1. "Dead in Sin" = Loss of Inheritance, through Transgression :
In Scripture, Being "Dead in Sin" is seen as being separated from the covenant promises of God - because of Transgression :
The Parable of the Prodigal Son illustrates the loss of covenant relationship, and inheritance - through transgression. (Also, see Covenant Theology):
NASB, Luke 15:21,30-32 21 And the son said to him, ‘Father, I have sinned against heaven and in your sight; I am no longer worthy to be called your son.’ 30 but when this son of yours came, who has devoured your wealth [his inheritance] ...’ 31 And he said to him, ‘Son, ... we had to celebrate and rejoice, for this brother of yours was dead and has begun to live, and was lost and has been found.’”
Hebrew and Greek Scriptures Consistently Associate Transgression with Loss of God's Blessings :
NASB, Ephesians 4:17-18 : So this I say, ... walk no longer just as the Gentiles also walk ... 18 being darkened in their understanding, excluded from the life of God ... because of the hardness of their heart;
NASB, Ezekiel 18:31 - Cast away from you all your transgressions which you have committed and make yourselves a new heart and a new spirit! For why will you die, O house of Israel? 32 For I have no pleasure in the death of anyone who dies,” declares the Lord God. “Therefore, repent and live.”
Note: All throughout Hebrew Scripture "כָּרַת" (Kareth, Wikipedia Link) is the term meaning to "Cut off". This meant to be separated from the covenant and promises of God because of disobedience. ("Cut off" word search).
2. "Alive in Christ" = Access to a Heavenly Inheritance, through Jesus :
In the New Testament, there are only two states: Alive in Covenant - through trust in Jesus; or outside of covenant, because of transgression - even Israel.
Ephesians, (beginning in Chapter 1), consistently speaks of heavenly blessings, (Ephesians 1:3), as a Spiritual Inheritance :
ESV, Ephesians 2:1 - And you were dead in the trespasses and sins ... 5 ... made us alive together ... in the heavenly places in Christ Jesus ... Eph. 3:6 - to be specific, that the Gentiles are fellow heirs and fellow members of the body ...
Note: "becoming alive" when "together with Christ" - through trust [faith], (Eph 2:21; 22; together with the body : 4:16; 4:17).
In Ephesians, the context repeatedly juxtaposes "reconciliation to" and "separation from" God, (as strangers, aliens, etc); to be specific ...
NASB, Ephesians 3:6 - to be specific, that the Gentiles are fellow heirs and fellow members of the body, and fellow partakers of the promise in Christ Jesus through the gospel, ...
Ephesians 2:11 - Therefore, remember that formerly you who are Gentiles ... 12 remember that at that time you were separate from Christ, excluded from citizenship in Israel and foreigners to the covenants of the promise, without hope and without God in the world. 13 But now in Christ Jesus you who once were far away have been brought near [vs. being "cut off"] by the blood of Christ.
Required for even Israel too, (those obligated under the law) :
NASB, Hebrews 9:15 - For this reason [Jesus] is the mediator of a new covenant, so that, since a death has taken place for the redemption of the transgressions that were committed under the first covenant, those who have been called may receive the promise of the eternal inheritance.
Obedience and Life in Hebrew Scripture :
NASB, Isaiah 55:3 - “Incline your ear and come to Me. Listen, that you may live; And I will make an everlasting covenant with you, According to the faithful mercies shown to David.