Papers by Indrani Chattopadhyay
arXiv (Cornell University), Mar 23, 2023
arXiv (Cornell University), Dec 20, 2022
No pure entangled state can be distilled from a 2 ⊗ 2 or 2 ⊗ 3 mixed state by separable operation... more No pure entangled state can be distilled from a 2 ⊗ 2 or 2 ⊗ 3 mixed state by separable operations. In 3 ⊗ 3, pure entanglement can be distilled by separable operation but not by LOCC. In this letter, we proved the conjecture [PRL. 103, 110502 (2009)] that it is possible to distill pure entanglement for 2 ⊗ 4 system by LOCC and further improve these in higher dimensions to distill a pure entangled state of Schmidt rank d from a m ⊗ n mixed state by separable operation when m + n 3d. We found results for tripartite systems with target state d-level GHZ-type state. These results provide a class of systems where separable operation is strictly stronger than LOCC.
International Journal of Quantum Information
Physical Review A
In 2016, A. Winter et al.(Physical Review Letters 116 (12) (2016) 120404) provided an operational... more In 2016, A. Winter et al.(Physical Review Letters 116 (12) (2016) 120404) provided an operational meaning to relative entropy of coherence and coherence of formation by introducing coherence distillation and dilation protocol in asymptotic setup. Though relative entropy of coherence introduced in 2014 by T. Baumgratz (Physical Review Letters 113 (14) (2014) 140401) as a coherence measure but it's operational meaning in single copy setup was unknown so far. Here we have provided relative entropy of coherence (via IO (Incoherent Operations)) and coherence of formation (via IO) and quantum incoherent relative entropy (via LQICC(Local Quantum Incoherent Operations with Classical Communications)) a clear operational significance in single copy setup using the concept of catalyst. We have proved an existential correspondence between asymptotic and catalytic state transformation using IO, LICC(Local Incoherent Operations with Classical Communications) and LQICC. We have also discussed two very important protocols, assisted distillation and quantum incoherent state merging, in single copy setup using catalyst. Monotone property of relative entropy of coherence, coherence of formation and quantum incoherent relative entropy under the catalytic transformation are also discussed here.
Physics Letters A
No pure entangled state can be distilled from a 2 ⊗ 2 or 2 ⊗ 3 mixed state by separable operation... more No pure entangled state can be distilled from a 2 ⊗ 2 or 2 ⊗ 3 mixed state by separable operations. In 3 ⊗ 3, pure entanglement can be distilled by separable operation but not by LOCC. In this letter, we proved the conjecture [PRL. 103, 110502 (2009)] that it is possible to distill pure entanglement for 2 ⊗ 4 system by LOCC and further improve these in higher dimensions to distill a pure entangled state of Schmidt rank d from a m ⊗ n mixed state by separable operation when m + n 3d. We found results for tripartite systems with target state d-level GHZ-type state. These results provide a class of systems where separable operation is strictly stronger than LOCC.
arXiv (Cornell University), Nov 29, 2021
A set of orthogonal product states of a composite Hilbert space is genuinely nonlocal if the stat... more A set of orthogonal product states of a composite Hilbert space is genuinely nonlocal if the states are locally indistinguishable across any bipartition. In this work, we construct a minimal set of party asymmetry genuine nonlocal set in arbitrary large dimensional composite quantum systems C d ⊗ C d ⊗ C d. We provide a local discriminating protocol by using a three qubit GHZ state as a resource. On the contrary, we observe that single-copy of two qubit Bell states provide no advantage for this discrimination task. Recently, Halder et al. [Phys. Rev. Lett. 122, 040403 (2019)], proposed the concept of strong nonlocality without entanglement and ask an open question whether there exist an incomplete strong nonlocal set or not. In [Phys. Rev. A 102, 042228 (2020)], an answer is provided by the authors. Here, we construct an incomplete party asymmetry strong nonlocal set which is more stronger than the set constructed in [Phys. Rev. A 102, 042228 (2020)] with respect to the consumption of entanglement as a resource for their respective discrimination tasks.
arXiv (Cornell University), Dec 11, 2020
Recently a new class of monogamy relations (actually, exponentially many) was provided by Christo... more Recently a new class of monogamy relations (actually, exponentially many) was provided by Christopher Eltschka et al. in terms of squared concurrence. Their approach restricted to the distribution of bipartite entanglement shared between different subsystems of a global state. We have critically analyzed those monogamy relations in three as well as in four qubit pure states using squared negativity. We have been able to prove that in case of pure three qubit states those relations are always true in terms of squared negativity. However, if we consider the pure four qubit states, the results are not always true. Rather, we find opposite behaviour in some particular classes of four qubit pure states where some of the monogamy relations are violated. We have provided analytical and numerical evidences in support of our claim.
Quantum Information Processing
The assumption of measurement independence is required for a local deterministic model to conduct... more The assumption of measurement independence is required for a local deterministic model to conduct a Bell test. The violation of a Bell inequality by such a model implies that this assumption must be relaxed. The degree to which the assumption needs to be relaxed to achieve violation of some bipartite Bell inequalities, has been investigated recently in [Phys. Rev. Lett. 105, 250404(2010), Phys. Rev. A 99, 012121(2019)]. In this work, we study the minimum degree of relaxation required to simulate violations of various well-known tripartite Bell inequalities and opens the possibility of relaxation in multipartite scenario. Local deterministic models are also provided to achieve the violations of these Bell inequalities.
Non existence of Universal NOT gate for arbitrary quantum mechanical states is a fundamental cons... more Non existence of Universal NOT gate for arbitrary quantum mechanical states is a fundamental constraint on the allowed operations performed on physical systems. The largest set of states that can be flipped by using a single NOT gate is the set of states lying on a great circle of the Bloch-sphere. In this paper, we show the impossibility of universal exact-flipping operation, first by using the fact that no faster than light communication is possible and then by using the principle of “non-increase of entanglement under LOCC”. Interestingly, in both the cases, there is no violation of the two principles if and only if the set of states to be flipped, form a great circle. PACS number(s): 03.67.Mn, 03.67.Hk
Quantum Information Processing, 2021
Recently, a new class of monogamy relations (actually, exponentially many) was provided by Christ... more Recently, a new class of monogamy relations (actually, exponentially many) was provided by Christopher Eltschka et al. in terms of squared concurrence. Their approach is restricted to the distribution of bipartite entanglement shared between different subsystems of a global state. We have critically analysed those monogamy relations in three as well as in four-qubit pure states using squared negativity. We have been able to prove that in the case of pure three-qubit states those relations are always true in terms of squared negativity. However, if we consider the pure four-qubit states, the results are not always true. Rather, we find opposite behaviour in some particular classes of four-qubit pure states where some of the monogamy relations are violated. We have provided analytical and numerical evidences in support of our claim.
We prove the existence of bound entangled states with negative partial transpose (NPT) in any d×d... more We prove the existence of bound entangled states with negative partial transpose (NPT) in any d×d(d ≥ 3) Hilbert space with simple assumptions on Schmidt rank two states. We have assumed that the Schmidt rank two states should satisfy some bounds. Obviously the class of NPT bound entangled states belong to the class of conjectured to be bound entangled states by Divincenzo et.al [Phys. Rev. A, 61, 062312(2000)] and by Dür et.al [Phys. Rev. A, 61, 062313(2000)]. PACS number(s): 03.67.Hk, 03.65.Ud. The basic issue on the classification of mixed state entanglement at least on the level of bipartite systems solely depends upon whether there exist bound entangled states or not. The existence of PPT-bound (PPT means positive partial transpose) entangled states [1] and also the existence of NPT N−copy undistillable states [2, 3] for every positive integer N naturally indicates there may exist NPT-bound entangled states. In this work we are able to show the existence of NPT-bound entangled ...
arXiv: Quantum Physics, 2019
Emerging from superposition principle, resource theory of coherence plays crucial role in many in... more Emerging from superposition principle, resource theory of coherence plays crucial role in many information processing tasks. Recently, a generalization to this resource theory were investigated with respect to arbitrary positive operator valued measurement (POVM). Here we introduce the notion of Block Incoherent Operation (BIO), Strictly Block Incoherent Operation (SBIO) and Physically Block Incoherent Operation (PBIO) and provide analytical expression for Kraus operators of these operations. These free operations would be helpful to find out conditions of state transformations and could be implemented in various protocols. Characterization of these free operations in POVM based framework is also considered in this work. We provide upper bounds on maximum number of Kraus operators for BIO and also for SBIO.
Physical Review A, 2020
Source independent quantum networks are considered as a natural generalization to the Bell scenar... more Source independent quantum networks are considered as a natural generalization to the Bell scenario where we investigate the nonlocal properties of quantum states distributed and measured in a network. Considering the simplest network of entanglement swapping, recently Gisin et. al. and Andreoli et. al. independently provided a systematic characterization of the set of quantum states leading to violation of the so-called 'bilocality' inequality. In this work, we consider the complexities in the quantum networks with an arbitrary number of parties distributed in chain-shaped and starshaped networks. We derive the maximal violation of the 'n-local' inequality that can be achieved by arbitrary two-qubit states for such chain and star-shaped networks. This would further provide us deeper understanding of quantum correlations in complex structures.
Quantum Information and Computation, 2007
In this work we show that the most general class of anti-unitary operators are nonphysical in nat... more In this work we show that the most general class of anti-unitary operators are nonphysical in nature through the existence of incomparable pure bipartite entangled states. It is also shown that a large class of inner-product-preserving operations defined only on the three qubits having spin-directions along x,y and z are impossible. If we perform such an operation locally on a particular pure bipartite state then it will exactly transform to another pure bipartite state that is incomparable with the original one. As subcases of the above results we find the nonphysical nature of universal exact flipping operation and existence of universal Hadamard gate. Beyond the information conservation in terms of entanglement, this work shows how an impossible local operation evolve with the joint system in a nonphysical way.
Quantum Information and Computation, 2005
Incomparability of pure bipartite entangled states under deterministic LOCC is a very strange phe... more Incomparability of pure bipartite entangled states under deterministic LOCC is a very strange phenomena. We find two possible ways of getting our desired pure entangled state which is incomparable with the given input state, by collective LOCC with certainty. The first one is by providing some pure entanglement through the lower dimensional maximally-entangled states or using further less amount of entanglement and the next one is by collective operation on two pairs which are individually incomparable. It is quite surprising that we are able to achieve maximally entangled states of any Schmidt rank from a finite number of 2x2 pure entangled states only by deterministic LOCC. We provide general theory for the case of 3x3 system of incomparable states by the above processes where incomparability seems to be the most hardest one.
Physical Review A, 2019
We show how nonclassical correlations in local bipartite states can act as a resource for quantum... more We show how nonclassical correlations in local bipartite states can act as a resource for quantum information processing. Considering the task of quantum random access codes (RAC) through separable Bell-diagonal states, we demonstrate the advantage of superunsteerability over classical protocols assisted with two-bits of shared randomness. We propose a measure of superunsteerability, which quantifies nonclassicality beyond quantum steering, and obtain its analytical expression for Bell-diagonal states in the context of the two-and three-setting steering scenarios that are directly related to the quantum 2 → 1 and 3 → 1 RAC protocols, respectively. The maximal values of our quantifier yield the optimal quantum efficiency for both of the above protocols, thus showing that superunsteerability provides a precise characterization of the nonclassical resource for implementing RACs with separable Bell-diagonal class of states.
Quantum Information Processing, 2019
The concept of entanglement fraction is generalized to define coherence fraction of a quantum sta... more The concept of entanglement fraction is generalized to define coherence fraction of a quantum state. Precisely, it quantifies the proximity of a quantum state to maximally coherent state and it can be used as a measure of coherence. Coherence fraction has a connection with l1-norm coherence and provides the criteria of coherence distillability. Optimal coherence fraction corresponding to a channel, defined from this new idea of coherence fraction, obeys a complementary relation with its decohering power. The connection between coherence fraction and l1-norm coherence turns to hold for bipartite pure states and X states too. The bipartite generalization shows that the local coherence fractions of a quantum state are not free and they are bounded by linear function of its global coherence fraction. Dynamics of optimal coherence fraction is also studied for single sided and both sided application of channels. Numerical results are provided in exploring properties of optimal coherence fraction.
International Journal of Quantum Information, 2016
In this paper, we discuss the issue of distinguishing a pair of quantum operation in general. We ... more In this paper, we discuss the issue of distinguishing a pair of quantum operation in general. We use Krause theorem for representing the operations in unitary form. This supports the existence of pair of quantum operations that are not locally distinguishable, but distinguishable in asymptotic sense in some higher dimensional system. The process can even be successful without any use of the entangled initial state.
Journal of Quantum Information Science, 2012
The entanglement of a pure bipartite state is uniquely measured by the von-Neumann entropy of its... more The entanglement of a pure bipartite state is uniquely measured by the von-Neumann entropy of its reduced density matrices. Though it cannot specify all the non-local characteristics of pure entangled states. It was proven that for every possible value of entanglement of a bipartite system, there exists an infinite number of equally entangled pure states, not comparable (satisfies Nielsen's criteria) to each other. In this work, we investigate other correlation measures of pure bipartite states that are able to differentiate the quantum correlations of the states with entropy of entanglement. In Schmidt rank 3, we consider the whole set of states having same entanglement and compare how minutely such states can be distinguished by other correlation measures. Then for different values of entanglement we compare the sets of states belonging to the same entanglement and also investigate the graphs of different correlation measures. We extend our search to Schmidt rank 4 and 5 also.
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Papers by Indrani Chattopadhyay