generated via spontaneous four-wave mixing in single-mode fiber. Unbalanced Mach-Zehnder interferometers transform selected time bins to polarization entanglement, allowing standard polarization-projective measurements to be used for complete quantum state tomographic reconstruction. Here we generate maximally entangled qubits (d=2)(d=2)(d=2), qutrits (d=3)(d=3)(d=3), and ququarts (d=4)(d=4)(d=4), as well as other phase-modulated nonmaximally entangled qubits and qutrits. We reconstruct and verify all generated states using maximum-likelihood estimation tomography.
We report on a system for the generation and measurement of polarization entangled photons. High speed quantum state tomographies with a raw fidelity of >; 91 % with respect to an ideal entangled state are recorded in <; 2 seconds, with longer-term accidental-count subtracted fidelities exceeding 99%. Two-photon interference measurements are recorded using an automated alignment and measurement procedure with the signal distributed over 20 km of fiber. These high speed measurement methods are useful for high rate monitoring of entangled states.
A single photon has many physical degrees of freedom (DOF) that can carry the state of a high-dimensional quantum system. Nevertheless, only a single DOF is usually used in any specific demonstration. Furthermore, when more DOF are being used, they are analyzed and measured one at a time. We introduce a two-qubit information system, realized by two degrees of freedom of a single photon: polarization and time. The photon arrival time is divided into two time bins representing a qubit, while its polarization state represents a second qubit. The time difference between the two time bins is created without an interferometer at the picosecond scale, which is much smaller than the detector's response time. The two physically different DOF are analyzed simultaneously by photon bunching between the analyzed photon and an ancilla photon. Full two-qubit states encoded in single photons were reconstructed using quantum state tomography, both when the two DOF were entangled and when they were not, with fidelities higher than 96%.
We present a method for measuring quantum states encoded in the temporal modes of photons. The basis for the multilevel quantum states is defined by the use of modes propagating in a dispersive medium, which is a fiber in this case. The propagation and time-resolved single-photon detection allow us to define a positive-operator valued measure (POVM). The POVM depends on the amount of dispersion and the characteristics of a detector. This framework is numerically tested by performing quantum state tomography on a large number of states for a set of realistic experimental settings. Finally, the average fidelity between the expected and reconstructed states is computed for qubits, qutrits, and entangled qubits.