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Physica Scripta

Quantum remote control: remotely and conclusively changing the overlap between two qubit states

Libing Chen, Haiping Lu

Published Sep 1, 2015• 0 citations
Publisher

Abstract

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.

DOI
10.1088/0031-8949/90/9/095102

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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.
Alice, Cindy, and Bob are three remote parties. We present a scheme which allows Alice and Cindy to transform probabilistically and conclusively Bob's unknown d-level quantum (qudit) state into another. In this scheme, the remote positive operator valued measurements (POVM) lies at the heart. Based on the knowledge of probability amplitudes and phase factors of Bob's original state and target state, Alice and Cindy could construct jointly the required optimal POVM, which acts remotely on Bob's (2d-1)-dimensional direct sum space. We construct a quantum network for realizing the remote POVM with 2(d-1) remote two-level unitary rotations, and thus provide a feasible physical means to realize the remote POVM. The fact that the remote POVM could be realized using only 2(d-1) two-level Bell states (ebits) and 3(d-1) two-level classical communications (cbits) is notable. This scheme can be generalized to implement conclusively the (N+2)-party remote qudit state transformation via (d-1) (N+1)-body two-level GHZ states, in which the phase factors of Bob's original state and target state are shared jointly by N agents. The success probability of implementing this remote state transformation is also investigated. This scheme is simpler but conclusive, and more efficient but with less resource, which will make it more feasible with the current experimental technology and more suitable for large-scale quantum network.
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Abstract The scheme for asymmetric and deterministic controlled bidirectional joint remote state preparation by using one ten-qubit entangled state as the quantum channel is proposed. In this scheme, Alice and David want to remotely prepare an arbitrary single-qubit state at Bob’s site, at the same time, Bob and Eve wish to help Alice remotely prepare an arbitrary two-qubit entangled state. Alice and Bob can simultaneously prepare the desired states with the cooperation of David and Eve under the control of Charlie .
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.
We study the remote implementation of a unitary transformation on the state of a qubit. We show the existence of nontrivial protocols (i.e., using less resources than bidirectional state teleportation) that allow the perfect remote implementation of certain continuous sets of quantum operations. We prove that, up to a local change of basis, only two subsets exist that can be implemented remotely with a nontrivial protocol: Arbitrary rotations around a fixed direction $\stackrel{\ensuremath{\rightarrow}}{n}$ and a $\ensuremath{\pi}$ rotation about an arbitrary direction lying in a plane orthogonal to $\stackrel{\ensuremath{\rightarrow}}{n}.$ The former operations effectively constitute the teleportation of arbitrary angles. The overall classical information and distributed entanglement cost required for the remote implementation depends on whether it is known, a priori, in which of the two teleportable subsets the transformation belongs. If it is known, the optimal protocol consumes one e-bit of entanglement and one c-bit in each direction. If it is not known in which subset the transformation belongs, two e-bits of entanglement need to be consumed and the classical channel becomes asymmetric with two c-bits being conveyed from Alice to Bob but only one from Bob to Alice.
Deterministically cloning (copying) nonorthogonal states is forbidden in quantum mechanics, but deterministic pseudo-unitary cloning is possible in a nonunitary system. We prove and show that, for any two nonorthogonal qubit states, we can find a linear, invertible Hermitian (metric) operator to make these states mutually orthogonal with respect to the corresponding pseudo-inner product. From this metric operator, we construct a pseudo-Hermitian Hamiltonian and its evolution operator as an ideal, deterministic pseudo-unitary cloner. For applicability, suppose Alice lives in our ordinary universe and Bob lives in a universe that has the desired pseudo-unitary evolution. Alice would send her nonorthogonal states to Bob and Bob would do the cloning deterministically and send back to Alice. The quantum channel will be lossy not due to Bob's universe's properties, but rather due to problems making a channel between the two universes. We experimentally demonstrate deterministic pseudo-unitary two-qubit cloning for a photonic pseudo-unitary two-qubit system. In our universe we have to demonstrate that universe by executing a postselected gate that effects loss-based pseudo-unitary evolution. Furthermore, we introduce an algorithmic method for designing experimental realizations of a generic class of nonunitary operators for pseudo-unitary cloning.