Regular measurements allow predicting the future and retrodicting the past of quantum systems. Time-nonlocal measurements can leave the future and the past uncertain, yet establish a relation between them. We show that continuous time-nonlocal measurements can be used to transfer a quantum state via teleportation or direct transmission. Considering two oscillators probed by traveling fields, we analytically identify strategies for performing the state transfer perfectly across a wide range of linear oscillator-field interactions beyond the pure beam-splitter and two-mode-squeezing types.
Regular measurements allow predicting the future and retrodicting the past of quantum systems. Time-nonlocal measurements can leave the future and the past uncertain, yet establish a relation between them. We show that continuous time-nonlocal measurements can be used to transfer a quantum state via teleportation or direct transmission. Considering two oscillators probed by traveling fields, we analytically identify strategies for performing the state transfer perfectly across a wide range of linear oscillator-field interactions beyond the pure beam-splitter and two-mode-squeezing types.
We show that the recently proposed scheme of teleportation of continuous variables [S.L. Braunstein and H.J. Kimble, Phys. Rev. Lett. 80, 869 (1998)] can be improved by a conditional measurement of the entangled state shared by the sender and the recipient. The conditional measurement subtracts photons from the original entangled two-mode squeezed vacuum, by transmitting each mode through a low-reflectivity beam splitter and performing a joint photon-number measurement on the reflected beams. In this way the degree of entanglement of the shared state is increased and so is the fidelity of the teleported state.
We propose a scheme for quantum teleportation between two qubits, coupled sequentially to a cavity field. An implementation of the scheme is analyzed with superconducting qubits and a transmission line resonator, where measurements are restricted to continuous probing of the field leaking from the resonator rather than instantaneous projective Bell state measurement. We show that the past quantum state formalism S. Gammelmark, B. Julsgaard, and K. M\o{}lmer, Phys. Rev. Lett. 111, 160401 (2013) can be successfully applied to estimate what would have been the most likely Bell measurement outcome conditioned on our continuous signal record. This information determines which local operation on the target qubit yields the optimal teleportation fidelity. Our results emphasize the significance of applying a detailed analysis of quantum measurements in feedforward protocols in nonideal leaky quantum systems.
What knowledge can be obtained from the record of a continuous measurement about the quantum state of the measured system at the beginning of the measurement? The task of quantum state retrodiction, the inverse of the more common state prediction, is rigorously addressed in quantum measurement theory through retrodictive positive operator-valued measures (POVMs). This introduction to this general framework presents its practical formulation for retrodicting Gaussian quantum states using continuous-time homodyne measurements and applies it to optomechanical systems. We identify and characterize achievable retrodictive POVMs in common optomechanical operating modes with resonant or off-resonant driving fields and specific choices of local oscillator frequencies in homodyne detection. In particular, we demonstrate the possibility of a near-ideal measurement of the quadrature of the mechanical oscillator, giving direct access to the position or momentum distribution of the oscillator at a given time. This forms the basis for complete quantum state tomography, albeit in a destructive manner.
Summary form only given. Quantum teleportation, first proposed as a method for teleporting an unknown spin-1/2 quantum state from a sender, "Alice", to a receiver, "Bob", has been extended to continuous-variable quantum teleportation (CVQT). In this variant of quantum teleportation, Bob and Alice share a nonlocal entangled two-mode field which, ideally, should have perfect correlations between in-phase quadrature ('position' x) and out-of-phase quadrature ('momentum' p), although the requirement of perfect correlations can be relaxed somewhat. The experimental success of CVQT has recently been reported, with two-mode squeezed light providing the nonlocal, entangled source shared between Alice and Bob. The objective here is to consider whether CVQT has indeed been achieved, or could ever be achieved, in optical experiments employing conventional laser sources. In particular we show that, in the context of this experiment, Alice and Bob may not employ independent laser sources for their operations if the state is to be teleported, yet this requires them to share more than just the Einstein-Podolsky-Rosen (EPR) resource.
Retrodictive quantum states are states that propagate backwards in time from a measurement event. Although retrodictive quantum mechanics appears to be very different from the usual predictive formalism, in that propagation of states into the past appears to violate causality, this is not so. Indeed causality is not manifest in the time direction of propagation of quantum states at all. Instead, causality is ensured by the different normalization conditions applied to the preparation and measurement device operators. It is this difference that introduces the arrow of time into quantum mechanics. Retrodictive states are useful for applications such as measurement, predictive quantum state engineering and quantum communication. Here we show how any optical retrodictive state that can be expressed to a good approximation in a finite‐dimensional Hilbert space can be generated from predictive coherent states, a lossless multiport device and photodetectors. The composition of the retrodictive state can be controlled by adjusting the input predictive coherent states. This allows, for example, projection synthesis for an optical state to be achieved with the exotic reciprocal binomial reference state replaced by a simple coherent state.
Continuous variable (CV) entanglement refers to the type of entanglement of quantum wave-like systems that are described by continuous variables in an inherently infinite-dimensional space. It can become a crucial resource for quantum communication, sensing, and computation. We propose the mechanism of transfer of quantum entanglement (TQE) from a nonlocal photon to two initially separate single-mode squeezed vacuum (SMSV) states. The nonlocal photon is the only original quantum resource from which entanglement is transferred to CV states of a certain parity in a deterministic manner without them directly interacting with each other. Measurement-induced CV parity entanglement is tuned using initial squeezing and the beam splitter (BS) parameter, allowing us to estimate the probability of transfer of maximum entanglement at sufficiently high brightness to be 0.2344 for initial SMSV states. If, instead of the original SMSV states, we use those from which one photon is initially subtracted, then the heralded technique can turn the maximum entanglement probabilistic transfer protocol into a nearly deterministic one, the probability of which is >0.98. Such a perfect TQE from the nonlocal photon to a maximally parity-entangled CV state can be considered the most suitable for applications, since it preserves the trade-off between the probability of its implementation and brightness of the output non-Gaussian states.