It is not possible to disentangle a qubit in an unknown state $|\ensuremath{\psi}〉$ from a set of $N\ensuremath{-}1$ ancilla qubits prepared in a specific reference state $|0〉.$ That is, it is not possible to perfectly perform the transformation $(|\ensuremath{\psi},0,\dots{},0〉+|0,\ensuremath{\psi},\dots{},0〉+\ensuremath{\cdot}\ensuremath{\cdot}\ensuremath{\cdot}+|0,0,\dots{},\ensuremath{\psi}〉)\ensuremath{\rightarrow}|0,\dots{},0〉\ensuremath{\bigotimes}|\ensuremath{\psi}〉.$ The question is then how well we can do? We consider a number of different methods of extracting an unknown state from an entangled state formed from that qubit and a set of ancilla qubits in a known state. Measuring the whole system is, as expected, the least effective method. We present various quantum ``devices'' which disentangle the unknown qubit from the set of ancilla qubits. In particular, we present the optimal universal disentangler which disentangles the unknown qubit with a fidelity that does not depend on the state of the qubit, and a probabilistic disentangler which performs the perfect disentangling transformation, but with a probability less than 1.It is not possible to disentangle a qubit in an unknown state $|\ensuremath{\psi}〉$ from a set of $N\ensuremath{-}1$ ancilla qubits prepared in a specific reference state $|0〉.$ That is, it is not possible to perfectly perform the transformation $(|\ensuremath{\psi},0,\dots{},0〉+|0,\ensuremath{\psi},\dots{},0〉+\ensuremath{\cdot}\ensuremath{\cdot}\ensuremath{\cdot}+|0,0,\dots{},\ensuremath{\psi}〉)\ensuremath{\rightarrow}|0,\dots{},0〉\ensuremath{\bigotimes}|\ensuremath{\psi}〉.$ The question is then how well we can do? We consider a number of different methods of extracting an unknown state from an entangled state formed from that qubit and a set of ancilla qubits in a known state. Measuring the whole system is, as expected, the least effective method. We present various quantum ``devices'' which disentangle the unknown qubit from the set of ancilla qubits. In particular, we present the optimal universal disentangler which disentangles the unknown qubit with a fidelity that does not depend on the state of the qubit, and a probabilistic disentangler which performs the perfect disentangling transformation, but with a probability less than 1.

arXiv:quant-ph/0006047Physical Review AOct 11, 20005 citations

Quantum Entanglements

Duke University Press eBooksJan 1, 20060 citations

Disentangling Quantum States while Preserving All Local Properties

Tal Mor

We consider here a disentanglement process which transforms a state $\ensuremath{\rho}$ of two subsystems into an unentangled (i.e., separable) state, while not affecting the reduced density matrix of either subsystem. Recently, Terno [Phys. Rev. A 59, 3320 (1999)] showed that an arbitrary state cannot be disentangled, by a physically allowable process, into a tensor product of its reduced density matrices. In this Letter we show that there are sets of states which can be disentangled, but only into separable states other than the product of the reduced density matrices, and other sets of states which cannot be disentangled at all. Thus, we prove that a universal disentangling machine cannot exist.We consider here a disentanglement process which transforms a state $\ensuremath{\rho}$ of two subsystems into an unentangled (i.e., separable) state, while not affecting the reduced density matrix of either subsystem. Recently, Terno [Phys. Rev. A 59, 3320 (1999)] showed that an arbitrary state cannot be disentangled, by a physically allowable process, into a tensor product of its reduced density matrices. In this Letter we show that there are sets of states which can be disentangled, but only into separable states other than the product of the reduced density matrices, and other sets of states which cannot be disentangled at all. Thus, we prove that a universal disentangling machine cannot exist.

Physical Review LettersAug 16, 199927 citations

Quantum entanglements

Jeff Hecht

Nature PhysicsApr 1, 20077 citations

Quantum Entanglement

Paul Cummins

Jul 5, 20100 citations

Topological disentangler for the valence-bond-solid chain

Kouichi Okunishi

We discuss the topological disentangler for $S=1$ quantum spin chains in the Haldane phase. We first point out that the Kennedy-Tasaki (KT) nonlocal unitary transformation is the perfect disentangler for the Affleck-Kennedy-Lieb-Tasaki model. We then demonstrate that the KT transformation can be reconstructed as an assembly of pair disentanglers. Finally, we show that the KT transformation can be regarded as a topological disentangler, which selectively disentangles the twofold degeneracy in the entanglement spectrum of the $S=1$ Heisenberg chain.We discuss the topological disentangler for $S=1$ quantum spin chains in the Haldane phase. We first point out that the Kennedy-Tasaki (KT) nonlocal unitary transformation is the perfect disentangler for the Affleck-Kennedy-Lieb-Tasaki model. We then demonstrate that the KT transformation can be reconstructed as an assembly of pair disentanglers. Finally, we show that the KT transformation can be regarded as a topological disentangler, which selectively disentangles the twofold degeneracy in the entanglement spectrum of the $S=1$ Heisenberg chain.

arXiv:1011.3277Physical Review BMar 21, 201116 citations

It is not possible to disentangle a qubit in an unknown state $|\ensuremath{\psi}〉$ from a set of $N\ensuremath{-}1$ ancilla qubits prepared in a specific reference state

|0〉.

That is, it is not possible to perfectly perform the transformation $(|\ensuremath{\psi},0,\dots{},0〉+|0,\ensuremath{\psi},\dots{},0〉+\ensuremath{\cdot}\ensuremath{\cdot}\ensuremath{\cdot}+|0,0,\dots{},\ensuremath{\psi}〉)\ensuremath{\rightarrow}|0,\dots{},0〉\ensuremath{\bigotimes}|\ensuremath{\psi}〉.$ The question is then how well we can do? We consider a number of different methods of extracting an unknown state from an entangled state formed from that qubit and a set of ancilla qubits in a known state. Measuring the whole system is, as expected, the least effective method. We present various quantum ``devices'' which disentangle the unknown qubit from the set of ancilla qubits. In particular, we present the optimal universal disentangler which disentangles the unknown qubit with a fidelity that does not depend on the state of the qubit, and a probabilistic disentangler which performs the perfect disentangling transformation, but with a probability less than 1.

We discuss the topological disentangler for

S=1

quantum spin chains in the Haldane phase. We first point out that the Kennedy-Tasaki (KT) nonlocal unitary transformation is the perfect disentangler for the Affleck-Kennedy-Lieb-Tasaki model. We then demonstrate that the KT transformation can be reconstructed as an assembly of pair disentanglers. Finally, we show that the KT transformation can be regarded as a topological disentangler, which selectively disentangles the twofold degeneracy in the entanglement spectrum of the

S=1

Heisenberg chain.