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International Journal of Modern Physics B

BETTING ON INTERFEROMETRIC PATHS AND PHASES USING TRANSLATIONAL-INTERNAL ENTANGLEMENT: THE GREEDY KING GAME

Michal Kolář, Tomáš Opatrný, Nir Bar‐Gill, Gershon Kurizki

Published May 20, 2006• 4 citations
Publisher

Abstract

The behavior of translationally–internally entangled (TIE) states in an interferometer of the Mach–Zehnder type is studied, by means of a game whose results show that TIE states allow near-certain guessing of both path (corpuscular) and phase (wavelike) features, as opposed to conventional states that are constrained by standard complementarity.

DOI
10.1142/s0217979206033991

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The behavior of translationally–internally entangled (TIE) states in an interferometer of the Mach–Zehnder type is studied, by means of a game whose results show that TIE states allow near-certain guessing of both path (corpuscular) and phase (wavelike) features, as opposed to conventional states that are constrained by standard complementarity.
The aim of this paper is to revisit the implications of complementarity when we inject into a Mach Zehnder interferometer particles with internal structure, prepared in special translational–internal entangled (TIE) intraparticle states. This correlation causes the path distinguishability to be interferometric phase-dependent in contrast to the standard case, where distinguishability depends on some external parameters (not interferometric phase). We show that such a TIE state permits us to detect small phase shifts along with almost perfect path distinguishability, beyond the constraints imposed by complementarity on simultaneous which-way and which-phase measurements for cases when distinguishability is uncoupled to interferometric phase.
Abstract. We examine two setups that reveal different operational implications of path-phase complementarity for single photons in a Mach-Zehnder interferometer (MZI). In both setups, the which-way (WW) information is recorded in the polarization state of the photon serving as a “flying which-way detector”. In the “predictive” variant, using a fixed initial state, one obtains duality relation between the probability to correctly predict the outcome of either a which-way (WW) or which-phase (WP) measurement (equivalent to the conventional path-distinguishibility-visibility). In this setup, only one or the other (WW or WP) prediction has operational meaning in a single experiment. In the second, “retrodictive ” protocol, the initial state is secretly selected for each photon by one party, Alice, among a set of initial states which may differ in the amplitudes and phases of the photon in each arm of the MZI. The goal of the other party, Bob, is to retrodict the initial state by measurements on the photon. Here, a similar duality relation between WP and WW probabilities, governs their simultaneous guesses in each experimental run.
We investigate the phase sensitivity of the SU(1,1) interfereometer [SU(1,1)I] and the modified Mach–Zehnder interferometer (MMZI) with the entangled coherent states (ECS) as inputs. We consider the ideal case and the situations in which the photon losses are taken into account. We find that, under ideal conditions, the phase sensitivity of both the MMZI and the SU(1,1)I can beat the shot-noise limit (SNL) and approach the Heisenberg limit (HL). In the presence of photon losses, the ECS can beat the coherent and squeezed states as inputs in the SU(1,1)I, and the MMZI is more robust against internal photon losses than the SU(1,1)I.
We study the entanglement between the two beams exiting a Mach-Zehnder interferometer fed by a couple of squeezed-coherent states with arbitrary squeezing parameter. The quantum correlations at the output are functions of the internal phase shift of the interferometer, with the output state ranging from a totally disentangled state to a state whose degree of entanglement is an increasing function of the input squeezing parameter. A couple of squeezed vacuums at the input lead to maximum entangled state at the output. The fringe visibilities resulting from measuring the coincidence counting rate or the squared difference photocurrent are evaluated and compared to each other. Homodynelike detection turns out to be preferable in almost all situations, with the exception of the very-low-signal regime.
The complementarity for wave-like and particle-like properties of a quantum mechanical particle in the Mach–Zehnder interferometer is investigated by means of the dynamical approach. Measurement devices are placed on the paths of the interferometer to obtain the information of a propagating particle. The which-path information of the particle and the fringe visibility of the interferometer are derived by considering the dynamics of the particle and devices. When each device consists of a single qubit, the maximum amount of the which-path information is obtained and the complementary relation is examined.