arXiv subjects

G. Vidal

Publications and source records attributed to G. Vidal.

52 records · Page 3Linked to original sources

arXiv2001

Optimal conversion of non--local unitary operations

We study when a non--local unitary operation acting on two $d$--level systems can probabilistically simulate another one when arbitrary local operations and classical communication are allowed. We provide necessary and sufficient conditions for the simulation to be possible. Probabilistic interconvertability is used to define an equivalence relation between gates. We show that this relation induces a finite number of classes, that we identify. In the case of two qubits, two classes of non--local operations exist. We choose the CNOT and SWAP as representatives of these classes. We show how the CNOT [SWAP] can be deterministically converted into any operation of its class. We also calculate the optimal probability of obtaining the CNOT [SWAP] from any operation of the corresponding class and provide a protocol to achieve this task.

quant-ph↗

arXiv2001

Optimal simulation of two-qubit Hamiltonians using general local operations

We consider the simulation of the dynamics of one nonlocal Hamiltonian by another, allowing arbitrary local resources but no entanglement nor classical communication. We characterize notions of simulation, and proceed to focus on deterministic simulation involving one copy of the system. More specifically, two otherwise isolated systems $A$ and $B$ interact by a nonlocal Hamiltonian $H \neq H_A+H_B$. We consider the achievable space of Hamiltonians $H'$ such that the evolution $e^{-iH't}$ can be simulated by the interaction $H$ interspersed with local operations. For any dimensions of $A$ and $B$, and any nonlocal Hamiltonians $H$ and $H'$, there exists a scale factor $s$ such that for all times $t$ the evolution $e^{-iH'st}$ can be simulated by $H$ acting for time $t$ interspersed with local operations. For 2-qubit Hamiltonians $H$ and $H'$, we calculate the optimal $s$ and give protocols achieving it. The optimal protocols do not require local ancillas, and can be understood geometrically in terms of a polyhedron defined by a partial order on the set of 2-qubit Hamiltonians.

quant-ph↗

arXiv2001

Entanglement capabilities of non-local Hamiltonians

We quantify the capability of creating entanglement for a general physical interaction acting on two qubits. We give a procedure for optimizing the generation of entanglement. We also show that a Hamiltonian can create more entanglement if one uses auxiliary systems.

quant-ph↗

arXiv2001

Catalysis in non--local quantum operations

We show how entanglement can be used, without being consumed, to accomplish unitary operations that could not be performed with out it. When applied to infinitesimal transformations our method makes equivalent, in the sense of Hamiltonian simulation, a whole class of otherwise inequivalent two-qubit interactions. The new catalysis effect also implies the asymptotic equivalence of all such interactions.

quant-ph↗

arXiv2001

When only two thirds of the entanglement can be distilled

We provide an example of distillable bipartite mixed state such that, even in the asymptotic limit, more pure-state entanglement is required to create it than can be distilled from it. Thus, we show that the irreversibility in the processes of formation and distillation of bipartite states, recently proved in [G. Vidal, J.I. Cirac, Phys. Rev. Lett. 86, (2001) 5803-5806], is not limited to bound-entangled states.

quant-ph↗

arXiv2001

Irreversibility in asymptotic manipulations of entanglement

We show that the process of entanglement distillation is irreversible by showing that the entanglement cost of a bound entangled state is finite. Such irreversibility remains even if extra pure entanglement is loaned to assist the distillation process.

quant-ph↗

arXiv2001

A computable measure of entanglement

We present a measure of entanglement that can be computed effectively for any mixed state of an arbitrary bipartite system. We show that it does not increase under local manipulations of the system, and use it to obtain a bound on the teleportation capacity and on the distillable entanglement of mixed states.

quant-ph↗

arXiv2001

Storing quantum dynamics in quantum states: stochastic programmable gate for U(1) operations

We show how quantum dynamics can be captured in the state of a quantum system, in such a way that the system can be used to stochastically perform, at a later time, the stored transformation perfectly on some other quantum system. Thus programmable quantum gates for quantum information processing are feasible if some probability of failure -that we show to decrease exponentially with the size of the storing resources- is allowed.

quant-ph↗

arXiv2001

Visible compression of commuting mixed states

We analyze the problem of quantum data compression of commuting density operators in the visible case. We show that the lower bound for the compression factor given by the Levitin--Holevo function is reached by providing an explicit protocol.

quant-ph↗

arXiv2000

Storage of quantum dynamics on quantum states: a quasi-perfect programmable quantum gate

We show how quantum dynamics (a unitary transformation) can be captured in the state of a quantum system, in such a way that the system can be used to perform, at a later time, the stored transformation almost perfectly on some other quantum system. Thus programmable quantum gates for quantum information processing are feasible if some small degree of imperfection is allowed. We discuss the possibility of using this fact for securely computing a secret function on a public quantum computer. Finally, our scheme for storage of operations also allows for a new form of quantum remote control.

quant-ph↗

arXiv2000

Optimal estimation of quantum dynamics

We construct the optimal strategy for the estimation of an unknown unitary transformation $U\in SU(d)$. This includes, in addition to a convenient measurement on a probe system, finding which is the best initial state on which $U$ is to act. When $U\in SU(2)$, such an optimal strategy can be applied to estimate simultaneously both the direction and the strength of a magnetic field, and shows how to use a spin 1/2 particle to transmit information about a whole coordinate system instead of only a direction in space.

quant-ph↗

arXiv2000

Optimal distillation of a GHZ state

We present the optimal local protocol to distill a Greenberger-Horne-Zeilinger (GHZ) state from a single copy of any pure state of three qubits.

quant-ph↗

arXiv2000

Three qubits can be entangled in two inequivalent ways

Invertible local transformations of a multipartite system are used to define equivalence classes in the set of entangled states. This classification concerns the entanglement properties of a single copy of the state. Accordingly, we say that two states have the same kind of entanglement if both of them can be obtained from the other by means of local operations and classical communcication (LOCC) with nonzero probability. When applied to pure states of a three-qubit system, this approach reveals the existence of two inequivalent kinds of genuine tripartite entanglement, for which the GHZ state and a W state appear as remarkable representatives. In particular, we show that the W state retains maximally bipartite entanglement when any one of the three qubits is traced out. We generalize our results both to the case of higher dimensional subsystems and also to more than three subsystems, for all of which we show that, typically, two randomly chosen pure states cannot be converted into each other by means of LOCC, not even with a small probability of success.

quant-ph↗

arXiv2000

Reversible combination of inequivalent kinds of multipartite entanglement

We present a family of tri-partite entangled states that, in an asymptotical sense, can be reversibly converted into EPR states shared by only two of parties (say B and C), and tripartite GHZ states. Thus we show that bipartite and genuine tripartite entanglement can be reversibly combined in several copies of a single tripartite state. For such states the corresponding fractions of GHZ and of EPR states represent a complete quantification of their (asymptotical) entanglement resources. More generally, we show that the three different kinds of bipartite entanglement (AB, AC and BC EPR states) and tripartite GHZ entanglement can be reversibly combined in a single state of three parties. Finally, we generalize this result to any number of parties.

quant-ph↗

arXiv1999

Optimal estimation of two-qubit pure-state entanglement

We present optimal measuring strategies for the estimation of the entanglement of unknown two-qubit pure states and of the degree of mixing of unknown single-qubit mixed states, of which N identical copies are available. The most general measuring strategies are considered in both situations, to conclude in the first case that a local, although collective, measurement suffices to estimate entanglement, a non-local property, optimally.

quant-ph↗

arXiv1998

Optimal minimal measurements of mixed states

The optimal and minimal measuring strategy is obtained for a two-state system prepared in a mixed state with a probability given by any isotropic a priori distribution. We explicitly construct the specific optimal and minimal generalized measurements, which turn out to be independent of the a priori probability distribution, obtaining the best guesses for the unknown state as well as a closed expression for the maximal mean averaged fidelity. We do this for up to three copies of the unknown state in a way which leads to the generalization to any number of copies, which we then present and prove.

quant-ph↗