The geometric quantum discord of a two-qudit state has been studied in many papers, however, its exact analytical value in the explicit form is known only for a general two-qubit state, a general qubit-qudit state and some special families of two-qudit states. Based on the general Bloch vectors formalism [J. Phys. A: Math. Theor. 54 195301 (2021)], we find the explicit exact analytical value of the geometric quantum discord for a general two-qudit state of an arbitrary dimension via the parameters of its correlation matrix and the Bloch vectors of its reduced states. This new general analytical result includes all the known exact results on the geometric quantum discord only as particular cases and proves rigorously that the lower bound on the geometric discord presented in [Phys. Rev. A 85, 024102 (2012)] constitutes its exact value for each two-qudit state. Moreover, our new general result allows us to find for an arbitrary two-qudit state, pure or mixed, the novel upper and lower bounds on its geometric quantum discord, expressed via the Hilbert space characteristics of this state.
We study the measurement-induced geometric discord based on the trace norm and generalize some properties known for qutrits to qudits. Previous preliminary results for bipartite qutrit systems (i.e. d=3 systems) are here strictly proved for arbitrary d. Present study supports observations, coming also from other approaches, that systems with $d \geq 3$ show similar behaviour when quantum correlations are concerned, but there is pronounced difference between d=2 and d=3. Qubit systems are exceptionally simple. Underlying geometry of state spaces and related Lie groups are responsible for that.
Quantum discord quantifies quantum correlations beyond entanglement and assumes nonzero values, which are notoriously hard to compute, for almost all quantum states. Here we provide computable tight bounds for the quantum discord for qubit-qudit states. In the case of two qubits our lower and upper bounds coincide for a 7-parameter family of filtered $X$-states, whose quantum discords can therefore be evaluated analytically. An application to the accessible information of the binary qubit channel is also presented. For the qubit-qudit state output by the circuit of deterministic computation wi…
We analyze a class of 2-qudit circulant states. They define generalization of well known 2-qubit X-states. We formula the necessary and sufficient criteria for vanishing quantum discord. We illustrate our analysis by an important subclass of circulant states -- so called Bell diagonal states.
Quantum discord, a kind of quantum correlation, is defined as the difference between quantum mutual information and classical correlation in a bipartite system. It has been discussed so far for small systems with only a few independent parameters. We extend here to a much broader class of states when the second party is of arbitrary dimension d, so long as the first, measured, party is a qubit. We present two formulae to calculate quantum discord, the first relating to the original entropic definition and the second to a recently proposed geometric distance measure which leads to an analytical…
By using the quantum-memory-assisted entropic uncertainty relation (EUR), we derive a computable tight upper bound for quantum discord, which applies to an arbitrary bipartite state. Detailed examples show that this upper bound is tighter than other known bounds in a wide regime. Furthermore, we show that for any tripartite pure state, the quantum-memory-assisted EUR imposes a constraint on the shareability of quantum correlations among the constituent parties. This conclusion amends the well accepted result that quantum discord is not monogamous.
We formulate and prove the main properties of the generalized Gell-Mann representation for traceless qudit observables with eigenvalues in $[-1,1]$ and analyze via this representation violation of the CHSH inequality by a general two-qudit state. For the maximal value of the CHSH expectation in a two-qudit state with an arbitrary qudit dimension $d\geq2$, this allows us to find two new bounds, lower and upper, expressed via the spectral properties of the correlation matrix for a two-qudit state. We have not yet been able to specify if the new upper bound improves the Tsirelson upper bound for …
Information is encoded in a qubit in the form of its Bloch vector. In this paper, we propose protocols for remote transfers of information in a known and an unknown qubit to qudits using $SU(2)$- invariant $\frac{1}{2}\otimes S$ discordant states as a channel. These states have been identified as separable equivalents of the two-qubit entangled Werner states in [Bharath & Ravishankar, Phys. Rev. A 89, 062110]. Due to $SU(2) \times SU(2)$ invariance of these states, the remote qudit can be changed by performing appropriate measurements on the qubit. We also propose a protocol for transferring i…
For an even qudit dimension $d\geq 2,$ we introduce a class of two-qudit states exhibiting perfect correlations/anticorrelations and prove via the generalized Gell-Mann representation that, for each two-qudit state from this class, the maximal violation of the original Bell inequality is bounded from above by the value $3/2$ - the upper bound attained on some two-qubit states. We show that the two-qudit Greenberger-Horne-Zeilinger (GHZ) state with an arbitrary even $d\geq 2$ exhibits perfect correlations/anticorrelations and belongs to the introduced two-qudit state class. These new results ar…
Quantum discord measures quantum correlation by comparing the quantum mutual information with the maximal amount of mutual information accessible to a quantum measurement. This paper analyzes the properties of diagonal discord, a simplified version of discord that compares quantum mutual information with the mutual information revealed by a measurement that correspond to the eigenstates of the local density matrices. In contrast to the optimized discord, diagonal discord is easily computable; it also finds connections to thermodynamics and resource theory. Here we further show that, for the ge…
Quantum discord, a kind of quantum correlation based on entropic measures, is defined as the difference between quantum mutual information and classical correlation in a bipartite system. Procedures are available for analytical calculation of discord when one of the parties is a qubit with dimension two and measurements made on it to get that one-way discord. We extend now to systems when both parties are of larger dimension, of interest to qudit-quDit with d, D > 2 or spin chains of spins > 1/2. While recognizing that no universal scheme is feasible, applicable to all density matrices, nevert…
Quantum mechanical properties like entanglement, discord and coherence act as fundamental resources in various quantum information processing tasks. Consequently, generating more resources from a few, typically termed as broadcasting is a task of utmost significance. One such strategy of broadcasting is through the application of cloning machines. In this article, broadcasting of quantum resources beyond $2 \otimes 2$ systems is investigated. In particular, in $2\otimes3$ dimension, a class of states not useful for broadcasting of entanglement is characterized for a choice of optimal universal…
Quantum discord and quantum uncertainty are two important features of the quantum world. In this work, the relation between entropic uncertainty relation and the shareability of quantum discord is studied. First, by using tripartite quantum-memory-assisted entropic uncertainty relation, an upper bound for the shareability of quantum discord among different partites of a composite system is obtained. It is also shown that, for a specific class of tripartite states, the obtained relation could be expressed as monogamy of quantum discord. Moreover, it is illustrated that the relation could be gen…
We introduce the general class of symmetric two-qubit states guaranteeing the perfect correlation or anticorrelation of Alice and Bob outcomes whenever some spin observable is measured at both sites. We prove that, for all states from this class, the maximal violation of the original Bell inequality is upper bounded by 3/2 and specify the two-qubit states where this quantum upper bound is attained. The case of two-qutrit states is more complicated. Here, for all two-qutrit states, we obtain the same upper bound 3/2 for violation of the original Bell inequality under Alice and Bob spin measurem…
We specify the local quasi hidden variable (LqHV) model reproducing the probabilistic description of all N-partite joint von Neumann measurements on an N-qudit state. Via this local probability model, we derive a new upper bound on the maximal violation by an N-qudit state of N-partite Bell inequalities of any type (either on correlation functions or on joint probabilities) for S observables per site. This new upper bound not only improves for all N, S and d the corresponding results available for general Bell inequalities in the literature but also, for the N-qubit case with two observables p…
We discuss a generalization of the conditional entropy and one-way information deficit in quantum systems, based on general entropic forms. The formalism allows to consider simple entropic forms for which a closed evaluation of the associated optimization problem in qudit-qubit systems is shown to become feasible, allowing to approximate that of the quantum discord. As application, we examine quantum correlations of spin pairs in the exact ground state of finite $XY$ spin chains in a magnetic field through the quantum discord and information deficit. While these quantities show a similar behav…
We extend the geometric measure of quantum discord, introduced and computed for two-qubit states in [B. Dakic, C. Brukner, and V. Vedral, Phys. Rev. Lett. 105, 190502 (2010)], to quantify non-classical correlations in composite Gaussian states of continuous variable systems. We lay the formalism for the evaluation of a Gaussian geometric discord in two-mode Gaussian states, and present explicit formulas for the class of two-mode squeezed thermal states. In such a case, under physical constraints of bounded mean energy, geometric discord is shown to admit upper and lower bounds for a fixed valu…
We revisit the upper bound of quantum discord given by the von Neumann entropy of the measured subsystem. Using the Koashi-Winter relation, we obtain a trade-off between the amount of classical correlation and quantum discord in the tripartite pure states. The difference between the quantum discord and its upper bound is interpreted as a measure on the classical correlative capacity. Further, we give the explicit characterization of the quantum states saturating the upper bound of quantum discord, through the equality condition for the Araki-Lieb inequality. We also demonstrate that the satura…
We consider a monogamy inequality of quantum discord in a pure tripartite state and show that it is equivalent to an inequality between quantum mutual information and entanglement of formation of two parties. Since this inequality does not hold for arbitrary bipartite states, quantum discord can generally be both monogamous and polygamous. We also carry out numerical calculations for some special states. The upper bounds of quantum discord and classical correlation are also discussed and we give physical analysis on the invalidness of a previous conjectured upper bound of quantum correlation. …
Multi-qudit systems are studied in tomographic probability representations of quantum qudit states. Results of calculations for Bell-type numbers within the framework of classical probability theory and in quantum tomography are compared. Violation of Bell-type inequalities are shown explicitly using the method of averaging in tomographic picture of quantum states.
Calculation of the quantum discord requires to find the minimum of the quantum conditional entropy $S(ρ^{AB}|\{Π^B_{k}\})$ over all measurements on the subsystem $B$. In this paper, we provide a simple relation for the conditional entropy as the difference of two Shannon entropies. The relation is suitable for calculation of the quantum discord in the sense that it can by used to obtain the quantum discord for some classes of two-qubit states, without the need for minimization. We also present an analytical procedure of optimization and obtain conditions under which the quantum conditional ent…
Quantum coherence and quantum entanglement are two strong pillars in quantum information theory. We study here for the possibility of any connection between these two important aspects of quantum mechanics while studying the entanglement detection problem for the detection of bipartite higher dimensional entangled states and multipartite entangled states. To achieve our goal, we derive the lower bound $L$ of $l_{1}$ norm of coherence of bipartite qubit-qudit system using the criterion that detect entanglement. Furthermore, we deduce the upper bound $U$ of $l_{1}$ norm of coherence of separable…
We investigate quantum states that posses both maximum entanglement and maximum discord between the pertinent parties. Since entanglement (discord) is defined only for bipartite (two qubit) systems, we shall introduce an appropriate sum over of all bi-partitions as the associated measure. The ensuing definition --not new for entanglement-- is thus extended here to quantum discord. Also, additional dimensions within the parties are considered ({\it qudits}). We also discuss nonlocality (in the form of maximum violation of a Bell inequality) for all multiqubit systems. The emergence of more nonl…
Absolute separable states is a kind of separable state that remain separable under the action of any global unitary transformation. These states may or may not have quantum correlation and these correlations can be measured by quantum discord. We find that the absolute separable states are useful in quantum computation even if it contains infinitesimal quantum correlation in it. Thus to search for the class of two-qubit absolute separable states with zero discord, we have derived an upper bound for $Tr(\varrho^{2})$, where $\varrho$ denoting all zero discord states. In general, the upper bound…
For any bipartite state, how strongly can one subsystem be quantum correlated with another? Using the Koashi-Winter relation, we study the upper bound of purified quantum discord, which is given by the sum of the von Neumann entropy of the unmeasured subsystem and the entanglement of formation shared between the unmeasured subsystem with the environment. In particular, we find that the Luo et al.'s conjecture on the quantum correlations and the Lindblad conjecture are all ture, when the entanglement of formation vanishes. Let the difference between the left discord and the right discord be cap…
Quantum correlations may be measured by means of the distance of the state to the subclass of states $Ω$ having well defined classical properties. In particular, a geometric measure of asymmetric discord [Dakic et al., Phys. Rev. Lett. 105, 190502 (2010)] was recently defined as the Hilbert-Schmidt distance of a given two-qubit state to the closest classical-quantum (CQ) correlated state. We analyze a geometric measure of symmetric discord defined as the Hilbert-Schmidt distance of a given state to the closest classical-classical (CC) correlated state. The optimal member of $Ω$ is just special…
We discuss some inequalities for N nonnegative numbers. We use these inequalities to obtain known inequalities for probability distributions and new entropic and information inequalities for quantum tomograms of qudit states. The inequalities characterize the degree of quantum correlations in addition to noncontextuality and quantum discord. We use the subadditivity and strong subadditivity conditions for qudit tomographic-probability distributions depending on the unitary-group parameters in order to derive new inequalities for Shannon, Renyi, and Tsallis entropies of spin states.
Several ways have been proposed in the literature to define a coherence measure based on Tsallis relative entropy. One of them is defined as a distance between a state and a set of incoherent states with Tsallis relative entropy taken as a distance measure. Unfortunately, this measure does not satisfy the required strong monotonicity, but a modification of this coherence has been proposed that does. We introduce three new Tsallis coherence measures coming from a more general definition that also satisfy the strong monotonicity, and compare all five definitions between each other. Using three c…
Quantum algorithms are known for presenting more efficient solutions to certain computational tasks than any corresponding classical algorithm. It has been thought that the origin of the power of quantum computation has its roots in non-classical correlations such as entanglement or quantum discord. However, it has been recently shown that even a single pure qudit is sufficient to design an oracle-based algorithm which solves a black-box problem faster than any classical approach to the same problem. In particular, the algorithm that we consider determines whether eight permutation functions d…
Last years, bounds on the maximal quantum violation of general Bell inequalities were intensively discussed in the literature via different mathematical tools. In the present paper, we analyze quantum violation of general Bell inequalities via the LqHV (local quasi hidden variable) modelling framework, correctly reproducing the probabilistic description of every quantum correlation scenario. The LqHV mathematical framework allows us to derive for all d and N a new upper bound (2d-1)^{N-1} on the maximal violation by an N-qudit state of all general Bell inequalities, also, new upper bounds on t…
We investigate the norms of the Bloch vectors for any quantum state with subsystems less than or equal to four. Tight upper bounds of the norms are obtained, which can be used to derive tight upper bounds for entanglement measure defined by the norms of Bloch vectors. By using these bounds a trade-off relation of the norms of Bloch vectors is discussed. Theses upper bounds are then applied on separability. Necessary conditions are presented for different kinds of separable states in four-partite quantum systems. We further present a complete classification of quantum states for four qudits qua…
We present observable lower and upper bounds for the entanglement of formation (EOF) and quantum discord (QD), which facilitates estimates of EOF and QD for arbitrary experimental unknown states in finite-dimensional bipartite systems. These bounds can be easily obtained by a few experimental measurements on a twofold copy $\varrho\otimes\varrho$ of the mixed states. Based on our results, we use the experimental measurement data of the real experiment given by Schmid \textit{et al.} [Phys. Rev. Lett. \textbf{101}, 260505 (2008)] to obtain the lower and upper bounds of EOF and QD for the experi…
Composite quantum systems can be in generic states characterized not only by entanglement, but also by more general quantum correlations. The interplay between these two signatures of nonclassicality is still not completely understood. In this work we investigate this issue focusing on computable and observable measures of such correlations: entanglement is quantified by the negativity N, while general quantum correlations are measured by the (normalized) geometric quantum discord D_G. For two-qubit systems, we find that the geometric discord reduces to the squared negativity on pure states, w…
Two-qubit X-state is a large class of quantum states which plays an important role in the quantification and dynamical study of quantum correlations. However, the corresponding quantification of quantum discord is still missing for bona fide discord measures, like original quantum discord, Bures distance of discord, and relative entropy of discord. In this paper, we consider the calculation of Bures distance of discord, which is a kind of correlation satisfying all criteria of a discord measure, for two-qubit X-states. Firstly, we derive an explicit expression for Bures distance of discord for…
The common use in literature of orthogonal measurements in obtaining quantum discord for two-qubit states is discussed and compared with more general measurements. We prove the optimality of orthogonal measurements for rank 2 states. While for rank 3 and 4 mixed states they are not optimal, we present strong numerical evidence showing that they give the correct quantum discord up to minimal corrections. Based on the connection, through purification with an ancilla, between discord and entanglement of formation (EoF), we give a tight upper bound for the EoF of a $2\otimes N$ mixed state of rank…
Motivated by recent numerous works on the interplay among various measures of quantum correlations, we aim to investigate the relationship between the violation of Clauser-Horne-Shimony-Holt (CHSH) Bell inequality and geometric measure of quantum discord for two-qubit systems. Exact lower and upper bounds of Bell violation versus geometric discord are obtained for a specific and significant class of states, Bell diagonal states, and the respective states which suffice those bounds are also characterized. The dynamical behavior of these two quantifiers is carefully analyzed in the presence of d…
We use singular value decomposition to derive a tight lower bound for geometric discord of arbitrary bipartite states. In a single shot this also leads to an upper bound of measurement-induced non locality which in turn yields that for Werner and isotropic states the two measures coincide. We also emphasize that our lower bound is saturated for all $2\otimes n$ states. Using this we show that both the generalized Greenberger-Horne-Zeilinger and $W$ states of $N$ qubits satisfy monogamy of geometric discord. Indeed, the same holds for all $N$-qubit pure states which are equivalent to $W$ states…
We present an analytical solution for classical correlation, defined in terms of linear entropy, in an arbitrary $d\otimes 2$ system when the second subsystem is measured. We show that the optimal measurements used in the maximization of the classical correlation in terms of linear entropy, when used to calculate the quantum discord in terms of von Neumann entropy, result in a tight upper bound for arbitrary $d\otimes 2$ systems. This bound agrees with all known analytical results about quantum discord in terms of von Neumann entropy and, when comparing it with the numerical results for $10^6$…
We present the new exact upper bounds on the maximal Bell violation for the generalized N-qubit GHZ state, the N-qudit GHZ state and, in general, for an arbitrary N-partite quantum state, possibly infinite-dimensional. Our results indicate that, for an N-partite quantum state of any Hilbert space dimension, violation of any Bell-type inequality (either on correlation functions or on joint probabilities) with S settings and any number of outcomes at each site cannot exceed (2S-1)^{N-1}.
In this brief review, we discuss the role that quantum correlations, as quantified by quantum discord, play in two interesting settings. The first one is discerning which unitaries have been applied on a quantum system, by taking advantage of knowledge regarding its initial configuration. Here discord captures the "quantum" component of this knowledge, useful only when we have access to a quantum memory. In particular, discord can be used to detect whether an untrusted party has certain quantum capabilities. The second setting is quantum cryptography. Here discord represents an important resou…
We introduce a monogamy inequality for quantum correlations, which implies that the sum of pairwise quantum correlations is upper limited by the amount of multipartite quantum correlations as measured by the global quantum discord. This monogamy bound holds either for pure or mixed quantum states provided that bipartite quantum discord does not increase under discard of subsystems. We illustrate the monogamy behavior for multipartite pure states with Schmidt decomposition as well as for W-GHZ mixed states. As a by-product, we apply the monogamy bound to investigate residual multipartite correl…
Symmetric extendibility of quantum states has recently drawn attention in the context of quantum cryptography to judge whether quantum states shared between two distant parties can be purified by means of one-way error correction protocols. In this letter we study the symmetric extendibility in a specific class of two-qudit states, i. e. states composed of two d-level systems, in order to find upper bounds on tolerable error rates for a wide class of qudit-based quantum cryptographic protocols using two-way error correction. In important cases these bounds coincide with previously known lower …
The behavior of total purely quantum correlation (discord) in dimers consisting of dipolar-coupled spins 1/2 is studied. We found that the discord Q=0 at the absolute zero temperature. With increasing the temperature $T$, at first the quantum correlations in the system increase, smoothly reach the maximum, and then turn again into zero according to the asymptotic law $T^{-2}$. It is also shown that in absence of external magnetic field $B$, the classical correlation $C$ at $T\to0$ is, vice versa, maximal. Our calculations predict that in crystalline gypsum ${\rm CaSO_4\cdot2H_2O}$ the value of…
Bounds, expressed in terms of d and N, on full Bell locality of a quantum state for $N\geq 3$ nonlocally entangled qudits (of a dimension $d\geq 2$) mixed with white noise are known, to our knowledge, only within full separability of this noisy N-qudit state. For the maximal violation of general Bell inequalities by an N-partite quantum state, we specify the analytical upper bound expressed in terms of dilation characteristics of this state, and this allows us to find new general bounds in $d, N$, valid for all $d\geq 2$ and all $N\geq 3$, on full Bell locality under generalized quantum measur…
Entanglement is one of important resources for quantum communication tasks. Most of results are focused on qubit entanglement. Our goal in this work is to characterize the multipartite high-dimensional entanglement. We firstly derive an entanglement polygon inequality for the $q$-concurrence, which manifests the relationship among all the "one-to-group" marginal entanglements in any multipartite qudit system. This implies lower and upper bounds for the marginal entanglement of any three-qudit system. We further extend to general entanglement distribution inequalities for high-dimensional entan…
We consider the task of performing quantum state tomography on a $d$-level spin qudit, using only measurements of spin projection onto different quantization axes. After introducing a basis of operators closely related to the spherical harmonics, which obey the rotational symmetries of spin qudits, we map our quantum tomography task onto the classical problem of signal recovery on the sphere. We then provide algorithms with $O(rd^3)$ serial runtime, parallelizable down to $O(rd^2)$, for (i) computing a priori upper bounds on the expected error with which spin projection measurements along $r$ …
Noisy quantum walks are studied from the perspective of comparing their quantumness as defined by two popular measures, measurement-induced disturbance (MID) and quantum discord (QD). While the former has an operational definition, unlike the latter, it also tends to overestimate non-classicality because of a lack of optimization over local measurements. Applied to quantum walks, we find that MID, while acting as a loose upper bound on QD, still tends to reflect correctly the trends in the behavior of the latter. However, there are regimes where its behavior is not indicative of non-classicali…
Quantum information masking is a protocol that hides the original quantum information from subsystems and spreads it over quantum correlation, which is available to multipartite except bipartite systems. In this work, we explicitly study the quantum information masking in multipartite scenario and prove that all the k-level quantum states can be masked into a m-qudit systems (m > 4) whose local dimension d < k and the upper bound of k is tighter than the quantum Singleton bound. In order to observe the masking process intuitively, explicitly controlled operations are provided. Our scheme well …
Most realistic solid state devices considered as qubits are not true two-state systems but multi-level systems. They can approximately be considered as qubits only if the energy separation of the upper energy levels from the lowest two is very large. If this condition is not met, the upper states may affect the evolution and therefore cannot be neglected. Here, we consider devices with double-well potential as basic logical elements, and study the effect of higher energy levels, beyond the lowest two, on adiabatic quantum optimization. We show that the extra levels can be modeled by adding add…
Shannon's entropy power inequality (EPI) can be viewed as a statement of concavity of an entropic function of a continuous random variable under a scaled addition rule: $$f(\sqrt{a}\,X + \sqrt{1-a}\,Y) \ge a f(X) + (1-a) f(Y) \quad \forall \, a \in [0,1].$$ Here, $X$ and $Y$ are continuous random variables and the function $f$ is either the differential entropy or the entropy power. König and Smith [arXiv:1205.3409] and De Palma, Mari, and Giovannetti [arXiv:1402.0404] obtained quantum analogues of these inequalities for continuous-variable quantum systems, where $X$ and $Y$ are replaced by bo…
We introduce measures of quantum coherence as the speed of evolution of a system under decoherence. That is, coherence is the ability to estimate a dephasing channel, quantified by the quantum Fisher information. We extend the analysis to interferometric noise estimation, proving that quantum discord is the minimum sensitivity to local dephasing. A physically motivated set of free operations for discord is proposed. The amount of discord created by strictly incoherent operations is upper-bounded by the initial coherence.
When a quantum system is divided into two local subsystems, measurements on the two subsystems can exhibit correlations beyond those possible in a classical joint probability distribution; these are partially explained by entanglement, and more generally by a wider class of measures such as the quantum discord. In this work, I introduce a simple thought experiment defining a new measure of quantum correlations, which I call the accord, and write the result as a minimax optimization over unitary matrices. I find the exact result for pure states as a simple function of the Schmidt coefficients a…
The geometric discord $\mathcal{D}$ of a state is a measure of the quantumness of the state and the negativity $\mathcal{N}$ is a measure of the entanglement of a state. It was proved by D. Girolami and G. Adesso that for states on $\mathbb{C}^2\otimes\mathbb{C}^2$, the geometric discord is always greater than or equal to the square of the negativity and conjectured that this holds in general. S. Rana and P. Parashar showed that this relation does not hold for all states on $\mathbb{C}^2\otimes\mathbb{C}^n$ for $n>2$. We provide several analytic families of states on $\mathbb{C}^2\otimes\mathb…
Any two-qubit state can be represented, geometrically, as an ellipsoid with a certain size and a center located within the Bloch sphere of one of the qubits. Points of this ellipsoid represent the post-measurement states when the other qubit is measured. Based on the most demolition concept in the definition of quantum discord, we study the amount of demolition when the two post-measurement states, represented as two points on the steering ellipsoid, have the most distinguishability. We use trace distance as a measure of distinguishability and obtain the maximum distinguishability for some cla…
