Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1802.08276 · Physical Review A

Quantum entropy and polarization measurements of the two-photon system

Moorad Alexanian, Vanik E. Mkrtchian

Published Feb 20, 2018• 3 citations
arXivHTMLPDF

Abstract

We consider the bipartite state of a two-photon polarization system and obtain the exact analytical expression for the von Neumann entropy in the particular case of a five-parameter polarization density matrix. We investigate and graphically illustrate the dependence of the entropy on these five parameters, in particular, the existence of exotic, transition from exotic to nonexotic, and nonexotic states, where the quantum conditional entropy is negative, both positive and negative, and positive, respectively. We study the ``cooling'' or ``heating'' effect that follows from the reduced density of photon 2 when a measurement is performed on photon 1.

DOI
10.1103/physreva.97.022326

Related papers

Polarization entropy of the two-photon system

Moorad Alexanian, Vanik E. Mkrtchian

We consider the bipartite state of a two-photon polarization system and obtain the exact analytical expression for the von Neumann entropy in the particular case of polarization when the entropy depends on only five parameters rather than the full fifteen parameters. We investigate and graphically illustrate the dependence of the entropy on these five parameters, in particular, theexistence of exotic to nonexotic statetransitions in single- and two-photon correlations.

•Apr 5, 2018•0 citations

Witnessing negative conditional entropy

Mahathi Vempati, Nirman Ganguly, Indranil Chakrabarty +1 more

Quantum states that possess negative conditional von Neumann entropy provide quantum advantage in several information-theoretic protocols including superdense coding, state merging, distributed private randomness distillation, and one-way entanglement distillation. While entanglement is an important resource, only a subset of entangled states have negative conditional von Neumann entropy. In this work, we characterize the class of density matrices having non-negative conditional von Neumann entropy as convex and compact. This allows us to prove the existence of a Hermitian operator (a witness) for the detection of states having negative conditional entropy for bipartite systems in arbitrary dimensions. We show two constructions of such witnesses. For one of the constructions, the expectation value of the witness in a state is an upper bound to the conditional entropy of the state. We pose the problem of obtaining a tight upper bound to the set of conditional entropies of states in which an operator gives the same expectation value. We solve this convex optimization problem numerically for a two qubit case and find that this enhances the usefulness of our witnesses. We also find that for a particular witness, the estimated tight upper bound matches the value of conditional entropy for Werner states. We explicate the utility of our work in the detection of useful states in several protocols.

arXiv:2001.11237•Physical Review A•Jul 19, 2021•22 citations

Negative conditional entropy of postselected states

Sina Salek, Roman Schubert, Karoline Wiesner

We define a quantum entropy conditioned on postselection which has the von Neumann entropy of pure states as a special case. This conditional entropy can take negative values, which is consistent with part of a quantum system containing less information than the whole, which can be in a pure state. The definition is based on generalized density operators for postselected ensembles. The corresponding density operators are consistent with the quantum generalization of classical conditional probabilities following Dirac's formalism of quasiprobability distributions.

arXiv:1305.0932•Physical Review A•Aug 25, 2014•46 citations

Entanglement measures of W-state in noninertial frames

Ariadna J. Torres-Arenas, Qian Dong, Guo-Hua Sun +2 more

In this work we present the entanglement measures of a tripartite W-State entangled system in noninertial frame through the coordinate transformation between Minkowski and Rindler. Two cases are considered, i.e., when one qubit goes in a uniform acceleration a and the others remain stationary and when two qubits undergo in a uniform acceleration and while the other is stationary. The analytical negativities for one-tangle, two-tangle and π -tangle in total are not written out explicitly except for some special cases due to complicated expressions, but we illustrate them in graphics and study their dependencies on the acceleration parameters r b and r c . We find that the negativities of the one-tangle, two-tangle and π -tangle decrease with the acceleration parameters except for the constant N A B = N B A . The negativity N C I ( A B ) and the π C I decrease faster than N A ( B C I ) and π A ( π B ) . The negativities N A C I ( N B ( A C I ) )and N B I C I decrease faster than those N A B and N A B I , respectively. It is interesting to see there exist turning points for the negativity N A ( B I C I ) at the coordinate position ( r b , r c ) with r b = r c , which implies that the N A ( B I C I ) has minimum value when Bob and Charlie are on the same position and the degree of the entanglement of the subsystem ρ A ( B I C I ) becomes smallest. The von Neumann entropy of tripartite system densities ρ A B C I and ρ A B I C I are obtained analytically. We notice that they all increase with the acceleration parameters r b and r c .

arXiv:1810.03951•Physics Letters B•Dec 14, 2018•104 citations

Conditional entropy and information of quantum processes

Siddhartha Das, Kaumudibikash Goswami, Vivek Pandey

What would be a reasonable definition of the conditional entropy of bipartite quantum processes, and what novel insight would it provide? We develop this notion using four information-theoretic axioms and define the corresponding quantitative formulas. Our definitions of the conditional entropies of channels are based on the generalized state and channel divergences, for instance, quantum relative entropy. We find that the conditional entropy of quantum channels has potential to reveal insights for quantum processes that aren't already captured by the existing entropic functions, entropy or conditional entropy, of the states and channels. The von Neumann conditional entropy $S[A|B]_{\mathcal{N}}$ of the channel $\mathcal{N}_{A'B'\to AB}$ is based on the quantum relative entropy, with system pairs $A',A$ and $B',B$ being nonconditioning and conditioning systems, respectively. We identify a connection between the underlying causal structure of a bipartite channel and its conditional entropy. In particular, we provide a necessary and sufficient condition for a bipartite quantum channel $\mathcal{N}_{A'B'\to AB}$ in terms of its von Neumann conditional entropy $S[A|B]_{\mathcal{N}}$, to have no causal influence from $A'$ to $B$. As a consequence, if $S[A|B]_{\mathcal{N}}< -\log|A|$ then the channel necessarily has causal influence (signaling) from $A'$ to $B$. Our definition of the conditional entropy establishes the strong subadditivity of the entropy for quantum channels. We also study the total amount of correlations possible due to quantum processes by defining the multipartite mutual information of quantum channels.

arXiv:2410.01740•Oct 2, 2024•0 citations

Correlations of polarizations and entangled states in the two-photon system

Vladimir Lvovich Lyuboshitz, Vladimir Lvovich Lyuboshitz

The correlations of the linear and circular polarizations in the system of two photons have been theoretically investigated. The polarization of a two-photon state is described by the one-photon Stokes parameters and by the components of the correlation “tensor” in the Stokes space. It is shown that in the case of two-photon decays π0 → 2γ, η → 2γ, K 0 → 2γ, K 0 → 2γ and the cascade process |0〉 → |1〉 + γ → |0〉 + 2γ(|0〉 and |1〉 are states with the spin 0 and 1, respectively) the final two-photon state represents a characteristic example of the entangled (nonfactorizable) state, and the correlations between the Stokes parameters in all these decays have the purely quantum character: the incoherence inequalities of the Bell type for the components of the correlation “tensor”, established previously for the case of classical “mixtures”, are violated. The general analysis of the registration procedure for two correlated photons by two one-photon detectors is performed.

Physics of Particles and Nuclei Letters•Nov 19, 2009•0 citations
We consider the bipartite state of a two-photon polarization system and obtain the exact analytical expression for the von Neumann entropy in the particular case of a five-parameter polarization density matrix. We investigate and graphically illustrate the dependence of the entropy on these five parameters, in particular, the existence of exotic, transition from exotic to nonexotic, and nonexotic states, where the quantum conditional entropy is negative, both positive and negative, and positive, respectively. We study the cooling'' or heating'' effect that follows from the reduced density of photon 2 when a measurement is performed on photon 1.
Quantum states that possess negative conditional von Neumann entropy provide quantum advantage in several information-theoretic protocols including superdense coding, state merging, distributed private randomness distillation, and one-way entanglement distillation. While entanglement is an important resource, only a subset of entangled states have negative conditional von Neumann entropy. In this work, we characterize the class of density matrices having non-negative conditional von Neumann entropy as convex and compact. This allows us to prove the existence of a Hermitian operator (a witness) for the detection of states having negative conditional entropy for bipartite systems in arbitrary dimensions. We show two constructions of such witnesses. For one of the constructions, the expectation value of the witness in a state is an upper bound to the conditional entropy of the state. We pose the problem of obtaining a tight upper bound to the set of conditional entropies of states in which an operator gives the same expectation value. We solve this convex optimization problem numerically for a two qubit case and find that this enhances the usefulness of our witnesses. We also find that for a particular witness, the estimated tight upper bound matches the value of conditional entropy for Werner states. We explicate the utility of our work in the detection of useful states in several protocols.
We define a quantum entropy conditioned on postselection which has the von Neumann entropy of pure states as a special case. This conditional entropy can take negative values, which is consistent with part of a quantum system containing less information than the whole, which can be in a pure state. The definition is based on generalized density operators for postselected ensembles. The corresponding density operators are consistent with the quantum generalization of classical conditional probabilities following Dirac's formalism of quasiprobability distributions.
In this work we present the entanglement measures of a tripartite W-State entangled system in noninertial frame through the coordinate transformation between Minkowski and Rindler. Two cases are considered, i.e., when one qubit goes in a uniform acceleration a and the others remain stationary and when two qubits undergo in a uniform acceleration and while the other is stationary. The analytical negativities for one-tangle, two-tangle and π -tangle in total are not written out explicitly except for some special cases due to complicated expressions, but we illustrate them in graphics and study their dependencies on the acceleration parameters r b and r c . We find that the negativities of the one-tangle, two-tangle and π -tangle decrease with the acceleration parameters except for the constant N A B = N B A . The negativity N C I ( A B ) and the π C I decrease faster than N A ( B C I ) and π A ( π B ) . The negativities N A C I ( N B ( A C I ) )and N B I C I decrease faster than those N A B and N A B I , respectively. It is interesting to see there exist turning points for the negativity N A ( B I C I ) at the coordinate position ( r b , r c ) with r b = r c , which implies that the N A ( B I C I ) has minimum value when Bob and Charlie are on the same position and the degree of the entanglement of the subsystem ρ A ( B I C I ) becomes smallest. The von Neumann entropy of tripartite system densities ρ A B C I and ρ A B I C I are obtained analytically. We notice that they all increase with the acceleration parameters r b and r c .
What would be a reasonable definition of the conditional entropy of bipartite quantum processes, and what novel insight would it provide? We develop this notion using four information-theoretic axioms and define the corresponding quantitative formulas. Our definitions of the conditional entropies of channels are based on the generalized state and channel divergences, for instance, quantum relative entropy. We find that the conditional entropy of quantum channels has potential to reveal insights for quantum processes that aren't already captured by the existing entropic functions, entropy or conditional entropy, of the states and channels. The von Neumann conditional entropy S[A∣B]NS[A|B]_{\mathcal{N}}S[A∣B]N​ of the channel NA′B′→AB\mathcal{N}_{A'B'\to AB}NA′B′→AB​ is based on the quantum relative entropy, with system pairs A′,AA',AA′,A and B′,BB',BB′,B being nonconditioning and conditioning systems, respectively. We identify a connection between the underlying causal structure of a bipartite channel and its conditional entropy. In particular, we provide a necessary and sufficient condition for a bipartite quantum channel NA′B′→AB\mathcal{N}_{A'B'\to AB}NA′B′→AB​ in terms of its von Neumann conditional entropy S[A∣B]NS[A|B]_{\mathcal{N}}S[A∣B]N​, to have no causal influence from A′A'A′ to BBB. As a consequence, if S[A∣B]N<−log⁡∣A∣S[A|B]_{\mathcal{N}}< -\log|A|S[A∣B]N​<−log∣A∣ then the channel necessarily has causal influence (signaling) from A′A'A′ to BBB. Our definition of the conditional entropy establishes the strong subadditivity of the entropy for quantum channels. We also study the total amount of correlations possible due to quantum processes by defining the multipartite mutual information of quantum channels.
The correlations of the linear and circular polarizations in the system of two photons have been theoretically investigated. The polarization of a two-photon state is described by the one-photon Stokes parameters and by the components of the correlation “tensor” in the Stokes space. It is shown that in the case of two-photon decays π0 → 2γ, η → 2γ, K 0 → 2γ, K 0 → 2γ and the cascade process |0〉 → |1〉 + γ → |0〉 + 2γ(|0〉 and |1〉 are states with the spin 0 and 1, respectively) the final two-photon state represents a characteristic example of the entangled (nonfactorizable) state, and the correlations between the Stokes parameters in all these decays have the purely quantum character: the incoherence inequalities of the Bell type for the components of the correlation “tensor”, established previously for the case of classical “mixtures”, are violated. The general analysis of the registration procedure for two correlated photons by two one-photon detectors is performed.