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.Shortly after the inception of the quantum state, Pauli questioned its measurability, and in particular, whether or not a wave function can be obtained from position and momentum measurements [1]. This question, now referred to as the Pauli problem, draws on concepts such as complementarity and measurement in an attempt to demystify the physical significance of the quantum state. Indeed, the task of determining a quantum state is a central issue in quantum physics due to both its foundational and practical implications. For instance, a method to verify the production of complicated states is desirable in quantum information and quantum metrology applications. Moreover, since a state fully characterizes a system, any possible measurement outcome can be predicted once the state is determined.A wave function describes a quantum system that can be isolated from its environment, meaning the two are non-interacting and the system is in a pure state. More generally, open quantum systems can interact with their environment and the two can become entangled. In such cases, or even in the presence of classical noise, the system is in a statistical mixture of states (i.e. mixed state), and one requires a density matrix to fully describe the quantum system. In fact, some regard the density matrix as more fundamental than the wave function because of its generality and its relationship to classical measurement theory [2].The standard way of measuring the density matrix is by using quantum state tomography (QST). In QST, one performs an often overcomplete set of measurements in incompatible bases on identically prepared copies of the state. Then, one fits a candidate state to the measurement results with the help of a reconstruction algorithm [3]. Many efforts have been made to optimize QST [4][5][6][7], but the scalability of the experimental apparatus and the complexity of the reconstruction algorithm renders the task increasingly difficult for large dimensional systems. In addition, since QST requires a global reconstruction, it ...

Optical quantum memories are devices that store and recall quantum light and are vital to the realisation of future photonic quantum networks. To date, much effort has been put into improving storage times and efficiencies of such devices to enable long-distance communications. However, less attention has been devoted to building quantum memories which add zero noise to the output. Even small additional noise can render the memory classical by destroying the fragile quantum signatures of the stored light. Therefore noise performance is a critical parameter for all quantum memories. Here we introduce an intrinsically noise-free quantum memory protocol based on two-photon off-resonant cascaded absorption (ORCA). We demonstrate successful storage of GHz-bandwidth heralded single photons in a warm atomic vapour with no added noise; confirmed by the unaltered photon number statistics upon recall. Our ORCA memory meets the stringent noise-requirements for quantum memories whilst combining high-speed and room-temperature operation with technical simplicity, and therefore is immediately applicable to low-latency quantum networks.

Quantum phenomena such as entanglement can improve fundamental limits on the sensitivity of a measurement probe. In optical interferometry, a probe consisting of N entangled photons provides up to a $$\sqrt{N}$$ N enhancement in phase sensitivity compared to a classical probe of the same energy. Here, we employ high-gain parametric down-conversion sources and photon-number-resolving detectors to perform interferometry with heralded quantum probes of sizes up to N = 8 (i.e. measuring up to 16-photon coincidences). Our probes are created by injecting heralded photon-number states into an interferometer, and in principle provide quantum-enhanced phase sensitivity even in the presence of significant optical loss. Our work paves the way toward quantum-enhanced interferometry using large entangled photonic states.

Variable measurement operators enable the optimization of strategies for testing quantum properties and the preparation of a range of quantum states. Here, we experimentally implement a weak-field homodyne detector that can continuously tune between performing a photon-number measurement and a field quadrature measurement on a quantum stateρ. We combineρ with a coherent state |α on a balanced beam splitter, and detect light at both output ports using photonnumber-resolving transition edge sensors. We observe that the discrete difference statistics converge to the quadrature distribution ofρ as we increase |α|. Moreover, in a proof-of-principle demonstration of state engineering, we show the ability to control the photon-number distribution of a state that is heralded using our weak-field homodyne detector.

Multi-photon interference in large multi-port interferometers is key to linear optical quantum computing and in particular to boson sampling. Silicon photonics enables complex interferometric circuits with many components in a small footprint and has the potential to extend these experiments to larger numbers of interfering modes. However, loss has generally limited the implementation of multi-photon experiments in this platform. Here, we make use of high-efficiency grating couplers to combine bright and pure quantum light sources based on ppKTP waveguides with silicon circuits. We interfere up to 5 photons in up to 15 modes, verifying genuine multi-photon interference by comparing the results against various models including partial distinguishability between photons.

Unlike regular time evolution governed by the Schrödinger equation, standard quantum measurement appears to violate time-reversal symmetry. Measurement creates random disturbances (e.g., collapse) that prevents back-tracing the quantum state of the system. The effect of these disturbances is explicit in the results of subsequent measurements. In this way, the joint result of sequences of measurements depends on the order in time in which those measurements are performed. One might expect that if the disturbance could be eliminated this time-ordering dependence would vanish. Following a recent theoretical proposal [A. Bednorz et al 2013 New J.Phys. 15 15 15 023043], we experimentally investigate this dependence for a kind of measurement that creates an arbitrarily small disturbance, weak measurement. We perform various sequences of a set of polarization weak measurements on photons. We experimentally demonstrate that, although the weak measurements are minimally disturbing, their time-ordering affects the outcome of the measurement sequence for quantum systems.A fundamental open question in physics is the role of time in quantum mechanics [1][2][3].While observables such as position and momentum are represented by operators, time in the Schrödinger equation appears only as ordinary number-parameter, just as in classical mechanics [2]. In view of relativistic theories of physics which famously treat time and space on equal footing, this distinction is problematic. In fact, while Heisenberg's uncertainty principle between energy and time appears to suggest that a time operator conjugate to the total energy operator exists, attempts to create such an operator lead to contradictions [4].Similar issues confound attempts to create an observable for the time it takes for a particle to tunnel through a potential barrier, or even the time of arrival of a particle at a detector [5][6][7].Another issue is that it is widely believed that information is conserved in quantum physics. This follows from the unitary time-reversible evolution in the Schrödinger equation. Yet,

When two equal photon-number states are combined on a balanced beam splitter, both output ports of the beam splitter contain only even numbers of photons. Consider the time-reversal of this interference phenomenon: the probability that a pair of photon-numberresolving detectors at the output ports of a beam splitter both detect the same number of photons depends on the overlap between the input state of the beam splitter and a state containing only even photon numbers. Here, we propose using this even-parity detection to engineer quantum states containing only even photon-number terms. As an example, we demonstrate the ability to prepare superpositions of two coherent states with opposite amplitudes, i.e. two-component Schrödinger cat states. Our scheme can prepare cat states of arbitrary size with nearly perfect fidelity. Moreover, we investigate engineering more complex even-parity states such as four-component cat states by iteratively applying our even-parity detector.

It is often said that measuring a system's position must disturb the complementary property, momentum, by some minimum amount due to the Heisenberg uncertainty principle. Using a 'weakmeasurement', this disturbance can be reduced. One might expect this comes at the cost of also reducing the measurement's precision. However, it was recently demonstrated that a sequence consisting of a weak position measurement followed by a regular momentum measurement can probe a quantum system at a single point, with zero width, in position-momentum space. Here, we study this 'joint weak-measurement' and reconcile its compatibility with the uncertainty principle. While a single trial probes the system with a resolution that can saturate Heisenberg's limit, we show that averaging over many trials can be used to surpass this limit. The weak-measurement does not trade away precision, but rather another type of uncertainty called 'predictability' which quantifies the certainty of retrodicting the measurement's outcome.