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Physical Review A

Conclusive modification of the overlap between two quantum states

Luis Roa, M. L. Ladrón de Guevara, A. Delgado

Published Mar 8, 2010• 8 citations
Publisher

Abstract

The task of changing the overlap between two quantum states cannot be performed by making use of unitary evolution only. However, by means of a unitary-reduction process, it could be modified. Here we study in detail the problem of mapping two known pure states onto two other states in such a way that the overlap between the outcome states is different from the one of the initial states. We show that the modulus of the overlap can be reduced only probabilistically, whereas it can be increased deterministically. Our analysis shows that the phases of the involved overlaps play an important role in the increase of the success probability of the desired process.

DOI
10.1103/physreva.81.034101

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The task of changing the overlap between two quantum states cannot be performed by making use of unitary evolution only. However, by means of a unitary-reduction process, it could be modified. Here we study in detail the problem of mapping two known pure states onto two other states in such a way that the overlap between the outcome states is different from the one of the initial states. We show that the modulus of the overlap can be reduced only probabilistically, whereas it can be increased deterministically. Our analysis shows that the phases of the involved overlaps play an important role in the increase of the success probability of the desired process.
The task of changing the overlap between two quantum states can not be performed by making use of a unitary evolution only. However, by means of a unitary-reduction process it can be probabilistically modified. Here we study in detail the problem of mapping two known pure states onto other two states in such a way that the final inner product between the outcome states is different from the inner product of the initial states. In this way we design an optimal non-orthogonal quantum state preparation scheme by starting from an orthonormal basis. In this scheme the absolute value of the inner product can be reduced only probabilistically whereas it can be increased deterministically. Our analysis shows that the phases of the involved inner products play an important role in the increase of the success probability of the desired process.
We propose a scheme for Alice to change remotely and conclusively the overlap between Bob’s two nonorthogonal qubit states with a finite probability of success. The remote nonunitary evolution of Bob’s primary system could be generated by performing a proper nonlocal unitary transformation on Bob’s primary system and Alice’s auxiliary system, followed by a local von Neumann projective measurement on Alice’s ancilla. The various desired inner product modifications between Bob’s primary states can be efficiently and fully controlled by Alice’s auxiliary states. We build a quantum network for implementing rapidly the remote nonunitary transformation, and thus provide a feasible physical means to realize the remote and controllable inner product modification. This scheme is feasible for current experimental technology.
A probabilistic method for the unambiguous modification of non-orthogonal quantum states is proposed. This is based on conclusive modifications of the inner product between two pure quantum states in a discrimination-like process. We experimentally implemented this protocol by using two-photon polarization states generated in the process of spontaneous parametric down conversion. In the experiment, for codifying initial quantum states, we consider single photon states and heralded detection. As application, we show that when our protocol is applied to partially entangled states it allows a fine control of the amount of entanglement of the modified states.
The processes for decreasing probabilistically and increasing deterministically the overlap between two quantum states must be assisted by an auxiliary quantum system. The probabilistic scheme is implemented through a unitary-reduction process, while the deterministic one is accomplished only with a joint unitary transformation. In both schemes a unitary operation is responsible for coupling the two involved systems thus introducing correlation between them. In this work we study the quantum correlations required to achieve the probabilistic scheme with optimal probability, and we characterize the quantum correlation involved in the deterministic procedure. We find a that both schemes can be accomplished with quantum discord and without entanglement. In addition, we propose a physical implementation of the probabilistic scheme with twin photons generated in the process of spontaneous parametric down-conversion. The states are encoded in the polarization of a single photon and the auxiliary system becomes its propagation path; the second photon is used for heralded detection.
We study the problem of driving a known initial quantum state onto a known pure state without using a unitary evolution. This task can be achieved by means of von Neumann measurement processes, introducing N observables which are consecutively measured in order to approach the state of the system to the target state. We proved that the probability of projecting onto the target state can be increased meaningfully by adding suitable observables to the process, that is, it converges to 1 when N increases. We also discuss a physical implementation of this scheme.