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Register a new userDevising local protocols for multipartite quantum measurements
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Scott M. Cohen
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We provide a method of designing protocols for implementing multipartite quantum measurements when the parties are restricted to local operations and classical communication (LOCC). For each finite integer number of rounds, $r$, the method succeeds in every case for which an $r$-round protocol exists for the measurement under consideration, and failure of the method has the immediate implication that the measurement under consideration cannot be implemented by LOCC no matter how many rounds of communication are allowed, including when the number of rounds is allowed to be infinite. It turns out that this method shows---often with relative ease---the impossibility by LOCC for a number of examples, including cases where this was not previously known, as well as the example that first demonstrated what has famously become known as nonlocality without entanglement.
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In a recent paper cite{mySEPvsLOCC}, we showed how to construct a quantum protocol for implementing a bipartite, separable quantum measurement using only local operations on subsystems and classical communication between parties (LOCC) within any fixed number of rounds of communication, whenever such a protocol exists. Here, we generalize that construction to one that applies for any number of parties. One important observation is that the construction automatically determines the ordering of the parties measurements, overcoming a significant apparent difficulty in designing protocols for more than two parties. We also present various other results about LOCC, including showing that if, in any given measurement operator of the separable measurement under consideration, the local parts for two different parties are rank-1 operators that are not repeated in any other measurement operator of the measurement, then this separable measurement cannot be exactly implemented by LOCC in any finite number of rounds.
Local quantum uncertainty captures purely quantum correlations excluding their classical counterpart. This measure is quantum discord type, however with the advantage that there is no need to carry out the complicated optimization procedure over measurements. This measure is initially defined for bipartite quantum systems and a closed formula exists only for $2 otimes d$ systems. We extend the idea of local quantum uncertainty to multi-qubit systems and provide the similar closed formula to compute this measure. We explicitly calculate local quantum uncertainty for various quantum states of three and four qubits, like GHZ state, W state, Dicke state, Cluster state, Singlet state, and Chi state all mixed with white noise. We compute this measure for some other well known three qubit quantum states as well. We show that for all such symmetric states, it is sufficient to apply measurements on any single qubit to compute this measure, whereas in general one has to apply measurements on all parties as local quantum uncertainties for each bipartition can be different for an arbitrary quantum state.
Given a quantum system on many qubits split into a few different parties, how much total correlations are there between these parties? Such a quantity -- aimed to measure the deviation of the global quantum state from an uncorrelated state with the same local statistics -- plays an important role in understanding multi-partite correlations within complex networks of quantum states. Yet, the experimental access of this quantity remains challenging as it tends to be non-linear, and hence often requires tomography which becomes quickly intractable as dimensions of relevant quantum systems scale. Here, we introduce a much more experimentally accessible quantifier of total correlations, which can be estimated using only single-qubit measurements. It requires far fewer measurements than state tomography, and obviates the need to coherently interfere multiple copies of a given state. Thus we provide a tool for proving multi-partite correlations that can be applied to near-term quantum devices.
In recent years, the use of information principles to understand quantum correlations has been very successful. Unfortunately, all principles considered so far have a bipartite formulation, but intrinsically multipartite principles, yet to be discovered, are necessary for reproducing quantum correlations. Here, we introduce local orthogonality, an intrinsically multipartite principle stating that events involving different outcomes of the same local measurement must be exclusive, or orthogonal. We prove that it is equivalent to no-signaling in the bipartite scenario but more restrictive for more than two parties. By exploiting this non-equivalence, it is then demonstrated that some bipartite supra-quantum correlations do violate local orthogonality when distributed among several parties. Finally, we show how its multipartite character allows revealing the non-quantumness of correlations for which any bipartite principle fails. We believe that local orthogonality is a crucial ingredient for understanding no-signaling and quantum correlations.
In this paper, we mainly study the local distinguishable multipartite quantum states by local operations and classical communication (LOCC) in $m_1otimes m_2otimesldotsotimes m_n$ , where the quantum system $m_1$ belongs to Alice, $m_2$ belongs to Bob, ldots and $m_n$ belongs to Susan. We first present the pure tripartite distinguishable orthogonal quantum states by LOCC in $m_1otimes m_2otimes m_3$. With the conclusion in $m_1otimes m_2otimes m_3$, we prove distinguishability or indistinguishability of some quantum states. At last, we give the $n$-party distinguishable quantum states in $m_1otimes m_2otimescdotsotimes m_n$. Our study further reveals quantum nonlocality in multipartite high-dimensional.
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