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See, for example, S. Steinke, Network Tutorial (CMP Books, San Francisco, 2003), p. 99
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Steinke, S.1
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70450125113
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In a classical setting, this is achieved by means of the so-called internet-protocol (IP) addresses. As the message arrives at each node, the corresponding device checks the destination address contained in the message to see if it matches its own address. If the two addresses match, the device processes the message, otherwise it does nothing. Clearly, no addressing is required in a point-to-point topology since any data transmitted from one port are intended for the other port.
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In a classical setting, this is achieved by means of the so-called internet-protocol (IP) addresses. As the message arrives at each node, the corresponding device checks the destination address contained in the message to see if it matches its own address. If the two addresses match, the device processes the message, otherwise it does nothing. Clearly, no addressing is required in a point-to-point topology since any data transmitted from one port are intended for the other port.
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This is not the same as the quantum cloning and entanglement distribution discussed in Refs., where the excitation is distributed among the output ports.
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This is not the same as the quantum cloning and entanglement distribution discussed in Refs., where the excitation is distributed among the output ports.
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70450151111
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A closed cycle is a permutation or subpermutation, which cannot be decomposed further. For example, the permutation Π= |3□ 0| + |2□ □1| + |1□ □2| + |0□ □3| is not a closed cycle as we can decompose it into two smaller permutations Π 0 = |0□ □3| + |3□ □0| and Π1=|1□ □2| + |2□ □1|. An example of a closed cycle, with more than two elements, is Π=|1□ □0| + |2□ □1| + |0□ □2|; it is clear that this permutation cannot be decomposed further.
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A closed cycle is a permutation or subpermutation, which cannot be decomposed further. For example, the permutation Π=|3□ □0| + |2□ □1| + |1□ □2| + |0□ □3| is not a closed cycle as we can decompose it into two smaller permutations Π 0 = |0□ □3| + |3□ □0| and Π 1=|1□ □2| + |2□ □1|. An example of a closed cycle, with more than two elements, is Π = |1□ □0| + |2□ □1| + |0□ □2|; it is clear that this permutation cannot be decomposed further.
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The fact that the current formalism is not contingent on the initial state of the network greatly reduces the difficulty in realizing PST.
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The fact that the current formalism is not contingent on the initial state of the network greatly reduces the difficulty in realizing PST.
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70450127496
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The assumption that the source node is initially decorrelated from the rest of the network is necessary for an unambiguous definition of PST.
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The assumption that the source node is initially decorrelated from the rest of the network is necessary for an unambiguous definition of PST.
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35
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70450149028
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As shown in, for one-dimensional networks, where each node has at most two nearest neighbors, nearest-neighbor interaction Hamiltonians cannot be obtained in the context of one-cycle permutations. Hence, in this case, the Hamiltonian of a universal bus cannot be of a nearest-neighbor type.
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As shown in, for one-dimensional networks, where each node has at most two nearest neighbors, nearest-neighbor interaction Hamiltonians cannot be obtained in the context of one-cycle permutations. Hence, in this case, the Hamiltonian of a universal bus cannot be of a nearest-neighbor type.
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A case in point is the permutation Π = |4□ □0| + |0□ □1| + |1□ □2| + |2□ □4| + |3□ □3|.
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A case in point is the permutation Π = |4□ □0| + |0□ □1| + |1□ □2| + |2□ □4| + |3□ □3|.
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37
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21244455660
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10.1088/1367-2630/7/1/143
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A. Kay and M. Ericsson, New J. Phys. 7, 143 (2005). 10.1088/1367-2630/7/ 1/143
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Kay, A.1
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|