Correlations In Quantum States Research Articles

Simultaneous continuous measurement of noncommuting observables: Quantum state correlations

We consider the temporal correlations of the quantum state of a qubit subject to simultaneous continuous measurement of two non-commuting qubit observables. Such qubit state correlators are defined for an ensemble of qubit trajectories, which has the same fixed initial state and can also be optionally constrained by a fixed final state. We develop a stochastic path integral description for the continuous quantum measurement and use it to calculate the considered correlators. Exact analytic results are possible in the case of ideal measurements of equal strength and are also shown to agree with solutions obtained using the Fokker-Planck equation. For a more general case with decoherence effects and inefficiency, we use a diagrammatic approach to find the correlators perturbatively in the quantum efficiency. We also calculate the state correlators for the quantum trajectories which are extracted from readout signals measured in a transmon qubit experiment, by means of the quantum Bayesian state update. We find an excellent agreement between the correlators based on the experimental data and those obtained from our analytical and numerical results.

Quantifying non-Gaussianity of quantum-state correlation

We consider how to quantify non-Gaussianity for the correlation of a bipartite quantum state by using various measures such as relative entropy and geometric distances. We first show that an intuitive approach, i.e., subtracting the correlation of a reference Gaussian state from that of a target non-Gaussian state, fails to yield a non-negative measure with monotonicity under local Gaussian channels. Our finding clearly manifests that quantum-state correlations generally have no Gaussian extremality. We therefore propose a different approach by introducing relevantly averaged states to address correlation. This enables us to define a non-Gaussianity measure based on, e.g., the trace-distance and the fidelity, fulfilling all requirements as a measure of non-Gaussian correlation. For the case of the fidelity-based measure, we also present readily computable lower bounds of non-Gaussian correlation.

Structures of Three Types of Local Quantum Channels Based on Quantum Correlations

In a bipartite quantum system, quantum states are classified as classically correlated (CC) and quantum correlated (QC) states, the later are important resources of quantum information and computation protocols. Since correlations of quantum states may vary under a quantum channel, it is necessary to explore the influence of quantum channels on correlations of quantum states. In this paper, we discuss CC-preserving, QC-breaking and strongly CC-preserving local quantum channels of the form \(\Phi _1\otimes \Phi _2\) and obtain the structures of these three types of local quantum channels. Moreover, we obtain a necessary and sufficient condition for a quantum state to be transformed into a CC state by a specific local channel \(\Phi _1\otimes \Phi _2\) in terms of the structure of the input quantum state. Lastly, as applications of the obtained results, we present a classification of local quantum channels \(\Phi _1\otimes \Phi _2\) and describe the quantum states which are transformed as CC ones by the corresponding local quantum channel.

Wick's theorem for matrix product states.

Matrix product states and their continuous analogues are variational classes of states that capture quantum many-body systems or quantum fields with low entanglement; they are at the basis of the density-matrix renormalization group method and continuous variants thereof. In this work we show that, generically, N-point functions of arbitrary operators in discrete and continuous translation invariant matrix product states are completely characterized by the corresponding two- and three-point functions. Aside from having important consequences for the structure of correlations in quantum states with low entanglement, this result provides a new way of reconstructing unknown states from correlation measurements, e.g., for one-dimensional continuous systems of cold atoms. We argue that such a relation of correlation functions may help in devising perturbative approaches to interacting theories.

Correlations in quantum states and the local creation of quantum discord

Quantum discord is usually referred to as a measure for quantum correlations. In the search of the fundamental resource to gain a quantum advantage in quantum information applications, quantum discord is considered a promising candidate. In this paper we present an alternative view on quantum correlations in terms of the rank of the correlation matrix as introduced by Daki\ifmmode \acute{c}\else \'{c}\fi{}, Vedral, and Brukner [Phys. Rev. Lett. 105, 190502 (2010)]. According to our analysis, information about the quantum discord does not necessarily determine the amount of quantum correlations but rather the quantumness of the state. Nonzero quantum discord is only a necessary but not a sufficient condition for correlations above the classically achievable limit. This becomes clear when we consider states of nonzero discord, which can be created from zero discord states only by a single local operation. We further show that the set of these states has measure zero.

Discord and Nonclassicality in Probabilistic Theories

Quantum discord quantifies nonclassical correlations in quantum states. We introduce discord for states in causal probabilistic theories, inspired by the original definition proposed by H. Ollivier and W. H. Zurek [Phys. Rev. Lett. 88, 017901 (2001)]. We show that the only probabilistic theory in which all states have null discord is classical probability theory. Non-null discord is then not just a quantum feature, but a generic signature of nonclassicality.

Irreducible Multiparty Correlations in Quantum States without Maximal Rank

The correlations of an n-partite quantum state are classified into a series of irreducible k-party ones (2<or=k<or=n), with the irreducible k-party correlation being the correlation in the states of k parties but nonexistent in the states of (k-1) parties. A measure of the degree of irreducible k-party correlation is defined based on the principle of maximal entropy. Adopting a continuity approach, we overcome the difficulties in calculating the degrees of irreducible multiparty correlations for the multipartite states without maximal rank. In particular, we obtain the degrees of irreducible multiparty correlations in the n-qubit stabilizer states and the n-qubit generalized Greenberger-Horne-Zeilinger states, which reveals the distribution of multiparty correlations.

Total versus quantum correlations in quantum states

On the premises that total correlations in a bipartite quantum state are measured by the quantum mutual information, and that separation of total correlations into quantum and classical parts satisfies an intuitive dominance relation, we examine to what extent various entropic entanglement measures, such as the distillable entanglement, the relative entropy entanglement, the squashed entanglement, the entanglement cost, and the entanglement of formation, can be regarded as consistent measures of quantum correlations. We illustrate that the entanglement of formation often overestimates quantum correlations and thus is too big to be a genuine measure of quantum correlations. This indicates that the entanglement of formation does not quantify the quantum correlations intrinsic to a quantum state, but rather characterizes the pure entanglement needed to build the quantum state via local operations and classical communication. Furthermore, it has the consequence that, if the additive conjecture for the entanglement of formation is true (as is widely believed), then the entanglement cost, which is an operationally defined measure of entanglement with significant physical meaning, cannot be a consistent measure of quantum correlations in the sense that it may exceed total correlations. Alternatively, if the entanglement cost is dominated by total correlations, as our intuition suggests, then we can immediately disprove the additive conjecture. Both scenarios have their counterintuitive and appealing aspects, and a natural challenge arising in this context is to prove or disprove that the entanglement cost is dominated by the quantum mutual information.

Phase shifting of an interferometer using nonlocal quantum-state correlations

We describe an experiment where the phase and amplitude of the interference pattern of light going through an interferometer was varied by doing operations on quantum-correlated light that did not go through the interferometer. This was accomplished by sending a pair of polarization-entangled photons in separate directions, one to an interferometer and the other one to a phase shifter, in principle in a remote location. The interferometer was set up to put the state of the pair in a superposition of maximally entangled states. The phase shifter inserted a phase between the product-state components that made up each entangled state. Polarizers located before the detectors projected the quantum state of the light. As a result, the phase and amplitude of the interference pattern were varied by changing the settings of the phase shifter and polarizer in the path of the photon in the remote location.

Locking classical correlations in quantum States.

We show that there exist bipartite quantum states which contain a large locked classical correlation that is unlocked by a disproportionately small amount of classical communication. In particular, there are (2n+1)-qubit states for which a one-bit message doubles the optimal classical mutual information between measurement results on the subsystems, from n/2 bits to n bits. This phenomenon is impossible classically. However, states exhibiting this behavior need not be entangled. We study the range of states exhibiting this phenomenon and bound its magnitude.

Photodissociation dynamics of formaldehyde: H2 (v,J) vector correlations

Several bipolar moments of the H2 (v,J) correlated angular momentum and velocity distribution produced from the photodissociation of formaldehyde near the threshold for dissociation have been measured by analysis of Doppler-resolved LIF line shapes. It is determined that the fragment H2 〈v⋅J〉 correlation is not at the limit of v⊥J, but is closer to the limit of v⊥J than to v∥J. The rotation of the excited H2CO during the 10−7–10−8 s before dissociation does not completely wash out the lab-frame vector correlations. Anisotropy parameters as large as 0.85 and as small as −0.41 have been measured; these are outside the limits imposed by classical models of parent rotation. A quantum mechanical model for parent rotation is introduced that accounts for the large magnitude of the measured anisotropy parameters. Photolysis on the rR0(0) line of the 43 band produces fragments with β&amp;lt;0 while photolysis on the same rotational transition of the 2141 band produces fragments with β&amp;gt;0. It is not known if the different anisotropies are caused by differences in the parent transition dipole moment or by differences in the dissociation dynamics. The simple impulsive model that reproduces the fragment rotational distributions and product quantum-state correlations does not adequately describe the measured H2 (v,J) vector correlations.

Vector and product quantum-state correlations for photofragmentation of formaldehyde

The vector correlations of para-H2(ν= 1, J= 0–8) produced form H2CO photolysis on the rR0(0)e line of the 21 41 S1â†� S0 transition have been measured by analysing Doppler-resolved laser-induced fluorescence line-shapes. The correlations of the H2CO transition dipole moment µ with the H2 recoil velocity v and µ with the angular momentum J are small, probably because H2CO rotates many times between excitation and fragmentation. The correlation of v with J has been found to be between the limiting cases of v∥J and v⊥J. In addition, the H2(ν, J) linewidths have been used to measure the product state correlation. H2 fragments in high vibrational states correlate with CO fragments in low rotational states.