There is a intriguing relation between quantum information theory and super gravity, discovered by M.J. Duff and S. Ferrara. It relates entanglement measures for qubits to black hole entropy, which in a certain case involves the quartic invariant on the 56-dimensional representation of the Lie group E7. In this paper we recall the relatively straightforward manner in which three-qubits lead to E7, or at least to the Weyl group of E7. We also show how the Fano plane emerges in this context.
We invoke some ideas from finite geometry to map bijectively 135 heptads of mutually commuting three-qubit observables into 135 symmetric four-qubit ones. After labeling the elements of the former set in terms of a seven-dimensional Clifford algebra, we present the bijective map and most pronounced actions of the associated symplectic group on both sets in explicit forms. This formalism is then employed to shed novel light on recently-discovered structural and cardinality properties of an aggregate of three-qubit Mermin's 'magic' pentagrams. Moreover, some intriguing connections with the so-ca…
In this paper, we present some monogamy relations of multiqubit quantum entanglement in terms of the βth power of concurrence, entanglement of formation and convex-roof extended negativity. These monogamy relations are proved to be tighter than the existing ones, together with detailed examples showing the tightness.
We propose an approach to nondestructively detect $N$ qubits by measuring the transmissions of a dispersively-coupled cavity. By taking into account all the cavity-qubits quantum correlations (i.e., beyond the usual coarse-grained/mean-field approximations), it is revealed that for an unknown normalized $N$-qubit state $|ψ_N>=\sum_{k=0}^{2^N-1}β_k|k>_N$, each detected peak in the cavity transmitted spectra marks one of the basis states $|k>_N$ and the relative height of such a peak is related to the corresponding superposed-probability $|β_k|^2$. Our results are able to unambiguously account f…
Radhakrishnan \emph{et.al} [Phys. Rev. Lett. \textbf{124}, 110401 (2020)] proposed quantum discord to multipartite systems and derived explicit formulae for any states. These results are significant in capturing quantum correlations for multi-qubit systems. In this paper, we evaluate the geometric measure of multipartite quantum discord and obtain results for a large family of multi-qubit states. %Intriguingly, our results demonstrate that for the family of states, multipartite geometric discord decreases exponentially as the number of parties increases while multipartite quantum discord not,t…
We present a proposal for quantum information processing with neutral atoms trapped in optical lattices as qubits. Initialization and coherent control of single qubits can be achieved with standard laser cooling and spectroscopic techniques. We consider entangling two-qubit logic gates based on optically induced dipole-dipole interactions, calculating a figure-of-merit for various protocols. Massive parallelism intrinsic to the lattice geometry makes this an intriguing system for scalable, fault-tolerant quantum computation.
The Pfaffian state is an attractive candidate for the observed quantized Hall plateau at Landau level filling fraction $ν=5/2$. This is particularly intriguing because this state has unusual topological properties, including quasiparticle excitations with non-Abelian braiding statistics. In order to determine the nature of the $ν=5/2$ state, one must measure the quasiparticle braiding statistics. Here, we propose an experiment which can simultaneously determine the braiding statistics of quasiparticle excitations and, if they prove to be non-Abelian, produce a topologically-protected qubit on …
In this Brief Report we show the relation between three-qubit entanglement invariants and two-qubit concurrence with the help of projective measurements. How to use these invariants to represent the entanglement property of three-qubit pure states is also investigated.
We analyze quantum state-transfer optimization within hybrid open systems, from a "noisy" (write-in) qubit to its "quiet" counterpart (storage qubit). Intriguing interplay is revealed between our ability to avoid bath-induced errors that profoundly depend on the bath-memory time and the limitations imposed by leakage out of the operational subspace. Counterintuitively, under no circumstances is the fastest transfer optimal (for a given transfer energy).
We study the trade-off relations satisfied by the genuine tripartite nonlocality in multipartite quantum systems. From the reduced three-qubit density matrices of the four-qubit generalized Greenberger-Horne-Zeilinger (GHZ) states and W states (4-qubit entangled state), we find that there exists a trade-off relation among the mean values of the Svetlichny operators associated with these reduced states. Namely, the genuine three-qubit nonlocalities are not independent. For four-qubit generalized GHZ states and W states, the summation of all their three-qubit maximal (squared) mean values of the…
Intriguing features of the distance between two arbitrary states of an open quantum system are identified that are induced by initial system-environment correlations. As an example, we analyze a qubit dephasingly coupled to a bosonic environment. Within tailored parameter regimes, initial correlations are shown to substantially increase a distance between two qubit states evolving to long-time limit states according to exact non-Markovian dynamics. It exemplifies the breakdown of the distance contractivity of the reduced dynamics.
We study the trade-off relations on the maximal violation of CHSH tests for the multi-qubit pure states. Firstly, according to the classification of 3-qubit pure states under stochastic local operations and classical communication, four trade-off relations on CHSH tests are provided. The process of proof also provides the method of calculating its exact value. Then we consider the multi-qubit quantum systems, and we prove that the conjecture in [PRA 94, 042105 (2016)] is right for some special 4-qubit or more qubit pure states.
We propose a method to detect genuine quantum correlation for multi-qubit pure states. We then derive a complementarity relations for pure quantum states of N qubits. We prove that in all many-qubit systems there exist strict monogamy laws for quantum correlations. On the other hand, it is known that the entanglement monogamy equality proposed by Coffman, Kundu, and Wootters is in general not true for multiqubit states. Inducing from the CKW equality, we find a proper form of entanglement monogamy equality for arbitrary quantum states. The total quantum correlation of qubit k with the remainin…
We investigate the nonlocality distributions among multiqubit systems based on the maximal violations of the Clauser-Horne-Shimony-Holt (CHSH) inequality of reduced pairwise qubit systems. We present a trade-off relation satisfied by these maximal violations, which gives rise to restrictions on the distribution of nonlocality among the subqubit systems. For a three-qubit system, it is impossible that all pairs of qubits violate the CHSH inequality, and once a pair of qubits violates the CHSH inequality maximally, the other two pairs of qubits must both obey the CHSH inequality. Detailed exampl…
It has been suggested that reality works like a quantum computer, but such claims are just words if they are not backed up by sound mathematics. In pursuit of the fundamental equations I look to string theory where physicists led by Mike Duff have noticed useful connections between the quantum gravity of black holes and quantum information theory. By building on my earlier work on universal symmetry in string theory and using links between elliptic curves and hyperdeterminants, I find intriguing clues that these connections may be deep as well as useful. Ultimately any theory of the foundation…
We prove that universal quantum computation is possible using only (i) the physically natural measurement on two qubits which distinguishes the singlet from the triplet subspace, and (ii) qubits prepared in almost any three different (potentially highly mixed) states. In some sense this measurement is a `more universal' dynamical element than a universal 2-qubit unitary gate, since the latter must be supplemented by measurement. Because of the rotational invariance of the measurement used, our scheme is robust to collective decoherence in a manner very different to previous proposals - in effe…
A new form of local unitary (LU) transformation invariant is given for multi-qubit states . The general relation between tangle and the LU transformation invariant of pure three and four-qubit states is given. We find that the tangle actually is a special LU transformation invariant. Furthermore, the tangle is a important local unitary (LU) transformation invariant which is a nessesary condition for maximally multi-qubit entangled state.
Operation speed and coherence time are two core measures for the viability of a qubit. Strong spin-orbit interaction (SOI) and relatively weak hyperfine interaction make holes in germanium (Ge) intriguing candidates for spin qubits with rapid, all-electrical coherent control. Here we report ultrafast single-spin manipulation in a hole-based double quantum dot in a germanium hut wire (GHW). Mediated by the strong SOI, a Rabi frequency exceeding 540 MHz is observed at a magnetic field of 100 mT, setting a record for ultrafast spin qubit control in semiconductor systems. We demonstrate that the s…
Nonclassical correlations have been found useful in many quantum information processing tasks, and various measures have been proposed to quantify these correlations. In this work, we mainly study one of nonclassical correlations, called measurement-induced nonlocality (MIN). First, we establish a close connection between this nonlocal effect and the Bell nonlocality for two-qubit states. Then, we derive a tight monogamy relation of MIN for any pure three-qubit state and provide an alternative way to obtain similar monogamy relations for other nonclassical correlation measures, including squar…
Characterizing trade-offs between simultaneous violations of multiple Bell inequalities in a large network of qubits is computationally demanding. We propose a graph-theoretic approach to efficiently produce Bell monogamy relations in arbitrary arrangements of qubits. All the relations obtained for bipartite Bell inequalities are tight and leverage only a single Bell monogamy relation. This feature is unique to bipartite Bell inequalities, as we show that there is no finite set of such elementary monogamy relations for multipartite inequalities. Nevertheless, many tight monogamy relations for …
We investigate the monogamy relations related to the concurrence and the entanglement of formation. General monogamy inequalities given by the αth power of concurrence and entanglement of formation are presented for N-qubit states. The monogamy relation for entanglement of assistance is also established. Based on these general monogamy relations, the residual entanglement of concurrence and entanglement of formation are studied. Some relations among the residual entanglement, entanglement of assistance, and three tangle are also presented.
We present a new kind of monogamous relations based on concurrence and concurrence of assistance. For $N$-qubit systems $ABC_1...C_{N-2}$, the monogamy relations satisfied by the concurrence of $N$-qubit pure states under the partition $AB$ and $C_1...C_{N-2}$, as well as under the partition $ABC_1$ and $C_2...C_{N-2}$ are established, which give rise to a kind of restrictions on the entanglement distribution and trade off among the subsystems.
Employing the fact that the geometry of the $N$-qubit ($N \geq 2$) Pauli group is embodied in the structure of the symplectic polar space $\mathcal{W}(2N-1,2)$ and using properties of the Lagrangian Grassmannian ${\rm LGr}(N,2N)$ defined over the smallest Galois field, it is demonstrated that there exists a bijection between the set of maximum sets of mutually commuting elements of the $N$-qubit Pauli group and a certain subset of elements of the $2^{N-1}$-qubit Pauli group. In order to reveal finer traits of this correspondence, the cases $N=3$ (also addressed recently by Lévay, Planat and Sa…
Following the spirit of a recent work of one of the authors (J. Phys. A: Math. Theor. 44 (2011) 045301), the essential structure of the generalized Pauli group of a qubit-qu$d$it, where $d = 2^{k}$ and an integer $k \geq 2$, is recast in the language of a finite geometry. A point of such geometry is represented by the maximum set of mutually commuting elements of the group and two distinct points are regarded as collinear if the corresponding sets have exactly $2^{k} - 1$ elements in common. The geometry comprises $2^{k} - 1$ copies of the generalized quadrangle of order two ("the doily") that…
By preparing an input state and measuring an observable for the output state, we can measure a quantum channel. Following the formulation given by Xiao et al., we study an uncertainty relation for ancilla-free measurements of random unitary channels acting on a qubit. We obtain an explicit formula and give a necessary and sufficient condition for this formula to be nontrivial.
The well-known Robertson-Schrödinger uncertainty relations have state-dependent lower bounds which are trivial for certain states. We present a general approach to deriving tight state-independent uncertainty relations for qubit measurements that completely characterise the obtainable uncertainty values. This approach can give such relations for any number of observables, and we do so explicitly for arbitrary pairs and triples of qubit measurements. We show how these relations can be transformed into equivalent tight entropic uncertainty relations. More generally, they can be expressed in term…
We investigate the generalized monogamy and polygamy relations $N$-qubit systems. We give a general upper bound of the $α$th ($0\leqα\leq2$) power of concurrence for $N$-qubit states. The monogamy relations satisfied by the $α$th ($0\leqα\leq2$) power of concurrence are presented for $N$-qubit pure states under the partition $AB$ and $C_1 . . . C_{N-2}$, as well as under the partition $ABC_1$ and $C_2\cdots C_{N-2}$. These inequalities give rise to the restrictions on entanglement distribution and the trade off of entanglement among the subsystems. Similar results are also derived for negativi…
Recently, Paolo Facchi et al. [Phys. Rev. A. 77, 060304 (R) (2008)] introduced the notion of maximally multipartite entangled states of n qubits. Here, we give a criterion for faithful controlled teleportation of an arbitrary two-qubit state via a five-qubit entangled state and obtain the general relation between the genuine five-qubit entangled state and controlled teleportation. This criterion can be extended to teleportation of an arbitrary N-qubit state using 2N+1-qubit entangled state. Furthermore, we study the optimal match of measuring basis and quantum channel.
Bipartite operations underpin both classical communication and entanglement generation. Using a superposition of classical messages, we show that the capacity of a two-qubit operation for error-free entanglement-assisted bidirectional classical communication can not exceed twice the entanglement capability. In addition we show that any bipartite two-qubit operation can increase the communication that may be performed using an ensemble by twice the entanglement capability.
The monogamy of entanglement means that entanglement cannot be freely shared. In 2014, Oliveira et al. [ Oliveira et al., Phys. Rev. A. 89, 034303 (2014)] proposed a monogamy relation in the linear version and considered it in terms of entanglement of formation. Here we generalize the above version and consider a multi-linear monogamy relation for a multi-qubit system in terms of entanglement of formation and concurrence. Based on the above results, we present an entanglement criterion for genuine entangled states, also we consider the absolutely maximally entangled states and present what an …
We investigate the monogamy relations related to the concurrence, the entanglement of formation, convex-roof extended negativity, Tsallis-q entanglement and R'enyi-α entanglement, the polygamy relations related to the entanglement of formation, Tsallis-q entanglement and R'enyi-α entanglement. Monogamy and polygamy inequalities are obtained for arbitrary multipartite qubit systems, which are proved to be tighter than the existing ones. Detailed examples are presented.
Monogamy relations characterize the distributions of entanglement in multipartite systems. We investigate monogamy relations related to the concurrence $C$ and the entanglement of formation $E$. We present new entanglement monogamy relations satisfied by the $α$-th power of concurrence for all $α\geq2$, and the $α$-th power of the entanglement of formation for all $α\geq\sqrt{2}$. These monogamy relations are shown to be tighter than the existing ones.
The quantum steering ellipsoid can be used to visualise two-qubit states, and thus provides a generalisation of the Bloch picture for the single qubit. Recently, a monogamy relation for the volumes of steering ellipsoids has been derived for pure 3-qubit states and shown to be stronger than the celebrated Coffman-Kundu-Wootters (CKW) inequality. We first demonstrate the close connection between this volume monogamy relation and the classification of pure 3-qubit states under stochastic local operations and classical communication (SLOCC). We then show that this monogamy relation does not hold …
Two different measures of operator entanglement of two-qubit gates, namely, Schmidt strength and linear entropy, are studied. While these measures are shown to have one-to-one relation between them for Schmidt number 2 class of gates, no such relation exists for Schmidt number 4 class, implying that the measures are inequivalent in general. Further, we establish a simple relation between linear entropy and local invariants of two-qubit gates. The implication of the relation is discussed.
We discuss the possibility to interpret the residual entanglement for more than three qubits in terms of distributed multipartite entanglement, or, in other words, possible extensions of the Coffman-Kundu-Wootters monogamy equality to higher qubit numbers. Existing knowledge on entanglement in multipartite systems puts narrow constraints on the form of such extensions. We study various examples for families of pure four-qubit states for which the characterization of three-qubit and four-qubit entanglement in terms of polynomial invariants is known. These examples indicate that, although famili…
We derive two complementarity relations that constrain the individual and bipartite properties that may simultaneously exist in a multi-qubit system. The first expression, valid for an arbitrary pure state of n qubits, demonstrates that the degree to which single particle properties are possessed by an individual member of the system is limited by the bipartite entanglement that exists between that qubit and the remainder of the system. This result implies that the phenomenon of entanglement sharing is one specific consequence of complementarity. The second expression, which holds for an arbit…
In this paper, we derive a general formula of the tangle for pure states of three qubits, and present three explicit local unitary (LU) polynomial invariants. Our result goes beyond the classical work of tangle, 3-tangle and von Neumann entropy of entanglement for Ac\'ın et al.' Schmidt decomposition (ASD) of three qubits by connecting the tangle, 3-tangle, and von Neumann entropy for ASD with Ac\'ın et al.'s LU invariants. In particular, our result reveals a general relation among tangle, 3-tangle, and von Neumann entropy, together with a relation among their averages. The relations can help …
A quantum analog of the fundamental classical NOT gate is a quantum gate that would transform any input qubit state onto an orthogonal state. Intriguingly, this universal NOT gate is forbidden by the laws of quantum physics. This striking phenomenon has far-reaching implications concerning quantum information processing and encoding information about directions and reference frames into quantum states. It also triggers the question under what conditions the preparation of quantum states orthogonal to input states becomes possible. Here we report on experimental demonstration of orthogonalizati…
We investigate the notion of uncertainty region using the variance based sum uncertainty relation for qubits and qutrits.We compare uncertainty region of the qubit (a 2-level system) with that of the qutrit (3-level system) by considering sum uncertainty relation for two non-commuting Pauli-like observables, acting on the two dimensional qubit Hilbert space. We identify that physically valid uncertainty region of a qubit is smaller than that of a qutrit. This implies that an enhanced precision can be achieved in the measurement of incompatible Pauli-like observables acting on the 2-dimensional…
The aim of presented research is to design a nanodevice based on a gate-defined quantum dot within a MoS$_2$ monolayer in which we confine a single electron. By applying control voltages to the device gates we modulate the confinement potential and force intervalley transitions. The present Rashba spin-orbit coupling additionally allows for spin operations. Moreover, both effects enable the spin-valley SWAP. The device structure is modeled realistically, taking into account feasible dot-forming potential and electric field that controls the Rasha coupling. Therefore, by performing reliable num…
Motivated by proposed thermometry measurement on an open quantum system, we present a simple model of an externally driven qubit interacting with a finite sized, fermion environment acting as calorimeter. The derived dynamics is governed by a stochastic Schrödinger equation coupled to the temperature change of the calorimeter. We prove a fluctuation relation and deduce from it a notion of entropy production. Finally, we discuss the first and second law associated to the dynamics.
We define a normal form for Clifford circuits, and we prove that every Clifford operator has a unique normal form. Moreover, we present a rewrite system by which any Clifford circuit can be reduced to normal form. This yields a presentation of Clifford operators in terms of generators and relations.
Two-qubit operations may be characterized by their capacities for communication, both with and without free entanglement, and their capacity for creating entanglement. We establish a set of inequalities that give an ordering to the capacities of two-qubit unitary operations. Specifically, we show that the capacities for entanglement creation and bidirectional communication without entanglement assistance are at least as great as half the bidirectional communication capacity with entanglement assistance. In addition, we show that the bidirectional communication that can be performed using an en…
The well-known Robertson-Schroedinger uncertainty relations miss an irreducible lower bound. This is widely attributed to the lower bound's state-dependence. Therefore, Abbott \emph{et al.} introduced a general approach to derive tight state-independent uncertainty relations for qubit measurements [Mathematics 4, 8 (2016)]. The relations are expressed in two measures of uncertainty, which are standard deviation and entropy, both functions of the expectation value. Here, we present a neutron optical test of the tight state-independent preparation uncertainty relations for non-commuting Pauli sp…
Four level quantum systems, known as quartits, and their relation to two- qubit systems are investigated group theoretically. Following the spirit of Klein's lectures on the icosahedron and their relation to Hopf sphere bra- tions, invariants of complex re ection groups occuring in the theory of qubits and quartits are displayed. Then, real gates over octits leading to the Weyl group of E8 and its invariants are derived. Even multilevel systems are of interest in the context of solid state nuclear magnetic resonance.
A tight information-theoretic measurement uncertainty relation is experimentally tested with neutron spin-1/2 qubits. The noise associated to the measurement of an observable is defined via conditional Shannon entropies and a tradeoff relation between the noises for two arbitrary spin observables is demonstrated. The optimal bound of this tradeoff is experimentally obtained for various non-commuting spin observables. For some of these observables this lower bound can be reached with projective measurements, but we observe that, in other cases, the tradeoff is only saturated by general quantum …
For two qubits in a pure state there exists a one-to-one relation between the entanglement measure (the concurrence ${\cal C}$) and the maximal violation ${\cal M}$ of a Bell inequality. No such relation exists for the three-qubit analogue of ${\cal C}$ (the tangle $τ$), but we have found that numerical data is consistent with a simple set of upper and lower bounds for $τ$ given ${\cal M}$. The bounds on $τ$ become tighter with increasing ${\cal M}$, so they are of practical use. The Svetlichny form of the Bell inequality gives tighter bounds than the Mermin form. We show that the bounds can b…
We show a simple relation connecting entangling power and local invariants of two-qubit gates. From the relation, a general condition under which gates have same entangling power is arrived. The relation also helps in finding the lower bound of entangling power for perfect entanglers, from which the classification of gates as perfect and nonperfect entanglers is obtained in terms of local invariants.
\indent In this article, we consider the monogamy relations for the generalized W class states. Here we first present an analytical formula on Tsallis-$q$ entanglement and Tsallis-$q$ entanglement of assistance of a reduced density matrix of the generalized W class states, then we present a monogamy relation in terms of the T$q$EE for the GW state, and we also present generalized monogamy relations in terms of T$q$EE for the GW states. At last, we present tighter polygamy relations in terms of T$q$EEoA when $q=2$ for the GWV states.
The Kibble-Zurek mechanism provides a description of the topological structure occurring in the symmetry breaking phase transitions, which may manifest as the cosmological strings in the early universe or vortex lines in the superfulid. A particularly intriguing analogy between Kibble-Zurek mechanism and a text book quantum phenomenon, Landau-Zener transition has been discovered, but is difficult to observe up to now. In recent years, there has been broad interest in quantum simulations using different well-controlled physical setups, in which full tunability allows access to unexplored parame…
For quantum computing applications, the electronic Hamiltonian for the electronic structure problem needs to be unitarily transformed to a qubit form. We found that mean-field procedures on the original electronic Hamiltonian and on its transformed qubit counterpart can give different results. We establish conditions of when fermionic and qubit mean fields provide the same or different energies. In cases when the fermionic mean-field (Hartree-Fock) approach provides an accurate description (electronic correlation effects are small), the choice of molecular orbitals for the electron Hamiltonian…
We explicitly show a protocol in which an arbitrary two qubit a|00> + b|01> + c|10> + d|11> is faithfully and deterministically teleported from Alice to Bob. We construct the 16 orthogonal generalized Bell states which can be used to teleport the two qubits. The local operations Bob must perform on his qubits in order to recover the teleported state is also constructed. They are restricted only to single qubit gates. This means that a CNOT gate is not necessary to complete the protocol. A generalization where N qubits is teleported is also shown. We define a generalized magic basis, which poss…
Information-theoretic uncertainty relations formulate the joint immeasurability of two non-commuting observables in terms of information entropies. The trade-off of the accuracy in the outcome of two successive measurements manifests in entropic noise-disturbance uncertainty relations. Recent theoretical analysis predicts that projective measurements are not optimal, with respect to the noise-disturbance trade-offs. Therefore the results in our previous letter [PRL 115, 030401 (2015)] are outperformed by general quantum measurements. Here, we experimentally test a tight information-theoretic m…
