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arXiv:quant-ph/0612172 · Physical Review A

Improving the entanglement transfer from continuous-variable systems to localized qubits using non-Gaussian states

Federico Casagrande, ALFREDO LULLI, Matteo G. A. Paris

Published Mar 26, 2007• 44 citations
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Abstract

We investigate the entanglement transfer from a bipartite continuous-variable (CV) system to a pair of localized qubits assuming that each CV mode couples to one qubit via the off-resonance Jaynes-Cummings interaction with different interaction times for the two subsystems. First, we consider the case of the CV system prepared in a Bell-like superposition and investigate the conditions for maximum entanglement transfer. Then we analyze the general case of two-mode CV states that can be represented by a Schmidt decomposition in the Fock number basis. This class includes both Gaussian and non-Gaussian CV states, as, for example, twin-beam (TWB) and pair-coherent (TMC, also known as two-mode-coherent) states, respectively. Under resonance conditions, equal interaction times for both qubits and different initial preparations, we find that the entanglement transfer is more efficient for TMC than for TWB states. In the perspective of applications such as in cavity QED or with superconducting qubits, we analyze in detail the effects of off-resonance interactions (detuning) and different interaction times for the two qubits, and discuss conditions to preserve the entanglement transfer.

DOI
10.1103/physreva.75.032336

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We investigate the entanglement transfer from a bipartite continuous-variable (CV) system to a pair of localized qubits assuming that each CV mode couples to one qubit via the off-resonance Jaynes-Cummings interaction with different interaction times for the two subsystems. First, we consider the case of the CV system prepared in a Bell-like superposition and investigate the conditions for maximum entanglement transfer. Then we analyze the general case of two-mode CV states that can be represented by a Schmidt decomposition in the Fock number basis. This class includes both Gaussian and non-Gaussian CV states, as, for example, twin-beam (TWB) and pair-coherent (TMC, also known as two-mode-coherent) states, respectively. Under resonance conditions, equal interaction times for both qubits and different initial preparations, we find that the entanglement transfer is more efficient for TMC than for TWB states. In the perspective of applications such as in cavity QED or with superconducting qubits, we analyze in detail the effects of off-resonance interactions (detuning) and different interaction times for the two qubits, and discuss conditions to preserve the entanglement transfer.
We study the entanglement transfer from a two-mode continuous variable system (initially in the two-mode SU(2) cat states) to a couple of discrete two-state systems (initially in an arbitrary mixed state), by use of the resonant Jaynes-Cummings (JC) interaction. We first quantitatively connect the entanglement transfer to non-Gaussianity of the two-mode SU(2) cat states and find a positive correlation between them. We then investigate the behaviors of the entanglement transfer and find that it is dependent on the initial state of the discrete systems. We also find that the largest possible value of the transferred entanglement exhibits a variety of behaviors for different photon number as well as for the phase angle of the two-mode SU(2) cat states. We finally consider the influences of the noise on the transferred entanglement.
We present two strategies to enhance the dynamical entanglement transfer from continuous-variable (CV) to finite-dimensional systems by employing multiple qubits. First, we consider the entanglement transfer to a composite finite-dimensional system of many qubits simultaneously interacting with a bipartite CV field. We show that, considering realistic conditions in the generation of CV entanglement, a small number of qubits resonantly coupled to the CV system are sufficient for an almost complete dynamical transfer of the entanglement. Our analysis also sheds further light on the transition between the microscopic and macroscopic behaviors of composite finite-dimensional systems coupled to bosonic fields (like atomic clouds interacting with light). Furthermore, we present a protocol based on sequential interactions of the CV system with some ancillary qubit systems and on subsequent measurements, allowing us to probabilistically convert CV entanglement into ``almost-perfect'' Bell pairs of two qubits. Our proposals are suited for realizations in various experimental settings, ranging from cavity-QED to cavity-integrated superconducting devices.
We consider a composite system of two remote mesoscopic Josephson junctions interacting locally with a two-mode non-classical cavity field and investigate entanglement transfer from a bipartite continuous-variable (CV) system to a pair of localized mesoscopic Josephson junctions. We obtain analytically the time-dependent characteristic functions in the Wigner representation for the two CV subsystems, where two cases are considered for the zero and finite temperatures. Furthermore, we analyse the influences of the temperature on the period recovery of the entanglement.
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.
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 without them directly interacting with each other in a deterministic manner. 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 . If, instead of the original SMSV states, we use those from which one photon is initially subtracted, then the heralded technique can turn the probabilistic maximum entanglement 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 and brightness of the output non-Gaussian states.
The problem of a controlled transfer of an entanglement initially encoded into two two-level atoms that are successively sent through two single-mode cavities is investigated. The atoms and the cavity modes form a four-qubit system and we demonstrate the conditions under which the initial entanglement encoded into the atoms can be completely transferred to other pairs of qubits. We find that in the case of non-zero detuning between the atomic transition frequencies and the cavity mode frequencies, no complete transfer of the initial entanglement is possible to any of the other pairs of qubits. In the case of exact resonance and equal coupling strengths of the atoms to the cavity modes, an initial maximally entangled state of the atoms can be completely transferred to the cavity modes. Complete transfer of the entanglement is restricted to the cavity modes, with transfer to the other pairs being limited to 50%. We find that complete transfer of an initial entanglement to other pairs of qubits may take place if the initial state is not the maximally entangled state and the atoms couple to the cavity modes with unequal strengths. Depending on the ratio between the coupling strengths, optimal entanglement can be created between the atoms and one of the cavity modes.