Measuring a Photonic Qubit without Destroying It

Abstract

Measuring the polarisation of a single photon typically results in its destruction. We propose, demonstrate, and completely characterise a quantum non-demolition (QND) scheme for realising such a measurement non-destructively. This scheme uses only linear optics and photo-detection of ancillary modes to induce a strong non-linearity at the single photon level, non-deterministically. We vary this QND measurement continuously into the weak regime, and use it to perform a nondestructive test of complementarity in quantum mechanics. Our scheme realises the most advanced general measurement of a qubit: it is non-destructive, can be made in any basis, and with arbitrary strength.At the heart of quantum mechanics is the principle that the very act of measuring a system disturbs it. A quantum non-demolition (QND) scheme seeks to make a measurement such that this inherent back-action feeds only into unwanted observables [1,2]. Such a measurement should satisfy the following criteria [3]: (1) The measurement outcome is correlated with the input; (2) The measurement does not alter the value of the measured observable; and (3) Repeated measurement yields the same result -quantum state preparation (QSP). Originally proposed for gravity wave detectors, most progress in QND has been in the continuous variable (CV) regime, involving measurement of the field quadrature of bright optical beams [3]. Demonstrations at the single photon level have been limited to intra-cavity photons due to the requirement of a strong non-linearity [4,5]. In addition, there has been no complete characterisation of a QND measurement due to a limited capacity to prepare input states, and thus inability to observe all the required correlations.The importance of single-photon measurements has been highlighted by schemes for optical quantum computation that proceed via a measurement induced nonlinearity [6,7]. Such schemes encode quantum information in the state (eg polarisation) of single photonsphotonic qubits. Measurement of single photon properties is traditionally a strong, destructive measurement employing direct photo-detection. However, quantum mechanics allows general measurements [8] that range from strong to arbitrarily weak -one obtains full to negligible information -and can be non-destructive (eg QND). Such general measurements are required [9] for tests of wave-particle duality [10], and other fundamental tests of quantum mechanics [11,12]. They may also find application in: optical quantum computing [7,13]; quantum communication protocols [14]; tests of such protocols [15,16]; nested entanglement pumping [17]; and quantum feedback [18].Here we propose, demonstrate, and completely characterise a scheme for the QND measurement of the polarisation of a free propagating single-photon qubit -a flying qubit. This is achieved non-deterministically by using a measurement induced non-linearity. The measurement can be performed on all possible input states. Eigenstate inputs result in strong correlation with the measurement outcome; coherent superp...

Quantum nondemolition measurement of a kicked qubit

“…The liability of this proposal is that one cannot detect what is happening while the coupling is turned off, so the qubit must have a reasonably high quality factor. However, this scheme has several advantages over the original proposal: (1) the coupling to the qubit needs only one qubit operator (the one we want to measure), (2) an arbitrary qubit Hamiltonian is allowed, (3) in the ideal case, no assumptions need to be made about the density matrix of the qubit, and (4) in the non-ideal case, the pulses may be noisy. These advantages make this kicked QND measurement feasible with existing technology.…”

Paradox in Wave-Particle Duality

“…With respect to the mutual exclusivity of complementary wave and particle natures as expressed in BPC, the applied technique appears to allow us to circumvent the limitations imposed by Heisenberg's uncertainty principle and the entanglement between the which-way marker and the interfering quantum object as employed in some welcher-weg experiments. (14)(15)(16)(17) Afshar's nonperturbative measurement technique (18)(19)(20) used in this work is conceptually different from quantum non-demolition (21) or non-destructive (22) techniques which do not destroy but perturb the photon wavefunction directly. The observation, that the presence of the wire grid decreases the photon count only negligibly, characterizes a confirmation null result.…”

Measurement of Quantum Weak Values of Photon Polarization

“…The probability of this event is given by the expectation value of the projector OA optic axis). A weak measurement of the polarization is made by interacting the photon with another (meter) photon in a weak measurement device, which operates via measurementinduced nonlinearity [25]. The interaction of the two photons can be controlled using HWP 2 .…”

“…Subsequently, we make a weak, nondestructive measurement on the photon's polarization in the H ÿ V basis. The weak measurement is made using a nondeterministic generalized photon polarization measurement device [25], which is deemed to have worked whenever a single photon is present at each of the signal and meter outputs. The generalized measurement device works by entangling the signal photon's polarization with that of a meter photon prepared in the state jHi jVi, before measuring the meter photon's polarization.…”