A mixed quantum state $\ensuremath{\rho}$ shared between two parties is said to be distillable if, by means of a protocol involving only local quantum operations and classical communication, the two parties can transform some number of copies of $\ensuremath{\rho}$ into a single shared pair of qubits having high fidelity with the maximally entangled state $|{\ensuremath{\varphi}}^{+}\ensuremath{\rangle}=(|00\ensuremath{\rangle}+|11\ensuremath{\rangle})/\sqrt{2}$. In this Letter it is proved that there exist states that are distillable, but for which an arbitrarily large number of copies is required before any distillation procedure can produce a shared pair of qubits with even a small amount of entanglement. Specifically, for every positive integer $n$ there exists a state $\ensuremath{\rho}$ that is distillable, but, given $n$ or fewer copies of $\ensuremath{\rho}$, every distillation procedure outputting a single shared pair of qubits outputs those qubits in a separable (i.e., unentangled) state.A mixed quantum state $\ensuremath{\rho}$ shared between two parties is said to be distillable if, by means of a protocol involving only local quantum operations and classical communication, the two parties can transform some number of copies of $\ensuremath{\rho}$ into a single shared pair of qubits having high fidelity with the maximally entangled state $|{\ensuremath{\varphi}}^{+}\ensuremath{\rangle}=(|00\ensuremath{\rangle}+|11\ensuremath{\rangle})/\sqrt{2}$. In this Letter it is proved that there exist states that are distillable, but for which an arbitrarily large number of copies is required before any distillation procedure can produce a shared pair of qubits with even a small amount of entanglement. Specifically, for every positive integer $n$ there exists a state $\ensuremath{\rho}$ that is distillable, but, given $n$ or fewer copies of $\ensuremath{\rho}$, every distillation procedure outputting a single shared pair of qubits outputs those qubits in a separable (i.e., unentangled) state.

arXiv:quant-ph/0312123Physical Review LettersJul 1, 200480 citations

Experimental Single-Copy Entanglement Distillation

Sebastian Ecker, Philipp Sohr, Lukas Bulla +3 more

The phenomenon of entanglement marks one of the furthest departures from classical physics and is indispensable for quantum information processing. Despite its fundamental importance, the distribution of entanglement over long distances through photons is unfortunately hindered by unavoidable decoherence effects. Entanglement distillation is a means of restoring the quality of such diluted entanglement by concentrating it into a pair of qubits. Conventionally, this would be done by distributing multiple photon pairs and distilling the entanglement into a single pair. Here, we turn around this paradigm by utilizing pairs of single photons entangled in multiple degrees of freedom. Specifically, we make use of the polarization and the energy-time domain of photons, both of which are extensively field tested. We experimentally chart the domain of distillable states and achieve relative fidelity gains up to 13.8%. Compared to the two-copy scheme, the distillation rate of our single-copy scheme is several orders of magnitude higher, paving the way towards high-capacity and noise-resilient quantum networks.The phenomenon of entanglement marks one of the furthest departures from classical physics and is indispensable for quantum information processing. Despite its fundamental importance, the distribution of entanglement over long distances through photons is unfortunately hindered by unavoidable decoherence effects. Entanglement distillation is a means of restoring the quality of such diluted entanglement by concentrating it into a pair of qubits. Conventionally, this would be done by distributing multiple photon pairs and distilling the entanglement into a single pair. Here, we turn around this paradigm by utilizing pairs of single photons entangled in multiple degrees of freedom. Specifically, we make use of the polarization and the energy-time domain of photons, both of which are extensively field tested. We experimentally chart the domain of distillable states and achieve relative fidelity gains up to 13.8%. Compared to the two-copy scheme, the distillation rate of our single-copy scheme is several orders of magnitude higher, paving the way towards high-capacity and noise-resilient quantum networks.

arXiv:2101.11503Physical Review LettersJul 23, 202194 citations

Entanglement Theory Beyond the Paradigm of Single-Copy Entanglement Characterization

Klára Baksová

Jul 1, 20260 citations

Threshold ( Q , P ) distillation of multipartite quantum correlations

Shashank Gupta, William J. Munro, Carlos Cid

We introduce a threshold quantum distillation protocol that enables the extraction of perfect quantum correlations from multiple imperfect copies of a multipartite quantum state using only a subset of the parties ( Q < P ) in the network. In particular, we show that for high-dimensional Greenberger–Horne–Zeilinger states, entanglement can be distilled by local filtering operations applied by just a single party, independent of the total number of parties in the network. In contrast, for the W states, at least P − 1 parties are required for successful distillation, highlighting a strong connection between distillability and separability. We provide explicit protocols for threshold entanglement distillation and threshold steering distillation (TSD), and establish a direct link between the two: Any assemblage that can be distilled via TSD necessarily corresponds to a distillable entangled state. Our framework introduces a scalable and experimentally viable approach to distillation in quantum networks, with potential applications in distributed quantum computing, communication, and cryptography.We introduce a threshold quantum distillation protocol that enables the extraction of perfect quantum correlations from multiple imperfect copies of a multipartite quantum state using only a subset of the parties ( Q < P ) in the network. In particular, we show that for high-dimensional Greenberger–Horne–Zeilinger states, entanglement can be distilled by local filtering operations applied by just a single party, independent of the total number of parties in the network. In contrast, for the W states, at least P − 1 parties are required for successful distillation, highlighting a strong connection between distillability and separability. We provide explicit protocols for threshold entanglement distillation and threshold steering distillation (TSD), and establish a direct link between the two: Any assemblage that can be distilled via TSD necessarily corresponds to a distillable entangled state. Our framework introduces a scalable and experimentally viable approach to distillation in quantum networks, with potential applications in distributed quantum computing, communication, and cryptography.

arXiv:2408.15274Physical Review ResearchJan 5, 20260 citations

n

there exists a state $\ensuremath{\rho}$ that is distillable, but, given

n

or fewer copies of $\ensuremath{\rho}$, every distillation procedure outputting a single shared pair of qubits outputs those qubits in a separable (i.e., unentangled) state.