Class Of Quantum States Research Articles

Efficient test to demonstrate genuine three particle nonlocality

According to the studies of genuine tripartite nonlocality in discrete variable quantum systems conducted so far, Svetlichny inequality is considered as the best Bell-type inequality to detect genuine (three way) nonlocality of pure tripartite genuine entangled states. In the present work, we have considered another Bell-type inequality (which has been reported as the 99th facet of NS2 local polytope in Bancal et al (2013 Phys. Rev. A 88 014102), to reveal genuine tripartite nonlocality of generalized GHZ (Greenberger–Horne–Zeilinger) class and a subclass of extended GHZ class states Acín et al (2000 Phys. Rev. Lett. 85 1560) thereby proving the conjecture given by Bancal et al (2013 Phys. Rev. A 88 014102) for the GGHZ class and the subclass of extended GHZ states. We compare the violation of this inequality with Svetlichny inequality which reveals the efficiency of the former inequality over the latter to demonstrate genuine nonlocality using the above classes of quantum states. Even in some cases discord monogamy score can be used as a better measure of quantum correlation over Svetlichny inequality for those classes of pure states. Besides, the 99th facet inequality is found efficient not only for revealing genuine nonlocal behavior of correlations emerging in systems using pure entangled states but also in some cases of mixed entangled states over Svetlichny inequality and some well known measures of entanglement.

Fidelity of recovery, squashed entanglement, and measurement recoverability

This paper defines the fidelity of recovery of a quantum state on systems $A$, $B$, and $C$ as a measure of how well one can recover the full state on all three systems if system $A$ is lost and a recovery operation is performed on system $C$ alone. The surprisal of the fidelity of recovery (its negative logarithm) is an information quantity which obeys nearly all of the properties of the conditional quantum mutual information $I(A;B|C)$, including non-negativity, monotonicity with respect to local operations, duality, invariance with respect to local isometries, a dimension bound, and continuity. We then define a (pseudo) entanglement measure based on this quantity, which we call the geometric squashed entanglement. We prove that the geometric squashed entanglement is a 1-LOCC monotone, that it vanishes if and only if the state on which it is evaluated is unentangled, and that it reduces to the geometric measure of entanglement if the state is pure. We also show that it is invariant with respect to local isometries, subadditive, continuous, and normalized on maximally entangled states. We next define the surprisal of measurement recoverability, which is an information quantity in the spirit of quantum discord, characterizing how well one can recover a share of a bipartite state if it is measured. We prove that this discord-like quantity satisfies several properties, including non-negativity, faithfulness on classical-quantum states, invariance with respect to local isometries, a dimension bound, and normalization on maximally entangled states. This quantity combined with a recent breakthrough of Fawzi and Renner allows to characterize states with discord nearly equal to zero as being approximate fixed points of entanglement breaking channels. Finally, we discuss a multipartite fidelity of recovery and several of its properties.

The POLIS interferometer for ponderomotive squeezed light generation

POLIS (POnderomotive LIght Squeezer) is a suspended interferometer, presently under construction, devoted to the generation of ponderomotive squeezed light and to the study of the interaction of non classical quantum states of light and macroscopic objects. The interferometer is a Michelson whose half-meter long arms are constituted by high-finesse cavities, suspended to a seismic isolation chain similar to the Virgo SuperAttenuator. The mass of the suspended cavity mirrors are chosen to be tens of grams: this value is sufficiently high to permit the use of the well-tested Virgo suspension techniques but also sufficiently small to generate the coupling among the two phase quadratures with a limited amount of light in the cavity, of the order of few tens of kW. In this short paper the main features of the interferometer are shown, together with the expected sensitivity and squeezing factor.

Excitation and depletion of entangled squeezed states: their properties and generation

Recently, two-mode entangled squeezed states have been produced using even and odd squeezed states. Based on such entangled states, we introduce two new classes of quantum states, namely single-mode excited (depleted) entangled squeezed states which are obtained via the iterated action of the creation (annihilation) operator on the first mode of the two-mode entangled squeezed states. In continuation, we study the amount of entanglement of the introduced states by calculating the ‘concurrence’ and ‘linear entropy’. In addition, we investigate several nonclassicality features such as the sub-Poissonian statistics, second-order correlation function between the two modes and quadrature squeezing. Finally, in order to establish the physical realization of the introduced states, a theoretical scheme for their generation based on the interaction of a two-level atom with a quantized cavity field is proposed.

General SIC measurement-based entanglement detection

We study the quantum separability problem by using general symmetric informationally complete measurements and present separability criteria for both $d$-dimensional bipartite and multipartite systems. The criterion for bipartite quantum states are effective in detecting several well known classes of quantum states. For isotropic states, it becomes both necessary and sufficient. Furthermore, our criteria can be experimentally implemented and the criterion for two-qudit states requires less local measurements than the one based on mutually unbiased measurements.

Computable measure of quantum correlation

A general state of an \(m\otimes n\) system is a classical-quantum state if and only if its associated \(A\)-correlation matrix (a matrix constructed from the coherence vector of the party \(A\), the correlation matrix of the state, and a function of the local coherence vector of the subsystem \(B\)), has rank no larger than \(m-1\). Using the general Schatten \(p\)-norms, we quantify quantum correlation by measuring any violation of this condition. The required minimization can be carried out for the general \(p\)-norms and any function of the local coherence vector of the unmeasured subsystem, leading to a class of computable quantities which can be used to capture the quantumness of correlations due to the subsystem \(A\). We introduce two special members of these quantifiers: The first one coincides with the tight lower bound on the geometric measure of discord, so that such lower bound fully captures the quantum correlation of a bipartite system. Accordingly, a vanishing tight lower bound on the geometric discord is a necessary and sufficient condition for a state to be zero-discord. The second quantifier has the property that it is invariant under a local and reversible operation performed on the unmeasured subsystem, so that it can be regarded as a computable well-defined measure of the quantum correlations. The approach presented in this paper provides a way to circumvent the problem with the geometric discord. We provide some examples to exemplify this measure.

Entanglement ofπ–locally-maximally-entangleable states and the satisfiability problem

In this paper we investigate the entanglement properties of the class of $\ensuremath{\pi}$--locally-maximally-entangleable $(\ensuremath{\pi}$-LME) states, which are also known as the real equally weighted states or the hypergraph states. The $\ensuremath{\pi}$-LME states comprise well-studied classes of quantum states (e.g., graph states) and exhibit a large degree of symmetry. Motivated by the structure of LME states, we show that the capacity to (efficiently) determine if a $\ensuremath{\pi}$-LME state is entangled would imply an efficient solution to the Boolean satisfiability problem. More concretely, we show that this particular problem of entanglement detection, phrased as a decision problem, is $\mathsf{NP}$-complete. The restricted setting we consider yields a technically uninvolved proof, and illustrates that entanglement detection, even when quantum states under consideration are highly restricted, still remains difficult.

Discord of response

The presence of quantum correlations in a quantum state is related to the stateʼs response to local unitary perturbations. Such a response is quantified by the distance between the unperturbed and perturbed states, minimized with respect to suitably identified sets of local unitary operations. In order to be a bona fide measure of quantum correlations, the distance function must be chosen among those that are contractive under completely positive and trace preserving (CPTP) maps. The most relevant instances of such physically well-behaved metrics include the trace, the Bures, and the Hellinger distance. To each of these metrics one can associate the corresponding discord of response, namely the trace, or Hellinger, or Bures minimum distance from the set of unitarily perturbed states. All these three discords of response satisfy the basic axioms for a proper measure of quantum correlations. In the present work we focus in particular on the Bures distance, which enjoys the unique property of being both Riemannian and contractive under CPTP maps, and admits important operational interpretations in terms of state distinguishability. We compute analytically the Bures discord of response for two-qubit states with maximally mixed marginals and we compare it with the corresponding Bures geometric discord, namely the geometric measure of quantum correlations defined as the Bures distance from the set of classical-quantum states. Finally, we investigate and identify the maximally quantum correlated two-qubit states according to the Bures discord of response. These states exhibit a remarkable nonlinear dependence on the global state purity.

Properties of subentropy

Subentropy is an entropy-like quantity that arises in quantum information theory; for example, it provides a tight lower bound on the accessible information for pure state ensembles, dual to the von Neumann entropy upper bound in Holevo's theorem. Here we establish a series of properties of subentropy, paralleling the well-developed analogous theory for von Neumann entropy. Further, we show that subentropy is a lower bound for min-entropy. We introduce a notion of conditional subentropy and show that it can be used to provide an upper bound for the guessing probability of any classical-quantum state of two qubits; we conjecture that the bound applies also in higher dimensions. Finally, we give an operational interpretation of subentropy within classical information theory.

On the Response of Quantum Linear Systems to Single Photon Input Fields

The purpose of this paper is to extend linear systems and signals theory to include single photon quantum signals. We provide detailed results describing how quantum linear systems respond to multichannel single photon quantum signals. In particular, we characterize the class of states (which we call photon-Gaussian states) that result when multichannel photons are input to a quantum linear system. We show that this class of quantum states is preserved by quantum linear systems. Multichannel photon-Gaussian states are defined via the action of certain creation and annihilation operators on Gaussian states. Our results show how the output states are determined from the input states through a pair of transfer function relations. We also provide equations from which output signal intensities can be computed. Examples from quantum optics are provided to illustrate the results.

A class of separable quantum states

We present a sufficient condition for a bipartite state to be separable via the strong positive partial transposition structure introduced in Chruściński et al (2008 Phys. Rev. A 77 022113), from which we obtain a class of separable states. In particular, we prove that any classical-quantum state is a state of our class but not vice versa. Both finite- and infinite-dimensional systems are considered.

Revival of quantum correlations without system-environment back-action

Revivals of quantum correlations have often been explained in terms of back-action on quantum systems by their quantum environment(s). Here we consider a system of two independently evolving qubits, each locally interacting with a classical random external field. The environments of the qubits are also independent, and there is no back-action on the qubits. Nevertheless, entanglement, quantum discord and classical correlations between the two qubits may revive in this model. We explain the revivals in terms of correlations in a classical-quantum state of the environments and the qubits. Although classical states cannot store entanglement on their own, they can play a role in storing and reviving entanglement. It is important to know how the absence of back-action, or modelling an environment as classical, affects the kind of system time evolutions one is able to describe. We find a class of global time evolutions where back-action is absent and for which there is no loss of generality in modelling the environment as classical. Finally, we show that the revivals can be connected with the increase of a parameter used to quantify non-Markovianity of the single-qubit dynamics.

Dynamics of Interacting Classical and Quantum Systems

We analyze the dynamics of coupled classical and quantum systems. The main idea is to treat both systems as true quantum ones and impose a family of superselection rules which imply that the corresponding algebra of observables of one subsystem is commutative and hence may be treated as a classical one. Equivalently, one may impose a special symmetry which restricts the algebra of observables to the 'classical' subalgebra. The characteristic feature of classical-quantum dynamics is that it leaves invariant a subspace of classical-quantum states, that is, it does not create quantum correlations as measured by the quantum discord.

Ultra-sensitive atom imaging for matter-wave optics

Quantum degenerate Fermi gases and Bose–Einstein condensates give access to a vast new class of quantum states. The resulting multi-particle correlations place extreme demands on the detection schemes. Here we introduce diffractive dark-ground imaging as a novel ultra-sensitive imaging technique. Using only moderate detection optics, we image clouds of less than 30 atoms with near-atom shot-noise-limited signal-to-noise ratio and show Stern–Gerlach separated spinor condensates with a minority component of only seven atoms. This presents an improvement of more than one order of magnitude when compared to our standard absorption imaging. We also examine the optimal conditions for absorption imaging, including saturation and fluorescence contributions. Finally, we discuss potentially serious imaging errors of small atom clouds whose size is near the resolution of the optics.

CHARACTERIZING QUANTUMNESS VIA ENTANGLEMENT CREATION

In [Piani et al., PRL106 (2011) 220403], an activation protocol was introduced which maps the general non-classical (multipartite) correlations between given systems into bipartite entanglement between the systems and local ancillae by means of a potentially highly entangling interaction. Here, we study how this activation protocol can be used to entangle the starting systems themselves via entanglement swapping through a measurement on the ancillae. Furthermore, we bound the relative entropy of quantumness (a naturally arising measure of non-classicality in the scheme of Piani et al. above) for a special class of separable states, the so-called classical–quantum states. In particular, we fully characterize the classical–quantum two-qubit states that are maximally non-classical.

QUANTUM LOCKING OF CLASSICAL CORRELATIONS AND QUANTUM DISCORD OF CLASSICAL-QUANTUM STATES

A locking protocol between two parties is as follows: Alice gives an encrypted classical message to Bob which she does not want Bob to be able to read until she gives him the key. If Alice is using classical resources, and she wants to approach unconditional security, then the key and the message must have comparable sizes. But if Alice prepares a quantum state, the size of the key can be comparatively negligible. This effect is called quantum locking. Entanglement does not play a role in this quantum advantage. We show that, in this scenario, the quantum discord quantifies the advantage of the quantum protocol over the corresponding classical one for any classical-quantum state.

Clocks and fisher information

In a broad sense, any parametric family of quantum states can be viewed as a quantum clock. The time, which is the parameter, is encoded in the corresponding quantum states. The quality of such a clock depends on how precisely we can distinguish the states or, equivalently, estimate the parameter. In view of the quantum Cramer—Rao inequalities, the quality of quantum clocks can be characterized by the quantum Fisher information. We address the issue of quantum clock synchronization in terms of quantum Fisher information and demonstrate its fundamental difference from the classical paradigm. The key point is the superadditivity of Fisher information, which always holds in the classical case but can be violated in quantum mechanics. The violation can occur for both pure and mixed states. Nevertheless, we establish the superadditivity of quantum Fisher information for any classical-quantum state. We also demonstrate an alternative form of superadditivity and propose a weak form of superadditivity. The violation of superadditivity can be exploited to enhance quantum clock synchronization.

On the non-classicality features of new classes of nonlinear coherent states

In this paper, using an exponential function of intensity of radiation field, two new classes of nonlinear coherent states will be constructed. For the first class, we choose the nonlinearity function as f β ( n) = exp( βn), where β characterizes the strength of the nonlinearity of the quantum system. We show that, the corresponding β-states possess a collection of non-classicality features, only for the particular values of β and z. But, interestingly there exists finite (threshold) values of β, for which all of the non-classicality signs will disappear, in appropriate regions around the origin of the complex plane ( z < | Z|). It is then illustrated that, using this threshold (or greater) value of β, the corresponding β-states behave very similar to canonical coherent states, as the most classical quantum states, in approximately whole of the space. In the continuation, we motivate to find another class of nonlinear coherent states, limited to a unit disk centered at the origin, looking like the canonical coherent states in behavior, in exactly the whole range of | z| < 1. This purpose also will be achieved by considering the nonlinearity function as f λ ( n ) = exp ( λ / n ) / n , where λ is a tunable nonlinearity parameter. The canonical coherent state's aspects of the corresponding λ-states will be refreshed, in particular cases, working with a threshold (or greater) value of λ.

On Quantum No-Broadcasting

We address the issue of one-side local broadcasting for correlations in a quantum bipartite state, and conjecture that the correlations can be broadcast if and only if they are classical–quantum, or equivalently, the quantum discord, as defined by Ollivier and Zurek (Phys Rev Lett 88:017901, 2002), vanishes. We prove this conjecture when the reduced state is maximally mixed and further provide various plausible arguments supporting this conjecture. Moreover, we demonstrate that the conjecture implies the following two elegant and fundamental no-broadcasting theorems: (1) The original no-broadcasting theorem by Barnum et al. (Phys Rev Lett 76:2818, 1996), which states that a family of quantum states can be broadcast if and only if the quantum states commute. (2) The no-local-broadcasting theorem for quantum correlations by Piani et al. (Phys Rev Lett 100:090502, 2008), which states that the correlations in a single bipartite state can be locally broadcast if and only if they are classical. The results provide an informational interpretation for classical–quantum states from an operational perspective and shed new lights on the intrinsic relation between non-commutativity and quantumness.

How quantum is a quantum ensemble?

In the Hilbert space operator formalism of quantum mechanics, a single quantum state, which is represented by a density operator, can be regarded as classical in the sense that it can always be diagonalized. However, a quantum ensemble, which is represented by a family of quantum states together with a probability distribution specifying the probability of the occurrence of each state, cannot be diagonalized simultaneously in generic cases, and possesses intrinsic quantum features as long as the involved quantum states are not commutative. The natural question arises as how to quantify its quantumness. By virtue of a canonical correspondence between quantum ensembles and classical-quantum bipartite states, we propose an intuitive entropic quantity which captures certain quantum features of quantum ensembles, and compare it with that defined as the gap between the Holevo quantity and the accessible information. Implications for quantum cryptography and relations to quantum channel capacities are indicated. Some illustrative examples are worked out.