It is well known that quantum switch is an example of indefinite causal order. Recently, application of quantum switch on quantum channels, became a hot topic of discussion. It is possible to achieve significant improvement in communication, when a q
uantum switch is applied on quantum channels. Though above-said improvement is not possible for all quantum channels. For some quantum channels, improvement can be very high. One such example has been discussed in [New J. of Phys. 23, 033039 (2021)] where perfect communication can be achieved. But incidentally that example of channel is unique up to unitary transformations. Therefore, it is important to study the application of quantum switch on other quantum channels where improvement may not be ultimate but significant. Here, we study the application of quantum switch on various quantum channels. In particular we show that if it is not possible to achieve improvement deterministically, it may be possible to achieve improvement probabilistically. It is known that if a quantum channel is useless for some information theoretic task, concatenation of quantum channels generally does not provide any advantage whenever that channel is used. But we show that if a quantum channel is useless even after use of quantum switch, concatenation of quantum channel can make it useful. We also show that quantum switch can help to get quantum advantage in quantum random access code when only useless channels are available for communication. Then we show that quantum switch can be useful to prevent the loss of coherence in a quantum system. We also discuss the fact that if noise is introduced in the switch, then improvement can significantly be decreased.
Detection of entanglement in quantum states is one of the most important problems in quantum information processing. However, it is one of the most challenging tasks to find a universal scheme which is also desired to be optimal to detect entanglemen
t for all states of a specific class--as always preferred by experimentalists. Although, the topic is well studied at least in case of lower dimensional compound systems, e.g., two-qubit systems, but in the case of continuous variable systems, this remains as an open problem. Even in the case of two-mode Gaussian states, the problem is not fully solved. In our work, we have tried to address this issue. At first, a limited number of Hermitian operators is given to test the necessary and sufficient criterion on the covariance matrix of separable two-mode Gaussian states. Thereafter, we present an interferometric scheme to test the same separability criterion in which the measurements are being done via Stokes-like operators. In such case, we consider only single-copy measurements on a two-mode Gaussian state at a time and the scheme amounts to the full state tomography. Although this latter approach is a linear optics based one, nevertheless it is not an economic scheme. Resource-wise a more economical scheme than the full state tomography is obtained if we consider measurements on two copies of the state at a time. However, optimality of the scheme is not yet known.
A beautiful idea about the incompatibility of Physical Context(IPC) was introduced in [Phys. Rev. A 102, 050201(R) (2020)]. Here, a context is defined as a set of a quantum state and two sharp rank-one measurements, and the incompatibility of physica
l context is defined as the leakage of information while implementing those two measurements successively in that quantum state. In this work, we show the limitations in their approach. The three primary limitations are that, (i) their approach is not generalized for POVM measurements and (ii), they restrict information theoretic agents Alice, Eve and Bob to specific quantum operations and do not consider most general quantum operations i.e., quantum instruments and (iii), their measure of IPC can take negative values in specific cases in a more general scenario which implies the limitation of their information measure. Thereby, we have introduced a generalization and modification to their approach in more general and convenient way, such that this idea is well-defined for generic measurements, without these limitations. We also present a comparison of the measure of the IPC through their and our method. Lastly, we show, how the IPC reduces in the presence of memory using our modification, which further validates our approach.
In the Bloch sphere based representation of qudits with dimensions greater than two, the Heisenberg-Weyl operator basis is not preferred because of presence of complex Bloch vector components. We try to address this issue and parametrize a qutrit usi
ng the Heisenberg-Weyl operators by identifying eight real parameters and separate them as four weight and four angular parameters each. The four weight parameters correspond to the weights in front of the four mutually unbiased bases sets formed by the eigenbases of Heisenberg-Weyl observables and they form a four-dimensional unit radius Bloch hypersphere. Inside the four-dimensional hypersphere all points do not correspond to a physical qutrit state but still it has several other features which indicate that it is a natural extension of the qubit Bloch sphere. We study the purity, rank of three level systems, orthogonality and mutual unbiasedness conditions and the distance between two qutrit states inside the hypersphere. We also analyze the two and three-dimensional sections centered at the origin which gives a close structure for physical qutrit states inside the hypersphere. Significantly, we have applied our representation to find mutually unbiased bases(MUBs) and to characterize the unital maps in three dimensions. It should also be possible to extend this idea in higher dimensions.
We obtain a formal characterization of the compatibility or otherwise of a set of positive-operator-valued measures (POVMs) via their Naimark extensions. We show that a set of POVMs is jointly measurable if and only if there exists a single Naimark e
xtension, specified by a fixed ancilla state on the same ancilla Hilbert space, that maps them to a set of commuting projective measurements (PVMs). We use our result to obtain an easily checkable sufficient condition for the compatibility of a pair of dichotomic observables in any dimension. This in turn leads to a characterization of the compatibility regions for some important classes of observables including a pair of unsharp qubit observables. Finally, we also outline as to how our result provides an alternate approach to quantifying the incompatibility of a general set of quantum measurements.
In this article, we analyse the relationship between the Bell violation and the secure key rate of entanglement assisted quantum key distribution (QKD) protocols. Specifically, we address the question whether Bell violation is necessary or sufficient
for secure communication. We construct a class of states which do not show Bell violation, however, which can be used for secure communication after local filtering. Similarly, we identify another class of states which show Bell violation but can not be used for generating secure key even after local filtering. The existence of these two classes of states demonstrates that Bell violation as an initial resource is neither necessary nor sufficient for QKD. Our work therefore forces a departure from traditional thinking that the degree of Bell violation is a key resource for quantum communication and brings out the role of local filtering.
Any kind of quantum resource useful in different information processing tasks is vulnerable to several types of environmental noise. Here we study the behaviour of quantum correlations such as entanglement and steering in two-qubit systems under the
application of the generalised amplitude damping channel and propose some protocols towards preserving them under this type of noise. First, we employ the technique of weak measurement and reversal for the purpose of preservation of correlations. We then show how the evolution under the channel action can be seen as an unitary process. We use the technique of weak measurement and most general form of selective positive operator valued measure (POVM) to achieve preservation of correlations for a significantly large range of parameter values.
We revisit the problem of detection of entanglement of an unknown two-qubit state using minimal resources. Using weak values and just two copies of an arbitrary two-qubit state, we present a protocol where a post selection measurement in the computat
ional basis provides enough information to identify if the state is entangled or not. Our protocol enables complete state identification with a single-setting post selection measurement on two copies of the state. It follows that by restricting to pure states, the global interaction required for determining the weak values can be realized by local operations. We further show that our protocol is robust against errors arising from inappropriate global interactions applied during weak value determination.
We study a quantum Stirling cycle which extracts work using quantized energy levels of a potential well. The work and the efficiency of the engine depend on the length of the potential well, and the Carnot efficiency is approached in a low temperatur
e limiting case. We show that the lack of information about the position of the particle inside the potential well can be converted into useful work without resorting to any measurement. In the low temperature limit, we calculate the amount of work extractable from distinguishable particles, fermions, and bosons.
The connection between coarse-graining of measurement and emergence of classicality has been investigated for some time, if not well understood. Recently in (PRL $textbf{112}$, 010402, (2014)) it was pointed out that coarse-graining measurements can
lead to non-violation of Bell-type inequalities by a state which would violate it under sharp measurements. We study here the effects of coarse-grained measurements on bipartite cat states. We show that while it is true that coarse-graining does indeed lead to non-violation of a Bell-type inequality, this is not reflected at the state level. Under such measurements the post-measurement states can be non-classical (in the quantum optical sense) and in certain cases coarse-graning can lead to an increase in this non-classicality with respect to the coarse-graining parameter. While there is no universal way to quantify non-classicality, we do so using well understood notions in quantum optics such as the negativity of the Wigner function and the singular nature of the Gluaber-Sudharshan P distribution.
