We propose a new method to directly measure a general multiparticle quantum wave function, a single matrix element in a multi-particle density matrix, by quantum teleportation. The density matrix element is embedded in a virtual logical qubit and is nondestructively teleported to a single physical qubit for readout. We experimentally implement this method to directly measure the wave function of a photonic mixed quantum state beyond a single photon using a single observable for the first time. Our method also provides an exponential advantage over the standard quantum state tomography in measurement complexity to fully characterize a sparse multiparticle quantum state.
We propose a new method to directly measure a general multiparticle quantum wave function, a single matrix element in a multi-particle density matrix, by quantum teleportation. The density matrix element is embedded in a virtual logical qubit and is nondestructively teleported to a single physical qubit for readout. We experimentally implement this method to directly measure the wave function of a photonic mixed quantum state beyond a single photon using a single observable for the first time. Our method also provides an exponential advantage over the standard quantum state tomography in measurement complexity to fully characterize a sparse multiparticle quantum state.
One drawback of conventional quantum state tomography is that it does not readily provide access to single density matrix elements since it requires a global reconstruction. Here, we experimentally demonstrate a scheme that can be used to directly measure individual density matrix elements of general quantum states. The scheme relies on measuring a sequence of three observables, each complementary to the last. The first two measurements are made weak to minimize the disturbance they cause to the state, while the final measurement is strong. We perform this joint measurement on polarized photons in pure and mixed states to directly measure their density matrix. The weak measurements are achieved using two walk-off crystals, each inducing a polarization-dependent spatial shift that couples the spatial and polarization degrees of freedom of the photons. This direct measurement method provides an operational meaning to the density matrix and promises to be especially useful for large dimensional states.
One drawback of conventional quantum state tomography is that it does not readily provide access to single density matrix elements since it requires a global reconstruction.Here, we experimentally demonstrate a scheme that can be used to directly measure individual density matrix elements of general quantum states.The scheme relies on measuring a sequence of three observables, each complementary to the last.The first two measurements are made weak to minimize the disturbance they cause to the state, while the final measurement is strong.We perform this joint measurement on polarized photons in pure and mixed states to directly measure their density matrix.The weak measurements are achieved using two walk-off crystals, each inducing a polarization-dependent spatial shift that couples the spatial and polarization degrees of freedom of the photons.This direct measurement method provides an operational meaning to the density matrix and promises to be especially useful for large dimensional states.
A direct measurement protocol allows reconstructing specific elements of the density matrix of a quantum state without using quantum state tomography. Until now, most direct measurement protocols have relied on ancillary pointers, which add complexity and are not always easy to implement experimentally. In this paper, we experimentally validate a direct measurement protocol requiring no ancillary pointers that calculates the value of a specific element of a quantum state's density matrix using only six projection measurements. We prepare path-encoded arbitrary four-dimensional quantum states on a silicon-based quantum photonic chip and measure the density-matrix elements of the four-dimensional quantum states using this protocol, with experimental results deviating from ideal values by an average of only $0.010\ifmmode\pm\else\textpm\fi{}0.004$. This approach has the potential to be applied to quantum information applications where only partial information about the quantum state needs to be extracted, for example, problems such as entanglement witnessing, fidelity estimation of quantum systems, and quantum coherence estimation.
A direct measurement protocol allows reconstructing specific elements of the density matrix of a quantum state without using quantum state tomography. However, the direct measurement protocols to date are primarily based on weak or strong measurements with an ancillary pointer, which interacts with the investigated system to extract information about the specified elements. Here, we present a direct measurement scheme based on phase-shifting operations which do not need ancillary pointers. In this method, estimates of at most six expectation values of projective observables suffice to determine any specific element of an unknown quantum density matrix. A concrete quantum circuit to implement this direct measurement protocol for multiqubit states is provided, which is composed of just single-qubit gates and two multiqubit controlled-phase gates. This scheme is also extended for the direct measurement of the density matrix of continuous-variable quantum states. Our method can be used in quantum information applications where only partial information about the quantum state needs to be extracted, for example, problems such as entanglement witnessing, fidelity estimation of quantum systems, and quantum coherence estimation.
Entanglement and the wave function description are two of the core concepts that make quantum mechanics such a unique theory. A method to directly measure the wave function, using weak values, was demonstrated by Lundeen et al. [Nature 474, 188 (2011)]. However, it is not applicable to a scenario of two disjoint systems, where nonlocal entanglement can be a crucial element, since that requires obtaining weak values of nonlocal observables. Here, for the first time, we propose a method to directly measure a nonlocal wave function of a bipartite system, using modular values. The method is experimentally implemented for a photon pair in a hyperentangled state, i.e., entangled both in polarization and momentum degrees of freedom.
Efficient acquiring information from a quantum state is important for research in fundamental quantum physics and quantum information applications. Instead of using standard quantum state tomography method with reconstruction algorithm, weak values were proposed to directly measure density matrix elements of quantum state. Recently, similar to the concept of weak value, modular values were introduced to extend the direct measurement scheme to nonlocal quantum wavefunction. However, this method still involves approximations, which leads to inherent low precision. Here, we propose a new scheme which enables direct measurement for ideal value of the nonlocal density matrix element without taking approximations. Our scheme allows more accurate characterization of nonlocal quantum states, and therefore has greater advantages in practical measurement scenarios.