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Photonic Hybrid State Entanglement Swapping using Cat State Superpositions

Ryan C. Parker, Jaewoo Joo, Timothy P. Spiller

Published Nov 18, 2020• 6 citations
OpenAlex

Abstract

We propose the use of hybrid entanglement in an entanglement swapping protocol, as means of distributing a Bell state with high fidelity to two parties, Alice and Bob. The hybrid entanglement used in this work is described as a discrete variable (Fock state) and a continuous variable (cat state superposition) entangled state. We model equal and unequal levels of photonic loss between the two propagating continuous variable modes, before detecting these states via a projective vacuum-one-photon measurement, and the other mode via balanced homodyne detection. We investigate homodyne measurement imperfections, and the associated success probability of the measurement schemes chosen in this protocol. We show that our entanglement swapping scheme is resilient to low levels of photonic losses, as well as low levels of averaged unequal losses between the two propagating modes, and show an improvement in this loss resilience over other hybrid entanglement schemes using coherent state superpositions as the propagating modes. Finally, we conclude that our protocol is suitable for potential quantum networking applications which require two nodes to share entanglement separated over a distance of 5-10 km when used with a suitable entanglement purification scheme.

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We propose the use of hybrid entanglement in an entanglement swapping protocol, as means of distributing a Bell state with high fidelity to two parties, Alice and Bob. The hybrid entanglement used in this work is described as a discrete variable (Fock state) and a continuous variable (cat state superposition) entangled state. We model equal and unequal levels of photonic loss between the two propagating continuous variable modes, before detecting these states via a projective vacuum-one-photon measurement, and the other mode via balanced homodyne detection. We investigate homodyne measurement imperfections, and the associated success probability of the measurement schemes chosen in this protocol. We show that our entanglement swapping scheme is resilient to low levels of photonic losses, as well as low levels of averaged unequal losses between the two propagating modes, and show an improvement in this loss resilience over other hybrid entanglement schemes using coherent state superpositions as the propagating modes. Finally, we conclude that our protocol is suitable for potential quantum networking applications which require two nodes to share entanglement separated over a distance of 5-10 km when used with a suitable entanglement purification scheme.
We propose the use of hybrid entanglement in an entanglement swapping protocol, as means of distributing a Bell state with high fidelity to two parties. The hybrid entanglement used in this work is described as a discrete variable (Fock state) and a continuous variable (cat state super- position) entangled state. We model equal and unequal levels of photonic loss between the two propagating continuous variable modes, before detecting these states via a projective vacuum-one-photon measurement, and the other mode via balanced homodyne detection. We investigate homodyne measurement imperfections, and the associated success probability of the measurement schemes chosen in this protocol. We show that our entanglement swapping scheme is resilient to low levels of photonic losses, as well as low levels of averaged unequal losses between the two propagating modes, and show an improvement in this loss resilience over other hybrid entanglement schemes using coherent state superpositions as the propagating modes. Finally, we conclude that our protocol is suitable for potential quantum networking applications which require two nodes to share entanglement separated over a distance of 5 -- 10 km , when used with a suitable entanglement purification scheme.
We propose a scheme of loss-resilient entanglement swapping between two distant parties in lossy optical fibre. In this scheme, Alice and Bob each begin with a pair of entangled non-classical states; these "hybrid states" of light are entangled discrete variable (Fock state) and continuous variable (coherent state) pairs. The continuous variable halves of each of these pairs are sent through lossy optical fibre to a middle location, where these states are then mixed (using a 50:50 beam-splitter) and measured. The detection scheme we use is to measure one of these modes via vacuum detection, and to measure the other mode using balanced homodyne detection. In this work we show that the |Φ+⟩=(|00⟩+|11⟩)/2–√ Bell state can theoretically be produced following this scheme with high fidelity and entanglement, even when allowing for a small amount of loss. It can be shown that there is an optimal amplitude value (α) of the coherent state, when allowing for such loss. We also investigate the realistic circumstance when the loss is not balanced in the propagating modes. We demonstrate that a small amount of loss mismatch does not destroy the overall entanglement, thus demonstrating the physical practicality of this protocol.
We propose a scheme of loss-resilient entanglement swapping between two distant parties in lossy optical fibre. In this scheme, Alice and Bob each begin with a pair of entangled non-classical states; these 'hybrid states' of light are entangled discrete variable (Fock state) and continuous variable (CVs) (coherent state) pairs. The CV halves of each of these pairs are sent through lossy optical fibre to a middle location, where these states are then mixed (using a 50:50 beam-splitter) and measured. The detection scheme we use is to measure one of these modes via vacuum detection, and to measure the other mode using balanced homodyne detection. In this work we show that the Bell state can theoretically be produced following this scheme with high fidelity and entanglement, even when allowing for a small amount of loss. It can be shown that there is an optimal amplitude value ( α ) of the coherent state, when allowing for such loss. We also investigate the realistic circumstance when the loss is not balanced in the propagating modes. We demonstrate that a small amount of loss mismatch does not destroy the overall entanglement, thus demonstrating the physical practicality of this protocol.
Distributing and sharing entanglement at a distance is a key ingredient in many future quantum communication protocols, however entanglement is a fragile resource and can break down upon interacting with the environment. Within this thesis we present two possible entanglement swapping protocols, and show that these protocols are resilient to small levels of photonic losses. We propose the use of these protocols in quantum communication schemes that require shared entangled qubits, in the form of a Bell state. \nThe input states to our proposed protocols are hybrid entangled states, which are discrete-variable and continuous-variable entangled states. We use the vacuum and \nsingle photon Fock state as our discrete half, which is stationary in our entanglement swapping protocol, whereas the continuous variable half is modelled as travelling through lossy optical fibre before being measured. The first protocol uses coherent states in a superposition as propagating modes in our entanglement swapping setup, \nwhereas the second, more complicated, protocol uses superposed cat states. \nWe model photonic losses by applying a beam-splitter of transmission T to our propagating continuous variable modes, along with an input vacuum state. We also model the more realistic circumstance in which the losses in these two continuous variable modes are not equal. We then detect these continuous variable modes using a vacuum projective measurement and balanced homodyne detection. We also investigate homodyne measurement imperfections and non-ideal outcomes, as well as success probabilities of these measurement schemes. We calculate the entanglement negativity and linear entropy of our final two qubit state, as well as fidelity against the |\\Phi^+> Bell state in the coherent state protocol, and a phase-rotated |\\Phi^+(\\alpha)> Bell state in the cat state regime. \nWe demonstrate that a small amount of loss mismatch does not destroy the overall entanglement, thus demonstrating the physical practicality of this protocol.
We propose a scheme of loss-resilient entanglement swapping between two distant parties via an imperfect optical channel. In this scheme, two copies of hybrid entangled states are prepared and the continuous-variable parts propagate through lossy media. In order to perform successful entanglement swapping, several different measurement schemes are considered for the continuous-variable parts such as single-photon detection for ideal cases and a homodyne detection for practical cases. We find that the entanglement swapping using hybrid states with small amplitudes offers larger entanglement than the discrete-variable entanglement swapping in the presence of large losses. Remarkably, this hybrid scheme still offers excellent robustness of entanglement to the detection inefficiency. Thus, the proposed scheme could be used for the practical quantum key distribution in hybrid optical states under photon losses.
Protocols for probabilistic entanglement-assisted quantum teleportation and for entanglement swapping of material qubits are presented. They are based on a protocol for postselective Bell- state projection which is capable of projecting two material qubits onto a Bell state with the help of ancillary coherent multiphoton states and postselection by balanced homodyne photodetection. Provided this photonic postselection is successful, we explore the theoretical possibilities of realizing unit-fidelity quantum teleportation and entanglement swapping with 2525%25 success probability. This photon-assisted Bell projection is generated by coupling almost resonantly the two material qubits to single modes of the radiation field in two separate cavities in a Ramsey-type interaction sequence and by measuring the emerged field states in a balanced homodyne detection scenario. As these quantum protocols require basic tools of quantum state engineering of coherent multiphoton states and balanced homodyne photodetection, they may offer interesting perspectives in particular for current quantum optical applications in quantum information processing.