Structure of the sets of mutually unbiased bases for<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>N</mml:mi></mml:math>qubits

Romero, José Luis; Björk, Gunnar; Klimov, A. B.; Sánchez-Soto, Luis L.

doi:10.1103/physreva.72.062310

Cited by 87 publications

(109 citation statements)

References 49 publications

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“…In such systems, while MUB complements exhibit only a single entanglement type for N = 2 (and all p), the number of distinct types proliferates with increasing N. The variety is illustrated in a number of recent discussions, mostly on multiple qubit systems but also multiple qutrit systems [6,13,[16][17][18][19][20]. In particular, a systematic study by Romero and collaborators [17] illustrates a broad range of entanglement patterns that occur naturally in a construction scheme for full MUB complements. Such complements are catalogued for up to 4 qubits.…”

Section: Introductionmentioning

confidence: 99%

Entanglement patterns in mutually unbiased basis sets

Lawrence

2011

Phys. Rev. A

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A few simply-stated rules govern the entanglement patterns that can occur in mutually unbiased basis sets (MUBs), and constrain the combinations of such patterns that can coexist (ie, the stoichiometry) in full complements of (p N + 1) MUBs. We consider Hilbert spaces of prime power dimension (as realized by systems of N prime-state particles, or qupits), where full complements are known to exist, and we assume only that MUBs are eigenbases of generalized Pauli operators, without using a particular construction. The general rules include the following: 1) In any MUB, a particular qupit appears either in a pure state, or totally entangled, and 2) in any full MUB complement, each qupit is pure in (p+1) bases (not necessarily the same ones), and totally entangled in the remaining (p N − p). It follows that the maximum number of product bases is p + 1, and when this number is realized, all remaining (p N − p) bases in the complement are characterized by the total entanglement of every qupit. This "standard distribution" is inescapable for two qupits (of any p), where only product and generalized Bell bases are admissible MUB types. This and the following results generalize previous results for qubits [13,17] Such MUBs should play critical roles in filling complements.

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Section: Introductionmentioning

confidence: 99%

Entanglement patterns in mutually unbiased basis sets

Lawrence

2011

Phys. Rev. A

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“…All the operators in each subset have a set of joint eigenvectors. The eigenvectors of all subsets then form MUB [39,40]. Table I illustrates such a MUB based partitioning of the 2-qubit Pauli operators.…”

Section: B Mutually Unbiased Bases Measurementsmentioning

confidence: 99%

Quantum-process tomography: Resource analysis of different strategies

2008

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Characterization of quantum dynamics is a fundamental problem in quantum physics and quantum information science. Several methods are known which achieve this goal, namely Standard Quantum Process Tomography (SQPT), Ancilla-Assisted Process Tomography (AAPT), and the recently proposed scheme of Direct Characterization of Quantum Dynamics (DCQD). Here, we review these schemes and analyze them with respect to some of the physical resources they require. Although a reliable figure-of-merit for process characterization is not yet available, our analysis can provide a benchmark which is necessary for choosing the scheme that is the most appropriate in a given situation, with given resources. As a result, we conclude that for quantum systems where two-body interactions are not naturally available, SQPT is the most efficient scheme. However, for quantum systems with controllable two-body interactions, the DCQD scheme is more efficient than other known QPT schemes in terms of the total number of required elementary quantum operations.

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“…Questions of this type have been considered in Refs. [32][33][34]; however, not much is known about the entanglement structure in MUBs beyond tripartite systems. In this respect, our descriptive formalism in terms of graphs may lead to new insights on the role of entanglement in MUBs for more complex manybody systems.…”

Section: Introductionmentioning

confidence: 99%

Graph-state formalism for mutually unbiased bases

Spengler

Kraus

2013

Phys. Rev. A

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A pair of orthonormal bases is called mutually unbiased if all mutual overlaps between any element of one basis with an arbitrary element of the other basis coincide. In case the dimension, d, of the considered Hilbert space is a power of a prime number, complete sets of d+1 mutually unbiased bases (MUBs) exist. Here, we present a novel method based on the graph-state formalism to construct such sets of MUBs. We show that for n p-level systems, with p being prime, one particular graph suffices to easily construct a set of p n + 1 MUBs. In fact, we show that a single n-dimensional vector, which is associated with this graph, can be used to generate a complete set of MUBs and demonstrate that this vector can be easily determined. Finally, we discuss some advantages of our formalism regarding the analysis of entanglement structures in MUBs, as well as experimental realizations.

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Structure of the sets of mutually unbiased bases forNqubits

Cited by 87 publications

References 49 publications

Entanglement patterns in mutually unbiased basis sets

Entanglement patterns in mutually unbiased basis sets

Quantum-process tomography: Resource analysis of different strategies

Graph-state formalism for mutually unbiased bases

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