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arXiv:quant-ph/0606165 · New Journal of Physics

How to hide a secret direction

E. Bagán, John Calsamiglia, Rafał Demkowicz-Dobrzański, R. Muñoz-Tapia

Published Aug 1, 2007• 1 citation
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Abstract

We present a procedure that uses a multipartite quantum state to communicate a secret spatial direction when there is no shared reference frame between the preparer and the group of recipients. The procedure guarantees that the recipients can determine the direction if they perform joint measurements on the state, but fail to do so if they restrict themselves to local operations and classical communication (LOCC). We calculate the fidelity for joint measurements, give bounds on the fidelity achievable by LOCC, and prove that there is a non-vanishing gap between the two of them, even in the limit of infinitely many copies. The robustness of the procedure under particle loss is also studied. Additionally, we find bounds on the probability of discriminating by LOCC between the invariant subspaces of total angular momentum N /2 and N /2−1 in a system of N elementary spins.

DOI
10.1088/1367-2630/9/8/244

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We present a procedure that uses a multipartite quantum state to communicate a secret spatial direction when there is no shared reference frame between the preparer and the group of recipients. The procedure guarantees that the recipients can determine the direction if they perform joint measurements on the state, but fail to do so if they restrict themselves to local operations and classical communication (LOCC). We calculate the fidelity for joint measurements, give bounds on the fidelity achievable by LOCC, and prove that there is a non-vanishing gap between the two of them, even in the limit of infinitely many copies. The robustness of the procedure under particle loss is also studied. Additionally, we find bounds on the probability of discriminating by LOCC between the invariant subspaces of total angular momentum N /2 and N /2−1 in a system of N elementary spins.
We show that a pair of two-qubit product measurements can be perfectly distinguished when accessed jointly, yet cannot be perfectly distinguished when their local components are distributed between distant parties restricted to local quantum operations and classical communication (LOCC). This establishes a measurement analogue of nonlocality without entanglement that, unlike its state-based counterpart, emerges in a remarkably simple setting. We further uncover a hierarchy of LOCC discrimination strategies: adaptive protocols, in which the probe used at one site may depend on classical information obtained from another, can strictly outperform restricted non-adaptive protocols, as demonstrated by a set of six bipartite qutrit product measurements. We also show that LOCC distinguishability of bipartite measurements can be intrinsically directional, depending on which party initiates the protocol. More generally, we construct pairs of nnn-qubit product measurements that are globally perfectly distinguishable but cannot be perfectly distinguished across any bipartition, even when all parties on either side of the bipartition are allowed arbitrary joint quantum operations. Finally, we show how quantum data hiding based on quantum-process nonlocality without entanglement can be realized using elementary optical components.
Quantum nonlocality, a form of nonclassicality, serves as a crucial resource in quantum information processing. Nonlocality in quantum systems is exemplified by the perfect discrimination of orthogonal quantum states through single joint measurements, which is unattainable using local operations and classical communication (LOCC). Bandyopadhyay [S. Bandyopadhyay, Phys. Rev. Lett. 106, 210402 (2011)] established that, with LOCC alone, at most $N\ensuremath{-}1$ copies of NNN orthogonal quantum states are required for perfect discrimination. Here, we present the experimental verification of orthogonal quantum state discrimination employing LOCC. Our results demonstrate that up to three copies suffice for the perfect distinction of four orthogonal two-qubit states via LOCC. The verified method of perfectly distinguishing orthogonal quantum state sets offers potential applications in quantum information processes, including quantum secret sharing and quantum teleportation.
The problem of unambiguous state discrimination consists of determining in which of a set of known quantum states a particular system is. One is allowed to fail but not to make a mistake. The optimal procedure is the one with the lowest failure probability. This procedure has been extended to bipartite states where the two parties Alice and Bob are allowed to manipulate their particles locally and communicate classically in order to determine which of two possible two-particle states they have been given. The failure probability of this local procedure is the same as if the two particles were together in the same location. Here we examine the effect of restricting the classical communication between the parties, either allowing none or eliminating the possibility that one party's measurement depends on the result of the other party's. These issues are studied for two-qubit states, and optimal procedures are found. In some cases the restrictions cause increases in the failure probability, but in other cases they do not. Applications of this procedure, in particular to secret sharing, are discussed.
We consider a quantum system of two nonorthogonal bipartite quantum states. We distribute the qubits between two parties, Alice and Bob. They each measure their qubits and then compare their measurement results to determine which state they were sent. This procedure is error-free, which implies that it must sometimes fail. In addition, no quantum memory is required; it is not necessary for one of the qubits to be stored until the result of the measurement on the other is known. We consider the cases in which, should a failure occur, both parties receive a failure signal or only one does. In the latter case, if the two states share the same Schmidt basis, the states can be discriminated with the same failure probability as would be obtained if the qubits were measured together. This scheme is sufficiently simple that it can be generalized to multipartite qubit and qudit states. Applications to quantum secret sharing are discussed.
We consider multiparty quantum state discrimination and present a multiparty quantum data-hiding scheme for one classical bit to be shared among multiple parties. In the proposed scheme, any pair of parties can collaborate to perfectly recover the hidden bit through a joint measurement, whereas measurements based on local operations and classical communication(LOCC) performed even by all parties reveal only an arbitrarily small amount of information. We further provide bounds on the optimal LOCC discrimination of multiparty quantum states. The proposed scheme can be implemented using only separable states of low-dimensional quantum systems, enhancing its practical feasibility.
We initially consider a quantum system consisting of two qubits, which can be in one of two nonorthogonal states $\ensuremath{\mid}{\ensuremath{\Psi}}_{0}⟩$ and $\ensuremath{\mid}{\ensuremath{\Psi}}_{1}⟩$. We distribute the qubits to two parties, Alice and Bob. They each measure their qubits and then compare their measurement results to determine which state they were sent. This procedure is error-free, which implies that it must sometimes fail. In addition, no quantum memory is required; it is not necessary for one of the qubits to be stored until the result of the measurement on the other is known. We consider the cases in which, should failure occur, both parties receive a failure signal or only one does. In the latter case, if the two states share the same Schmidt basis, the states can be discriminated with the same failure probability that would be obtained if the qubits were measured together. This scheme is sufficiently simple that it can be generalized to multipartite qubit, and qudit, states. Applications to quantum secret sharing are discussed. Finally, we present an optical scheme to experimentally realize the protocol in the case of two qubits.