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Erasing the path information stored by a qudit in a symmetric Mach-Zehnder interferometer

Soroush Khademi, Ali Reza Bahrampour

Published Feb 15, 2016• 0 citations
OpenAlex

Abstract

In an interferometer, no interference happens if the quanta's path information is available in an ancillary system. One can erase this information by an appropriate measurement and recognize subensembles of the interferometry data showing interference. We consider symmetric Mach-Zehnder or Michelson interferometers in which a qudit, initially prepared in a pure state, provides the path information. We set measures of which-path information and which-phase information (knowledge about the phase difference between the interferometer's arms) by use of Shannon entropy and show that by erasing the which-path information, one can obtain the same amount of which-phase information. As an example, we propose a new modified Michelson interferometer, feasible by today's technology, in which a qubit (an atom trapped in a cavity) gathers the photon's path information. Erasing is done by measuring the atom's energy.

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In an interferometer, no interference happens if the quanta's path information is available in an ancillary system. One can erase this information by an appropriate measurement and recognize subensembles of the interferometry data showing interference. We consider symmetric Mach-Zehnder or Michelson interferometers in which a qudit, initially prepared in a pure state, provides the path information. We set measures of which-path information and which-phase information (knowledge about the phase difference between the interferometer's arms) by use of Shannon entropy and show that by erasing the which-path information, one can obtain the same amount of which-phase information. As an example, we propose a new modified Michelson interferometer, feasible by today's technology, in which a qubit (an atom trapped in a cavity) gathers the photon's path information. Erasing is done by measuring the atom's energy.
Abstract In interferometers, the more information about a quantum’s path that is available in an ancillary quantum system (AQS), the less visibility the interference has. By use of Shannon entropy, we try to compare the amount of which-phase information with the amount of which-way information stored in the AQS of two-path interferometers with symmetric beam merging. We show that the former is less than or equal to the latter if the bipartite system of the single quantum and the AQS is initially prepared in a pure state and the interaction between the two parts is unitary. The equality holds when symmetry exists. No which-way information is obtained by the measurement that we use for extracting the which-phase information and vice versa. In order to verify the results experimentally, we propose assembling a new single-photon interferometer.
We propose a solid-state quantum eraser in which electrons are injected into a mesoscopic conductor in the quantum Hall regime. The conductor is composed of a two-path interferometer, an electronic analog of the optical Mach-Zehnder interferometer, and a quantum point-contact detector capacitively coupled to the interferometer. While the interference of the output current at the interferometer is suppressed by the which-path information, we show that the which-path information is erased and the interference reappears in the cross-correlation measurement between the interferometer and the detector output leads. We also investigate a modified setup in which the detector is replaced by a two-path interferometer. We show that the distinguishability of the path and the visibility of joint detection can be controlled in a continuous manner and satisfy a complementarity relation for the entangled electrons.
An operational way of measuring entanglement in a balanced two-path interferometers is presented, where path information is carried by some internal degree of freedom which, in turn, gets entangled with an ancilla system. The analysis is based on a tripartite description involving paths, an internal qubit degree of freedom, and some ancillary states entangled with the internal degree of freedom. It is then applied to two physically distinct experimental situations: a modified Stern-Gerlach interferometer with spin-1/2 particles and a Mach-Zehnder interferometer with photons carrying polarization. The ancilla degree of freedom may not be experimentally accessible. Tracing out the ancillary system, and employing a quantum erasing procedure based on the internal degree of freedom, it is demonstrated that a concurrence-based measure of the entanglement, between the internal degree of freedom and the ancilla, can be extracted directly from measurable asymmetry of the two output channels. These results show that loss of coherence, quantum erasure, and entanglement estimation in interferometric experiments arise from the same underlying correlation structure and provide a compact experimentally accessible framework for quantifying entanglement in qubit systems.
In the conventional interpretation of quantum mechanics the interference of particles in a two-beam interferometer is closely related to the problem of which-way information. One of the mysteries of quantum mechanics relies on the assumption that the wavefunction of each photon propagates simultaneously along both classically allowed paths, and that interference arises as a consequence of the indistinguishability of those paths. Any attempt to obtain which-way information by putting individual labels on the photons in each pathway inevitably destroys interference. However, even in cases in which the photons carry which-way labels, it is possible to erase those labels after the particle has left the interferometer. The erasing process (partly or completely) destroys the which-way information, and thereby restores interference. This phenomenon is known as quantum erasing. Here we present a lecture demonstration experiment of quantum erasing based on a Mach–Zehnder interferometer operated with single photons.
Complementarity of wave-like and particle-like properties in the Mach–Zehnder and Michelson interferometers is investigated by means of the exactly solvable model for a quantum measurement process. When the error-minimum measurement and unambiguous measurement are used for extracting the which-path information, the fringe visibility and which-path information are derived and their complementary relation is examined. It is shown that there is a possibility of the recovery of the quantum coherence in the Michelson interferometer since the which-path information can be erased by the propagating particle itself.
Which-path information of a quantum particle in interferometers is the key to infer the past of the quantum particle. It has led to many extensive discussions, including discussions of quantum complementarity and the path-visibility relation. The basics of these discussions are the description, detection, and control of which-path information. In this paper, we focus on the investigation of multidimensional which-path information in a nested Mach-Zehnder interferometer. A general expression of which-path information is given and can be partially extracted by different detection methods. Further analysis shows that the which-path information can be controlled by the phase differences and beam-splitting ratios between the arms of the nested Mach-Zehnder interferometer. Moreover, an alternative which-path information elimination phenomenon has been predicted and demonstrated experimentally. Our work can help us to understand the physics of quantum particles, with potential applications for quantum information processing and quantum metrology.